Laba_10 (1).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "X-uMNhYV0iLq"
   },
   "source": [
    "# Лабораторная работа 10. Динамическое программирование."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "SHkPGr-f0iLt"
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import pylab\n",
    "import numpy as np\n",
    "import time\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rWzyXdti0iLv"
   },
   "source": [
    "# Пример №1. Числа Фибоначчи\n",
    "\n",
    "Последовательность чисел Фибоначчи задаётся рекуррентным выражением:\n",
    "\n",
    "$$ F_n =  \\begin{cases}\n",
    "           0, n = 0, \\\\\n",
    "           1, n = 1, \\\\\n",
    "           F_{n-1}+F_{n-2}, n > 1.\n",
    "          \\end{cases} $$\n",
    "\n",
    "Что даёт следующую последовательность {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …}."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VV4RJhm-0iLv"
   },
   "source": [
    "Один из способов решения, который может показаться логичным и эффективным, — решение с помощью рекурсии:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "BqoNru2w0iLw"
   },
   "outputs": [],
   "source": [
    "def Fibonacci_Recursion(n):\n",
    "    if n == 0:\n",
    "        return 0\n",
    "    if n == 1:\n",
    "        return 1\n",
    "    return Fibonacci_Recursion (n-1) + Fibonacci_Recursion (n-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dBPG5vv70iLw"
   },
   "source": [
    "Используя такую функцию, мы будем решать задачу «с конца» — будем шаг за шагом уменьшать n, пока не дойдем до известных значений.\n",
    "\n",
    "Но, как мы видели ранее эта реализация многократно повторяет решение одних и тех же задач. Это связано с тем, что одни и те же промежуточные данные вычисляются по несколько раз, а число операций нарастает с той же скоростью, с какой растут числа Фибоначчи — экспоненциально.\n",
    "\n",
    "Один из выходов из данной ситуации — сохранение уже найденных промежуточных результатов с целью их повторного использования (кеширование). Причём кеш должен храниться во внешней области памяти."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "gaJ5WuGP0iLx"
   },
   "outputs": [],
   "source": [
    "def Fibonacci_Recursion_cache(n, cache):\n",
    "    if n == 0:\n",
    "        return 0\n",
    "    if n == 1:\n",
    "        return 1\n",
    "    if cache[n] > 0:\n",
    "        return cache[n]\n",
    "    cache[n] = Fibonacci_Recursion_cache (n-1, cache) + Fibonacci_Recursion_cache (n-2, cache)\n",
    "    return cache[n]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nQpKXxBD0iLx"
   },
   "source": [
    "Приведенное решение достаточно эффективно (за исключением накладных расходов на вызов функций). Но можно поступить ещё проще:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "ITKfxjYt0iLy"
   },
   "outputs": [],
   "source": [
    "def Fibonacci(n):\n",
    "    \n",
    "    fib = [0]*max(2,n)\n",
    "    fib[0] = 1\n",
    "    fib[1] = 1\n",
    "    for i in range(2, n):\n",
    "        fib[i] = fib[i - 1] + fib[i - 2]\n",
    "        \n",
    "    return fib[n-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "p3wgUeKf0iL0"
   },
   "source": [
    "Такое решение можно назвать решением «с начала» — мы первым делом заполняем известные значения, затем находим первое неизвестное значение, потом следующее и т.д., пока не дойдем до нужного.\n",
    "\n",
    "Так и работает динамическое программирование: сначала решили все подзадачи (нашли все F[i] для i < n), затем, зная решения подзадач, нашли решение исходной задачи."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "s-wc9Mqj0iL0"
   },
   "source": [
    "Проверим правильность работы этих программ:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "orka0id-0iL1"
   },
   "outputs": [],
   "source": [
    "N = 9\n",
    "cache = [0]*(N+1)\n",
    "assert Fibonacci_Recursion(N) == 34\n",
    "assert Fibonacci_Recursion_cache(N, cache) == 34\n",
    "assert Fibonacci(N) == 34"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bAb076Pe0iL1"
   },
   "source": [
    "И их производительность:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "lSw59JQE0iL1"
   },
   "outputs": [],
   "source": [
    "n=25\n",
    "a = np.zeros(n)\n",
    "cache = [0]*(n+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "6VE-VAYA0iL2",
    "outputId": "2e6d6fd2-543c-4cdb-b853-a611e6a68b77"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fibonacci_Recursion:         5.965996e-02 sec\n",
      "Fibonacci_Recursion_cache:   2.503395e-04 sec\n",
      "Fibonacci:                   1.611710e-04 sec\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "for i in range (n): a[i] = Fibonacci_Recursion(i)\n",
    "print('%-28s %12.6e sec' % ('Fibonacci_Recursion:', time.time()-start_time))\n",
    "\n",
    "start_time = time.time()\n",
    "for i in range (n): \n",
    "    cache = [0]*(i+1)\n",
    "    a[i] = Fibonacci_Recursion_cache(i,cache)\n",
    "print('%-28s %12.6e sec' % ('Fibonacci_Recursion_cache:', time.time()-start_time))\n",
    "    \n",
    "start_time = time.time()\n",
    "for i in range (n): a[i] = Fibonacci(i)\n",
    "print('%-28s %12.6e sec' % ('Fibonacci:', time.time()-start_time))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-M0YenhX0iL2"
   },
   "source": [
    "# Пример №2. Задача о возрастающей подпоследовательности\n",
    "\n",
    "Пусть имеется последовательность чисел $a_1, a_2, … a_N$. Подпоследовательность $a_{i_1}, a_{i_2}, a_{i_3}$, ... называется возрастающей, если\n",
    "$$ 1 < i_1 < i_2 < ... < i_k < n $$\n",
    "и\n",
    "$$ a_{i_1} < a_{i_2} < ... < a_{i_k} $$\n",
    "Требуется найти максимальную длину возрастающей подпоследовательности. Например, для последовательности $a_i = {10, 4, 13, 7, 3, 6, 17, 33}$ одна из возрастающих подпоследовательностей есть ${4, 7, 17, 33}$.\n",
    "\n",
    "В этой задаче длина наибольшего пути к вершине i (уравнение Беллмана) есть максимум из наибольших путей к предыдущим вершинам плюс единица:\n",
    "$$ L_i = 1 + max(L_{i-1, j}, j = 1, N_{L_{i-1}}) $$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "WnEqmVL40iL3"
   },
   "outputs": [],
   "source": [
    "def f(a, k):\n",
    "    # k - номер конечного элемента\n",
    "    m=0\n",
    "    for i in range(k):      # для всех слева\n",
    "        if (a[i] < a[k]):   # есть путь?\n",
    "            p = f(a,i)      # его длина\n",
    "            print('p',p)\n",
    "            print('m',m)\n",
    "            if (p>m): m=p   # m = max(m,p)\n",
    "    return m+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "UpqtNRI_0iL3",
    "outputId": "0ebd231f-9675-4706-87ae-b92fcc798e2d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p 1\n",
      "m 0\n",
      "p 1\n",
      "m 0\n",
      "p 2\n",
      "m 1\n",
      "p 1\n",
      "m 0\n",
      "p 2\n",
      "m 2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [1, 4, 2, 5, 3]\n",
    "f(a,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xllB-had0iL4"
   },
   "source": [
    "Чтобы повторно не решать решённые подзадачи, введём массив c размером N, хранящий значения вычисленных функций. Начальные значения его равны нулю — значению, которое не может быть верным решением любой из подзадач. Это позволит нам определить, решали ли мы эту подзадачу или нет. Если нет — запускаем решение для требуемого аргумента, и после получения результата сохраняем его."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "id": "fdTVK2IH0iL4"
   },
   "outputs": [],
   "source": [
    "def f(a, N, k, cache):\n",
    "    # k - номер конечного элемента\n",
    "    if(cache[k]!=0): return cache[k]\n",
    "    m=0\n",
    "    for i in range(k-1):          # для всех слева\n",
    "        if (a[i] < a[k]):         # есть путь?\n",
    "            p = f(a,N,i,cache)    # его длина\n",
    "            if (p>m): m=p         # m = max(m,p)\n",
    "    cache[k] = m+1\n",
    "    return cache[k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "84mX-c2L0iL4",
    "outputId": "ebb9e9be-526a-4dc2-ba71-11e3ad228c26"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = [0]*5\n",
    "a = [1, 4, 2, 5, 3]\n",
    "f(a,5,4,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "R-9VQ4Tk0iL4"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "g8DxHGOR0iL4"
   },
   "source": [
    "# Пример №3. Задача о банкомате\n",
    "\n",
    "Если в задаче о рюкзаке сделать варианты предметов неисчерпаемыми можно перейти к задаче о банкомате. \n",
    "Постановка: В банкомате имеется неограниченное количество банкнот (b1, b2, . . . , bn) заданных номиналов. Нужно выдать требуемую сумму денег наименьшим количеством банкнот.\n",
    "Как мы уже выяснили, жадное решение возможно не для всех наборов входных данных. Например, при b = {1, 6, 10} и x = 12 жадное решение даст ответ 3 (10 + 1 + 1), хотя существует более оптимальное решение 2 (6 + 6). \n",
    "Сделаем задачу о банкомате похожей на задачу о количестве маршрутов.\n",
    "\n",
    "Для каждой суммы проведём стрелку к узлу с новой разрешённой суммой. Уравнение Беллмана:\n",
    "\n",
    "$$ f(x) =  \\begin{cases}\n",
    "            min(f(x-b_i))+1, x > 0 \\\\\n",
    "            \\quad 0 \\quad, x = 0 \\\\\n",
    "            \\quad \\infty \\quad, x < 0\n",
    "           \\end{cases} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "id": "IvpHG4W20iL5"
   },
   "outputs": [],
   "source": [
    "googol = 999999999\n",
    "def f(x,b,n,cache):\n",
    "    if (x<0): return googol\n",
    "    elif(x==0): return 0\n",
    "    elif(cache[x]>=0): return cache[x]\n",
    "    minim = googol\n",
    "    for i in range(n):\n",
    "        r = f(x-b[i],b,n, cache)\n",
    "        if (r<minim): minim=r\n",
    "    cache[x] = minim + 1\n",
    "    return cache[x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "4U9ALrlH0iL5",
    "outputId": "9611963b-72f3-4726-9d05-e6f09f122609"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cache = [-1]*10\n",
    "b = [1, 4, 6]\n",
    "f(9,b,3,cache)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "oHKUC7yG0iL5"
   },
   "source": [
    "Доведя решение задачи до ответа и имея кэш-таблицу, можно восстановить решение без дополнительной информации.\n",
    "Предположим, что мы знаем, что точный ответ при заданных начальных значениях есть 7. Тогда возникает вопрос: какой предыдущий ход мы сделали, чтобы попасть в заключительную позицию? Введём термин ранг для обозначения наименьшего числа ходов, требуемого для достижения текущей позиции из начальной. Тогда каждый ход решения всегда переходит в позицию с рангом, большим строго на единицу, и это позволяет нам придумать следующий алгоритм:\n",
    "\n",
    "1. решение основной задачи дало в ответе k, это — ранг заключительной позиции,\n",
    "2. делаем позицию текущей,\n",
    "3. если текущая позиция имеет ранг 0, то это — начальная позиция и алгоритм завершён,\n",
    "4. рассматриваем позиции, ведущие в текущую, и выбираем из них произвольную с рангом k − 1,\n",
    "5. запоминаем ход, который привёл из позиции ранга k − 1 в ранг k,\n",
    "6. понижаем ранг – k → k − 1 и переходим к 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "id": "aOXe2Gdw0iL5"
   },
   "outputs": [],
   "source": [
    "def buildSolution(x, b, n, cache):\n",
    "    ret = []\n",
    "    for k in range (cache[x],-1,-1):\n",
    "        for i in range(n):\n",
    "            r = x - b[i]\n",
    "            if (r >= 0 and cache[r] == k-1):\n",
    "                x = r\n",
    "                ret.append(b[i])\n",
    "                break\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Jt1H609t0iL6",
    "outputId": "763a51ff-d7fc-4c70-f331-b6481a21f1d6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 4]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "buildSolution(9, b, 3, cache)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dxX3Xi7P0iL6"
   },
   "source": [
    "# Пример №4. Задача о кузнечике.\n",
    "\n",
    "Рассмотрим следующую задачу. На числовой прямой сидит кузнечик, который может прыгать вправо на одну или на две единицы. Первоначально кузнечик находится в точке с координатой 1. Определите количество различных маршрутов кузнечика, приводящих его в точку с координатой n.\n",
    "\n",
    "Обозначим количество маршрутов кузнечика, ведущих в точку с координатой n, как K[n]. Прежде всего заметим, что существует ровно один маршрут из точки 1 в точку 1 — он не содержит ни одного прыжка. В точку 2 можно прыгнуть единственным способом — из точки 1.\n",
    "\n",
    "Как вычислить K[n]? В точку кузнечик может попасть двумя способами — из точки при помощи прыжка длиной 2 и из точки прыжком длины 1. То есть число способов попасть в точку n равно сумме числа способов попасть в точку (n-1) и (n-2), что позволяет выписать рекуррентное соотношение: \n",
    "\n",
    "$$K[n] = K[n-1] + K[n-2]$$.\n",
    "\n",
    "Можно заметить, что данная задача по сути свелась к числам Фибоначчи, поэтому мы не будем выписывать её решение."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hEwMKAQp0iL6"
   },
   "source": [
    "# Упражнение №1\n",
    "\n",
    "Решите задачу о количестве способов достичь точки n из точки 1, если кузнечик умеет прыгать +1, +2 и +3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "id": "WMmzWevE0iL6"
   },
   "outputs": [],
   "source": [
    "def grasshopper(n):\n",
    "    GH = [0] * max(3, n)\n",
    "    GH[0] = 0 # уже в первой точке\n",
    "    GH[1] = 1\n",
    "    GH[2] = 2\n",
    "    for i in range(3, n):\n",
    "        GH[i] = GH[i - 1] + GH[i - 2] + GH[i - 3]\n",
    "    return GH[n - 1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Sr-w2ES7__5Y",
    "outputId": "28de1bba-6a8e-4909-f5a6-a5694c511c25"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grasshopper(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XJ-Ul0R90iL6"
   },
   "source": [
    "# Упражнение №2 Задача о кузнечике со стоимостями посещения точек\n",
    "\n",
    "Пусть кузнечик прыгает на одну или две точки вперед, а за прыжок в каждую точку необходимо заплатить определенную стоимость, различную для различных точек. Стоимость прыжка в точку i задается значением price[i] списка price. Необходимо найти минимальную стоимость маршрута кузнечика из точки 0 в точку n.\n",
    "\n",
    "На этот раз нам необходимо модифицировать определение целевой функции. Пусть C[n] — минимальная стоимость пути из 1 в n.\n",
    "\n",
    "Выведем рекуррентное соотношение для этой функции.Чтобы попасть в точку n мы должны попасть в неё последним прыжком из (n-1) или (n-2). Минимальные стоимости этих маршрутов будут равны С[n-1] и С[n-2] соответственно, к ним придется добавить значение price[n] за прыжок в клетку n. Но из двух клеток мы можем выбрать любую.\n",
    "\n",
    "Нужно выбрать тот маршрут, который имеет наименьшую стоимость. Ур. Беллмана: \n",
    "\n",
    "$$C[n] = min(C[n-1], C[n-2]) + price[n]$$.\n",
    "\n",
    "Вычислить значение целевой функции также лучше при помощи динамического программирования, а не рекурсии.\n",
    "\n",
    "Напишите функцию вычисления наименьшей стоимость достижения клетки n из клетки 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "id": "MWSC0PJA0iL7"
   },
   "outputs": [],
   "source": [
    "def grasshopperWithCost(n, prices):\n",
    "    if len(prices) < 2:\n",
    "        return\n",
    "    costs = [0] * max(2, n + 1)\n",
    "    costs[0] = 0\n",
    "    costs[1] = prices[0]\n",
    "    for i in range(2, n + 1):\n",
    "        costs[i] = min(costs[i - 1], costs[i - 2]) + prices[i - 1]\n",
    "    return costs[n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1HEm9ERdAPj8",
    "outputId": "0c31bf41-e183-4cef-c0e8-6d6736559f93"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите через пробел стоимости попадания в точки 2 - N: 5 3 4 2 1\n"
     ]
    }
   ],
   "source": [
    "prices = list(map(float, input('Введите через пробел стоимости попадания в точки 2 - N: ').split()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "991qJyHGAflY",
    "outputId": "ce602d83-2297-4c01-f15f-3518eac566ae"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите точку, в которую нужно рассчитать маршрут минимальной стоимости: 4\n",
      "Стоимость пути равна 7.0\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    k = int(input('Введите точку, в которую нужно рассчитать маршрут минимальной стоимости: ')) - 1\n",
    "    if not 1 <= k < len(prices) + 1:\n",
    "        print('Не назначена стоимость пути до точки.')\n",
    "    else:\n",
    "        print('Стоимость пути равна', grasshopperWithCost(k, prices))\n",
    "except:\n",
    "    print('Точка должна быть обозначена целым числом от 1 до N.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6PfTfQAA0iL7"
   },
   "source": [
    "# Упражнение №3 Восстановление наиболее выгодной траектории\n",
    "Итак, мы нашли список С, где будет записана минимальная стоимость маршрута для всех точек от 1 до n.\n",
    "\n",
    "Но помимо нахождения наименьшей стоимости маршрута, разумеется, хотелось бы найти и сам маршрут минимальной стоимости. Такая задача называется задачей «восстановления ответа».\n",
    "\n",
    "Для восстановления ответа будем для каждой точки запоминать номер точки prev[i], из которой кузнечик попал в точку i, если он будет передвигаться по пути минимальной стоимости. То есть prev[i] — это точка, предшествующая точке с номером i на пути минимальной стоимости (также говорят, что Prev — это массив предшественников). Как определить prev[i]? Если C[i-1] < C[i-2], то кузнечик попал в точку i из точки (i-1), поэтому prev[i] = i - 1, иначе prev[i] = i - 2.\n",
    "\n",
    "Для восстановления пути необходимо начать с точки n и переходить от каждой точки к ее предшественнику, пока путь не дойдет до начальной точки с номером 0. Номера всех вершин будем добавлять в список path. В конце в список path добавляется начальная вершина номер 1, которая не была обработана в основном цикле, а затем весь список path разворачивается в обратном порядке (т. к. вершины добавляются в обратном порядке, от конечной к начальной).\n",
    "\n",
    "Модифицируйте алгоритм вычисления значений целевой функции так, чтобы вычислить значения prev[i], и восстановите траекторию наименьшей стоимости из точки 1 в точку n."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "id": "RGbIYR0M0iL7"
   },
   "outputs": [],
   "source": [
    "def grasshopperWithCostAndPath(n, prices):\n",
    "    if len(prices) < 2:\n",
    "        print('')\n",
    "        return\n",
    "    if n == 1:\n",
    "        return 0, []\n",
    "    elif n == 2:\n",
    "        return prices[0], [1]\n",
    "    paths = []\n",
    "    costs = [0] * max(2, n + 1)\n",
    "    costs[0] = 0\n",
    "    costs[1] = prices[0]\n",
    "    paths.append([])\n",
    "    paths.append([1])\n",
    "    for i in range(2, n):\n",
    "        if costs[i - 1] >= costs[i - 2]:\n",
    "            costs[i] = costs[i - 2] + prices[i - 1]\n",
    "            paths.append(paths[i - 2] + [i - 1])\n",
    "        else:\n",
    "            costs[i] = costs[i - 1] + prices[i - 1]\n",
    "            paths.append(paths[i - 1] + [i])\n",
    "    return costs[n - 1], paths[n - 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "eIhtzzKBA47c",
    "outputId": "856c3c64-de4a-4005-8043-b2829a503e83"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите через пробел стоимости попадания в точки 2 - N: 6 2 5 1 4\n"
     ]
    }
   ],
   "source": [
    "prices = list(map(float, input('Введите через пробел стоимости попадания в точки 2 - N: ').split()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "y2nXJewpA40E",
    "outputId": "dd254377-cf40-40a6-dc2b-f93ddca10e35"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите точку, в которую нужно рассчитать маршрут минимальной стоимости: 5\n",
      "Стоимость пути равна 3.0.\n",
      "Путь: 1 -> 3 -> 5\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    k = int(input('Введите точку, в которую нужно рассчитать маршрут минимальной стоимости: '))\n",
    "    if not 0 < k <= len(prices) + 1:\n",
    "        print('Не назначена стоимость пути до точки.')\n",
    "    else:\n",
    "        cost, path = grasshopperWithCostAndPath(k, prices)\n",
    "        print('Стоимость пути равна ' + str(cost) + '.')\n",
    "        print('Путь: ', end='')\n",
    "        for i in range(len(path)):\n",
    "            print(path[i], end=' -> ')\n",
    "        print(k)\n",
    "except:\n",
    "    print('Точка должна быть обозначена целым числом от 1 до N.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "id": "UbJC1Og5A4p0"
   },
   "outputs": [],
   "source": [
    "def onlyPathDefinderForOptimalCost(dot, prices):\n",
    "    # по условию путь оптимален, так как его стоимость минимальна\n",
    "    prices = [0] + prices\n",
    "    price = prices[dot]\n",
    "    while dot > 1:\n",
    "        if prices[dot - 1] >= prices[dot - 2]:\n",
    "            price += prices[dot - 2]\n",
    "            dot -= 2\n",
    "        else:\n",
    "            price += prices[dot - 1]\n",
    "            dot -= 1\n",
    "    return price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "IT3m3QZ9BX3M",
    "outputId": "f4b322a4-7882-455b-8ba2-c30763330451"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите точку, из которой хотите рассчитать оптимальную стоимость: 4\n",
      "Стоимость пути равна: 7.0\n"
     ]
    }
   ],
   "source": [
    "print('Стоимость пути равна:', \n",
    "      onlyPathDefinderForOptimalCost(int(input('Введите точку, из которой хотите ' +\n",
    "                                               'рассчитать оптимальную стоимость: ')) - 1, prices))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9UAqdHDJ0iL7"
   },
   "source": [
    "# Пример №5. Расстояние редактирования\n",
    "\n",
    "Часто текстовый редактор, подозревая опечатку, предлагает заменить написанное слово на близкое. Что значит «близкое»? \n",
    "\n",
    "Количество операций для превращения одного слова в другое называется расстоянием редактирования или расстоянием Левенштейна (ИПМ им. Келдыша). Это расстояние — мера различия между двумя строками. Этой мерой измеряют сходство или различие двух генных последовательностей и т.д.\n",
    "Задача. Определить минимальное количество операций для преобразования одного слова в другое, при следующих допустимых операциях:\n",
    "- замена одной буквы на другую;\n",
    "- вставка одной буквы;\n",
    "- удаление одной буквы.\n",
    "\n",
    "Например, сколько нужно операций, чтобы превратить слово СЛОН в слово ОГОНЬ? Например, это можно сделать следующей последовательностью:\n",
    "СЛОН → СГОН → СГОНЬ → ОГОНЬ.\n",
    "Последовательность переходов, которую мы описали, не обладает нужными свойствами (последовательным увеличением сложности задачи).А есть ли нужная нам последовательность, в которой каждая подзадача решается на подстроке всё более возрастающей длины? Конечно:\n",
    "1. В префиксах строк длины 1 С и О меняем букву С на О. СЛОН → ОЛОН.\n",
    "2. В префиксах длины 2 меняем Л на Г. ОЛОН → ОГОН.\n",
    "3. В префиксах длины 4 добавляем букву Ь. ОГОН → ОГОНЬ.\n",
    "\n",
    "И так, необходимо найти расстояние редактирования между $x[1...m]$ и $y[1...n]$. Будем искать расстояние редактирования между префиксами первой строки, $x[1...i]$, и префиксами второй, $y[1...j]$, обозначив эти расстояния $E[i,j]$. Конечная цель – вычисление $E[m, n]$.\n",
    "\n",
    "Например, $E[7,5]$:\n",
    "$$ \\fbox{E X P O N E N} T I A L $$\n",
    "$$ \\fbox{P O L Y N} O M I A L $$\n",
    "\n",
    "Значения $E[i,j]$ удобно представлять в виде таблицы. Для удобства добавим один лишний левый столбеци одну лишнюю верхнюю строку к этой таблице. Заполним их последовательно возрастающими числами. Эти числа означают, что пустая строка может превратиться в образец за число операций, равное длине образца. \n",
    "\n",
    "Очевидно, что при такой записи в каждуюследующую клетку можно попасть только из левой, верхне или по диагонали из левой верхне. При этом из этих вариантов выбирается минимальный и к нему прибавляются затраты на новое редактирование: 0 - если на пересечении текущего столбца и строки стоят одинаковые буквы и 1 - если разные. Т.е. ур. Беллмана:\n",
    "\n",
    "$$ E[i,j] = min(1 + E[i-1, j], 1 + E[i, j-1], d(i, j) + E[i-1, j-1]), $$\n",
    "$$ d(i, j) = \\begin{cases}\n",
    "                 0, x[i] = y[j] \\\\\n",
    "                 1, x[i] \\neq y[j]\n",
    "                 \\end{cases} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "8mXVOA_p0iL7",
    "outputId": "d807faf2-9539-4747-a598-7f91f516d599"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Так можно добавлять картинки\n",
    "\n",
    "from IPython.display import Image             # вызов из библиотеки определённой функции\n",
    "Image(\"Расстояние редактирования.png\")        # вызов функции и передача ей в качестве аргумента пути к файлу \n",
    "\n",
    "# (в данном случае фаил находится в той же папке)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mgM71M8H0iL8"
   },
   "source": [
    "# Упражнение №4.\n",
    "\n",
    "Напишите программу вычисляющую расстояние редактирования."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "id": "QOaSbMbN0iL8"
   },
   "outputs": [],
   "source": [
    "def LEVENSTEIN(first, second):\n",
    "    E = np.zeros((len(first) + 1, len(second) + 1))\n",
    "    # начальное заполнение матрицы\n",
    "    for i in range(1, len(first) + 1):\n",
    "        E[i][0] = i\n",
    "    for j in range(1, len(second) + 1):\n",
    "        E[0][j] = j\n",
    "    for j in range(1, len(second) + 1):\n",
    "        for i in range(1, len(first) + 1):\n",
    "            E[i][j] = min(1 + E[i - 1][j],\n",
    "                          1 + E[i][j - 1],\n",
    "                          int(not first[i - 1] == second[j - 1]) + E[i - 1][j - 1])\n",
    "    print(E)\n",
    "    return E[len(first)][len(second)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jb6_YNOnB080",
    "outputId": "896da105-1b4d-4301-a6b6-dcd829fcbc79"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 2. 3. 4. 5.]\n",
      " [1. 1. 2. 3. 4. 5.]\n",
      " [2. 2. 2. 3. 4. 5.]\n",
      " [3. 3. 3. 3. 4. 5.]\n",
      " [4. 4. 4. 4. 4. 4.]\n",
      " [5. 5. 5. 5. 5. 5.]\n",
      " [6. 6. 6. 6. 6. 6.]]\n",
      "6.0\n"
     ]
    }
   ],
   "source": [
    "print(LEVENSTEIN('фонарь', 'улица'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "IIN-WRkzB8nk"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    }
   ],
   "source": [
    "a = \"фонарь\"\n",
    "b = \"улица\"\n",
    "\n",
    "\n",
    "## The One-Liner\n",
    "ls = lambda a, b: len(b) if not a else len(a) if not b \\\n",
    "         else min(ls(a[1:], b[1:])+(a[0] != b[0]),\n",
    "                  ls(a[1:], b)+1,\n",
    "                  ls(a, b[1:])+1)\n",
    "\n",
    "## The Result\n",
    "print(ls(a,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FIX4j6DN0iL8"
   },
   "source": [
    "# Домашнее задание (базовое):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RRzP0fPK0iL8"
   },
   "source": [
    "# Задание №1. Гиперкузнечик.\n",
    "\n",
    "Решите задачу о количестве способов достичь точки n из точки 1, если кузнечик умеет прыгать +1, +2 и *3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "id": "fzvFR7ly0iL8"
   },
   "outputs": [],
   "source": [
    "def HYPERgrasshopper(n):\n",
    "    GH = [None] + ([0] * max(3, n))\n",
    "    GH[1] = 1\n",
    "    GH[2] = 1\n",
    "    for i in range(3, n + 1):\n",
    "        GH[i] = GH[i - 1] + GH[i - 2]\n",
    "        if i % 3 == 0:\n",
    "            GH[i] += GH[i // 3]\n",
    "    return GH[n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "eWrYiGb6CBos",
    "outputId": "0b7e205c-e4ea-4536-f770-cb36e142f49d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите конечную точку: 6\n",
      "Количество способов достичь её: 12\n"
     ]
    }
   ],
   "source": [
    "print('Количество способов достичь её:',\n",
    "      HYPERgrasshopper(int(input('Введите конечную точку: '))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RH1-QHnk0iL8"
   },
   "source": [
    "# Задание №2. Наибольшая общая подпоследовательность.\n",
    "\n",
    "Рассмотрим две строки (или числовые последовательности) A и B. Пусть первая строка состоит из n символов $a_0, ... a_n$, вторая строка состоит из m символов $b_0, ..., b_m$. Подпоследовательностью данной строки (последовательности) называется некоторое подмножество символов исходной строки, следующих в том же порядке, в котором они идут в исходной строке, но не обязательно подряд. Если в строке n символов, то у нее $2^n$ различных подпоследовательностей: каждый из n символов строки может либо входить, либо не входить в любую выбранную подпоследовательность. Пустая подпоследовательность не содержит ни одного элемента и также является подпоследовательностью любой строки.\n",
    "\n",
    "Рассмотрим задачу для двух данных строк найти такую строку наибольшей длины, которая была бы подпоследовательностью каждой из них. Например, если A='abcabaac', B='baccbca' то у строк A и B них есть общая подпоследовательность длины 4, например, 'acba' или 'acbc'.\n",
    "\n",
    "Данную задачу можно решить перебором  например, перебрав все $2^n$ подпоследовательностей первой строки и для каждой их них проверив, является ли она подпоследовательностью второй строки. Но при помощи динамического программирования эту же задачу можно решить за сложность O(nm).\n",
    "\n",
    "Напишите программу решающую данную задачу с помощью алгоритма, полученного на основе динамического программирования. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "id": "gc6JRKwB0iL9"
   },
   "outputs": [],
   "source": [
    "def maxCommonSequence(first, second):\n",
    "    commonSequences = []\n",
    "    i = 0\n",
    "    while i < len(first) - 1:\n",
    "        j = 0\n",
    "        while j < len(second) - 1:\n",
    "            if first[i] == second[j]:\n",
    "                if first[i + 1] == second[j + 1]:\n",
    "                    commonSequences.append(first[i])\n",
    "                    commonSequences[-1] += first[i + 1]\n",
    "                    i1 = i + 2\n",
    "                    j1 = j + 2\n",
    "                    while (i1 < len(first)) and (j1 < len(second)):\n",
    "                        if first[i1] == second[j1]:\n",
    "                            commonSequences[-1] += first[i1]\n",
    "                        else:\n",
    "                            break\n",
    "                        i1 += 1\n",
    "                        j1 += 1\n",
    "            j += 1\n",
    "        i += 1\n",
    "    if len(commonSequences) == 0:\n",
    "        return ''\n",
    "    else:\n",
    "        mx = 0\n",
    "        for i in range(1, len(commonSequences)):\n",
    "            if len(commonSequences[mx]) < len(commonSequences[i]):\n",
    "                mx = i\n",
    "        return commonSequences[mx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "id": "XWaOdpXFChEt"
   },
   "outputs": [],
   "source": [
    "def maxCommonSequence_Dynamically(first, second):\n",
    "    first.insert(0, '1')\n",
    "    second.insert(0, '2')\n",
    "    E = np.zeros((len(first) + 1, len(second) + 1))\n",
    "    H = np.zeros((len(first) + 1, len(second) + 1))\n",
    "    for j in range(1, len(second) + 1):\n",
    "        for i in range(1, len(first) + 1):\n",
    "            if first[i - 1] == second[j - 1]:\n",
    "                E[i][j] = 1 + E[i - 1][j - 1]\n",
    "                H[i][j] = -1\n",
    "            else:\n",
    "                if E[i - 1][j] >= E[i][j - 1]:\n",
    "                    E[i][j] = E[i - 1][j]\n",
    "                    H[i][j] = 2 #l\n",
    "                else:\n",
    "                    E[i][j] = E[i][j - 1]\n",
    "                    H[i][j] = 1 #u\n",
    "    # теперь восстановим подпоследовательность с помощью H:\n",
    "    i = len(first)\n",
    "    j = len(second)\n",
    "    commonSequences = []\n",
    "    commonSequence = ''\n",
    "    while H[i][j] != 0:\n",
    "        if H[i][j] == -1:\n",
    "            commonSequence += first[i - 1]\n",
    "            i -= 1\n",
    "            j -= 1\n",
    "        elif H[i][j] == 1:\n",
    "            if commonSequence != '':\n",
    "                commonSequence\n",
    "                commonSequences.append(commonSequence)\n",
    "                commonSequence = ''\n",
    "            j -= 1\n",
    "        elif H[i][j] == 2:\n",
    "            if commonSequence != '':\n",
    "                commonSequences.append(commonSequence)\n",
    "                commonSequence = ''\n",
    "            i -= 1\n",
    "    # ну, отберём \n",
    "    if len(commonSequences) == 0:\n",
    "        return\n",
    "    else:\n",
    "        mx = 0\n",
    "        for i in range(1, len(commonSequences)):\n",
    "            if len(commonSequences[mx]) < len(commonSequences[i]):\n",
    "                mx = i\n",
    "        CS = list(commonSequences[mx])\n",
    "        CS.reverse()\n",
    "        CS = ''.join(CS)\n",
    "        return CS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "RNBz8_84CnM0",
    "outputId": "c5125f92-3a69-4df2-ee2d-052a774ab517"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите первую последовательность: wwwtrtt\n",
      "Введите вторую последовательность: efwwwqtrt\n",
      "www\n"
     ]
    }
   ],
   "source": [
    "print(maxCommonSequence(list(str(input('Введите первую последовательность: '))), \n",
    "                        list(str(input('Введите вторую последовательность: ')))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ynOG5N0FCnD9",
    "outputId": "7b3f89fd-10ce-40e1-acae-52cbfe7f4e4c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите первую последовательность: wwwtrtt\n",
      "Введите вторую последовательность: efwwwqtrt\n",
      "www\n"
     ]
    }
   ],
   "source": [
    "print(maxCommonSequence_Dynamically(list(str(input('Введите первую последовательность: '))),\n",
    "                                    list(str(input('Введите вторую последовательность: ')))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hdKAYYuR0iL9"
   },
   "source": [
    "# Задание №3. \n",
    "\n",
    "Даны две последовательности целых чисел $a_0, ... a_n$ и $b_0, ..., b_m$. Выяснить, является ли вторая последовательность подпоследовательностью первой, то есть можно ли из первой вычеркнуть некоторые члены так, чтобы осталась вторая."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "id": "L11fRtj30iL9"
   },
   "outputs": [],
   "source": [
    "def isSecondSequenceASubsequence(first, second):\n",
    "    l, k = 0, 0 # length of curr subseq and index of last found char\n",
    "    j = 0\n",
    "    i = 0\n",
    "    while i < len(first):\n",
    "        if first[i] == second[j]:\n",
    "            k = i\n",
    "            l += 1\n",
    "            i += 1\n",
    "            if j < len(second) - 1:\n",
    "                j += 1\n",
    "            elif l < len(second):\n",
    "                return False\n",
    "        else:\n",
    "            i += 1\n",
    "        if l == len(second):\n",
    "            return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "OvxoJZ9tDGGW",
    "outputId": "18ff025d-ccce-4235-bfc9-dfd8e9611598"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите первую последовательность: ew466jjl\n",
      "Введите вторую последовательность: 466\n",
      "Является ли вторая последовательность подпоследовательностью первой? Ответ: True\n"
     ]
    }
   ],
   "source": [
    "print('Является ли вторая последовательность подпоследовательностью первой? Ответ:', \n",
    "      isSecondSequenceASubsequence(str(input('Введите первую последовательность: ')), \n",
    "                                   str(input('Введите вторую последовательность: '))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IsZ1AoiZ0iL9"
   },
   "source": [
    "# Задание №4. Мячик на лесенке.\n",
    "\n",
    "На вершине лесенки, содержащей N ступенек, находится мячик, который начинает прыгать по ним вниз, к основанию. Сначала мячик может прыгнуть максимум на N/2, но с каждым ударом о ступеньку эта величина сокращается вдвое пока он не начинает катиться, перекатываясь с одной ступеньке на другую. Так мячик может прокатиться ещё N/16 ступенек. \n",
    "\n",
    "Определите число всевозможных \"маршрутов\" мячика и найдите максимально возможную длину лестницы N."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "id": "y6AyhxWQ0iL9"
   },
   "outputs": [],
   "source": [
    "def ballOnStairs(init, n, step, show = False):\n",
    "    if init >= n:\n",
    "        return 0\n",
    "    if n // 2 ** step < 1:\n",
    "        return min(n // 16, n - init)\n",
    "    routes = min(n // 2 ** step, n - init)\n",
    "    for i in range(init + 1, min(init + n // 2 ** step, n) + 1):\n",
    "        if show: print(init, '->', i)\n",
    "        routes += ballOnStairs(i, n, step + 1, show)\n",
    "    return routes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "-isB7aPGDftE",
    "outputId": "91c96153-e148-4a3c-cd59-31f0e2445e4b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 -> 2\n",
      "2 -> 3\n",
      "1 -> 3\n",
      "3 -> 4\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ballOnStairs(1, 4, 1, show = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "pLiPKZqUDp7k",
    "outputId": "e5c5c930-85da-4862-e962-ede590712918"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ballOnStairs(1, 8, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "7uJFanzyDs_l",
    "outputId": "47d46297-b0a8-43eb-c496-b856dfdb2b62"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "231"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ballOnStairs(1, 16, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "AAVh_jVaDwgM",
    "outputId": "69872252-7854-44ef-d14e-e46512705975"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Введите n: 4\n",
      "Показывать все возможные ходы? (y/n) y\n",
      "1 -> 2\n",
      "2 -> 3\n",
      "1 -> 3\n",
      "3 -> 4\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "print(ballOnStairs(1, int(input('Введите n: ')), 1, \n",
    "                   show = (True if input('Показывать все возможные ходы? (y/n) ') == 'y' \n",
    "                           else False)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xCZU4rIU0iL9"
   },
   "source": [
    "# Домашнее задание (дополнительное):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "4nwBJ2Ru0iL9",
    "outputId": "a1ebe77a-e1e5-4e22-8dda-ae2991572f5d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Так можно добавлять картинки\n",
    "\n",
    "from IPython.display import Image # вызов из библиотеки определённой функции\n",
    "Image(\"официант.png\")             # вызов функции и передача ей в качестве аргумента пути к файлу \n",
    "\n",
    "# (в данном случае фаил находится в той же папке)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fDl_SDGf0iL9"
   },
   "source": [
    "# Задача о рюкзаке.\n",
    "\n",
    "Решите задачу о рюкзаке методом динамического программирования.\n",
    "\n",
    "Естественно важно правильно выбрать подзадачи. В данном случае есть два естественных способа: рассмотреть рюкзак меньшей ёмкости или же меньшее число предметов. \n",
    "\n",
    "Для того чтобы понять, какой подход действительно работает, обычно приходится немного поэкспериментировать."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "id": "RVZRPUY-EzyN"
   },
   "outputs": [],
   "source": [
    "stuffdict = {'couch_s':(300,75), \n",
    "             'couch_b':(500,80), \n",
    "             'bed':(400,100), \n",
    "             'closet':(200,50), \n",
    "             'bed_s':(200,40), \n",
    "             'desk':(200,70), \n",
    "             'table':(300,80),\n",
    "             'tv_table':(200,30),\n",
    "             'armchair':(100,30),\n",
    "             'bookshelf':(200,60), \n",
    "             'cabinet':(150,20),\n",
    "             'game_table':(150,30),\n",
    "             'hammock':(250,45),\n",
    "             'diner_table_with_chairs':(250,70),\n",
    "             'stools':(150,30),\n",
    "             'mirror':(100,20),\n",
    "             'instrument':(300,70),\n",
    "             'plant_1':(25,10),\n",
    "             'plant_2':(30,20),\n",
    "             'plant_3':(45,25),\n",
    "             'sideboard':(175,30),\n",
    "             'chest_of_drawers':(25,40),\n",
    "             'guest_bed':(250,40),\n",
    "             'standing_lamp':(20,30), \n",
    "             'garbage_can':(30,35), \n",
    "             'bar_with_stools':(200,40), \n",
    "             'bike_stand':(100,80),\n",
    "             'chest':(150,25),\n",
    "             'heater':(100,25)\n",
    "            }\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "id": "A17UG7hkE7wt"
   },
   "outputs": [],
   "source": [
    "def get_area_and_value(stuffdict):\n",
    "    area = [stuffdict[item][0] for item in stuffdict]\n",
    "    value = [stuffdict[item][1] for item in stuffdict]        \n",
    "    return area, value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "id": "yuqkGncxE9ON"
   },
   "outputs": [],
   "source": [
    "def get_memtable(stuffdict, A=2000):\n",
    "      area, value = get_area_and_value(stuffdict)\n",
    "      n = len(value) # находим размеры таблицы\n",
    "      \n",
    "      # создаём таблицу из нулевых значений\n",
    "      V = [[0 for a in range(A+1)] for i in range(n+1)]\n",
    "\n",
    "      for i in range(n+1):\n",
    "            for a in range(A+1):\n",
    "                  # базовый случай\n",
    "                  if i == 0 or a == 0:\n",
    "                        V[i][a] = 0\n",
    "\n",
    "                  # если площадь предмета меньше площади столбца,\n",
    "                  # максимизируем значение суммарной ценности\n",
    "                  elif area[i-1] <= a:\n",
    "                        V[i][a] = max(value[i-1] + V[i-1][a-area[i-1]], V[i-1][a])\n",
    "\n",
    "                  # если площадь предмета больше площади столбца,\n",
    "                  # забираем значение ячейки из предыдущей строки\n",
    "                  else:\n",
    "                        V[i][a] = V[i-1][a]       \n",
    "      return V, area, value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "id": "sLAqDnCQFAd0"
   },
   "outputs": [],
   "source": [
    "def get_selected_items_list(stuffdict, A=2000):\n",
    "      V, area, value = get_memtable(stuffdict)\n",
    "      n = len(value)\n",
    "      res = V[n][A]      # начинаем с последнего элемента таблицы\n",
    "      a = A              # начальная площадь - максимальная\n",
    "      items_list = []    # список площадей и ценностей\n",
    "    \n",
    "      for i in range(n, 0, -1):  # идём в обратном порядке\n",
    "            if res <= 0:  # условие прерывания - собрали \"рюкзак\" \n",
    "                  break\n",
    "            if res == V[i-1][a]:  # ничего не делаем, двигаемся дальше\n",
    "                  continue\n",
    "            else:\n",
    "                  # \"забираем\" предмет\n",
    "                  items_list.append((area[i-1], value[i-1]))\n",
    "                  res -= value[i-1]   # отнимаем значение ценности от общей\n",
    "                  a -= area[i-1]  # отнимаем площадь от общей\n",
    "            \n",
    "      selected_stuff = []\n",
    "\n",
    "      # находим ключи исходного словаря - названия предметов\n",
    "      for search in items_list:\n",
    "            for key, value in stuffdict.items():\n",
    "                  if value == search:\n",
    "                        selected_stuff.append(key)\n",
    "            \n",
    "      return selected_stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Z31Uvt37FMG0",
    "outputId": "c81711db-047d-4f82-9dd5-6d025cac919e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['bike_stand', 'garbage_can', 'standing_lamp', 'chest_of_drawers', 'plant_3', 'plant_2', 'diner_table_with_chairs', 'bookshelf', 'armchair', 'table', 'desk', 'bed', 'couch_s']\n"
     ]
    }
   ],
   "source": [
    "#мы нашли список:\n",
    "stuff = get_selected_items_list(stuffdict)\n",
    "print(stuff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "9E4Jpom5FT7N",
    "outputId": "618ae279-9181-4c06-e829-18e86660482a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 715)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Проверим суммарные площадь и ценность собранных предметов:\n",
    "totarea = sum([stuffdict[item][0] for item in stuff])\n",
    "totvalue = sum([stuffdict[item][1] for item in stuff])\n",
    "\n",
    "totarea, totvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Jub_S6dk0iL-"
   },
   "source": [
    "# Задача коммивояжёра.\n",
    "\n",
    "Коммивояжёр должен посетить по разу каждый город из большого списка и вернуться в свой родной город. Он знает расстояния между всеми парами городов. В каком порядке лучше всего посещать города, чтобы минимизировать пройденное расстояние?\n",
    "\n",
    "Если перебирать все маршруты (их $(n-1)!$), потребуется время $O(n!)$ (вычисление длины маршрута производится за время $O(n)$). Однако, динамическое программирование позволяет решить эту задачу быстрее, хоть и не слишком.\n",
    "\n",
    "При испотльзовании динамического программирования поскольку мы ищем маршрут, естественной подзадачей является нахождение начальной части маршрута. Предположим, мы вышли из города 1, посетили несколько городов и сейчас находимся в городе j. Существенной информацией об этом частичном маршруте является где мы находимся (j), а также где мы уже побывали (чтобы не идти туда второй раз). Это и приводит нас к необходимой подзадаче.\n",
    "\n",
    "Всего есть не более $2^nn$ подзадач, и решение для каждой из них находится за линейное время. Поэтому общее время работы есть $O(n^22^n)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wbK3VXRcMXAG"
   },
   "source": [
    "Долгое решение"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 209
    },
    "id": "IFRmtBzaGMYG",
    "outputId": "0c469be5-7d4f-47cc-89b8-f0a7ca6a3476"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "0 10 1 1\n",
      "10 0 1 5\n",
      "1 1 0 10\n",
      "1 5 10 0\n",
      "----------------------------------\n",
      "[3, 2, 2, 4, 4, 1]\n",
      "8\n",
      "----------------------------------\n",
      "3\n"
     ]
    },
    {
     "data": {
      "application/vnd.google.colaboratory.intrinsic+json": {
       "type": "string"
      },
      "text/plain": [
       "'3'"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Функция нахождения минимального элемента, исключая текущий элемент\n",
    "def Min(lst,myindex):\n",
    "    return min(x for idx, x in enumerate(lst) if idx != myindex)\n",
    "\n",
    "#функция удаления нужной строки и столбцах\n",
    "def Delete(matrix,index1,index2):\n",
    "    del matrix[index1]\n",
    "    for i in matrix:\n",
    "        del i[index2]\n",
    "    return matrix\n",
    "\n",
    "#Функция вывода матрицы\n",
    "def PrintMatrix(matrix):\n",
    "    print(\"---------------\")\n",
    "    for i in range(len(matrix)):\n",
    "        print(matrix[i])\n",
    "    print(\"---------------\")\n",
    "\n",
    "n=int(input())\n",
    "matrix=[]\n",
    "H=0\n",
    "PathLenght=0\n",
    "Str=[]\n",
    "Stb=[]\n",
    "res=[]\n",
    "result=[]\n",
    "StartMatrix=[]\n",
    "\n",
    "#Инициализируем массивы для сохранения индексов\n",
    "for i in range(n):\n",
    "    Str.append(i)\n",
    "    Stb.append(i)\n",
    "\n",
    "#Вводим матрицу\n",
    "for i in range(n): matrix.append(list(map(int, input().split())))\n",
    "\t\n",
    "#Сохраняем изначальную матрицу\n",
    "for i in range(n):StartMatrix.append(matrix[i].copy())\n",
    "\n",
    "#Присваеваем главной диагонали float(inf)\n",
    "for i in range(n): matrix[i][i]=float('inf')\n",
    "\n",
    "while True:\n",
    "    #Редуцируем\n",
    "    #--------------------------------------\n",
    "    #Вычитаем минимальный элемент в строках\n",
    "    for i in range(len(matrix)):\n",
    "        temp=min(matrix[i])\n",
    "        H+=temp\n",
    "        for j in range(len(matrix)):\n",
    "            matrix[i][j]-=temp\n",
    "\n",
    "    #Вычитаем минимальный элемент в столбцах    \n",
    "    for i in range(len(matrix)):\n",
    "        temp = min(row[i] for row in matrix)\n",
    "        H+=temp\n",
    "        for j in range(len(matrix)):\n",
    "            matrix[j][i]-=temp\n",
    "    #--------------------------------------\n",
    "\t\n",
    "    #Оцениваем нулевые клетки и ищем нулевую клетку с максимальной оценкой\n",
    "    #--------------------------------------\n",
    "    NullMax=0\n",
    "    index1=0\n",
    "    index2=0\n",
    "    tmp=0\n",
    "    for i in range(len(matrix)):\n",
    "        for j in range(len(matrix)):\n",
    "            if matrix[i][j]==0:\n",
    "                tmp=Min(matrix[i],j)+Min((row[j] for row in matrix),i)\n",
    "                if tmp>=NullMax:\n",
    "                    NullMax=tmp\n",
    "                    index1=i\n",
    "                    index2=j\n",
    "    #--------------------------------------\n",
    "\n",
    "\t#Находим нужный нам путь, записываем его в res и удаляем все ненужное\n",
    "    res.append(Str[index1]+1)\n",
    "    res.append(Stb[index2]+1)\n",
    "\t\n",
    "    oldIndex1=Str[index1]\n",
    "    oldIndex2=Stb[index2]\n",
    "    if oldIndex2 in Str and oldIndex1 in Stb:\n",
    "        NewIndex1=Str.index(oldIndex2)\n",
    "        NewIndex2=Stb.index(oldIndex1)\n",
    "        matrix[NewIndex1][NewIndex2]=float('inf')\n",
    "    del Str[index1]\n",
    "    del Stb[index2]\n",
    "    matrix=Delete(matrix,index1,index2)\n",
    "    if len(matrix)==1:break\n",
    "\t\n",
    "#Формируем порядок пути\n",
    "for i in range(0,len(res)-1,2):\n",
    "\tif res.count(res[i])<2:\n",
    "\t\tresult.append(res[i])\n",
    "\t\tresult.append(res[i+1])\n",
    "for i in range(0,len(res)-1,2):\n",
    "\tfor j in range(0,len(res)-1,2):\n",
    "\t\tif result[len(result)-1]==res[j]:\n",
    "\t\t\tresult.append(res[j])\n",
    "\t\t\tresult.append(res[j+1])\n",
    "print(\"----------------------------------\")\n",
    "print(result)\n",
    "\n",
    "#Считаем длину пути\n",
    "for i in range(0,len(result)-1,2):\n",
    "    if i==len(result)-2:\n",
    "        PathLenght+=StartMatrix[result[i]-1][result[i+1]-1]\n",
    "        PathLenght+=StartMatrix[result[i+1]-1][result[0]-1]\n",
    "    else: PathLenght+=StartMatrix[result[i]-1][result[i+1]-1]\n",
    "print(PathLenght)\n",
    "print(\"----------------------------------\")\n",
    "input()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yjET1hDKK18V",
    "outputId": "bcac9dd7-673a-491d-8768-e9b15321da41"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting python-tsp\n",
      "  Downloading python_tsp-0.2.1-py3-none-any.whl (14 kB)\n",
      "Collecting tsplib95<0.8.0,>=0.7.1\n",
      "  Downloading tsplib95-0.7.1-py2.py3-none-any.whl (25 kB)\n",
      "Requirement already satisfied: numpy<2.0.0,>=1.18.5 in /usr/local/lib/python3.7/dist-packages (from python-tsp) (1.21.6)\n",
      "Collecting Deprecated~=1.2.9\n",
      "  Downloading Deprecated-1.2.13-py2.py3-none-any.whl (9.6 kB)\n",
      "Requirement already satisfied: tabulate~=0.8.7 in /usr/local/lib/python3.7/dist-packages (from tsplib95<0.8.0,>=0.7.1->python-tsp) (0.8.9)\n",
      "Requirement already satisfied: networkx~=2.1 in /usr/local/lib/python3.7/dist-packages (from tsplib95<0.8.0,>=0.7.1->python-tsp) (2.6.3)\n",
      "Requirement already satisfied: Click>=6.0 in /usr/local/lib/python3.7/dist-packages (from tsplib95<0.8.0,>=0.7.1->python-tsp) (7.1.2)\n",
      "Requirement already satisfied: wrapt<2,>=1.10 in /usr/local/lib/python3.7/dist-packages (from Deprecated~=1.2.9->tsplib95<0.8.0,>=0.7.1->python-tsp) (1.14.1)\n",
      "Installing collected packages: Deprecated, tsplib95, python-tsp\n",
      "Successfully installed Deprecated-1.2.13 python-tsp-0.2.1 tsplib95-0.7.1\n"
     ]
    }
   ],
   "source": [
    "#!pip install python-tsp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wDg0b9p3McPr"
   },
   "source": [
    "Решение штатными средствами"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "id": "oDSRwOGBLDkG"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from python_tsp.exact import solve_tsp_dynamic_programming"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "R-Gm4Mw0LVtV",
    "outputId": "25f611c7-4a14-4f21-f2bf-693549f224ce"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0, 2, 1, 3], 8)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_matr = np.array([[0, 10, 1, 1],\n",
    "                      [10, 0, 1, 5],\n",
    "                      [1, 1, 0, 10],\n",
    "                      [1, 5, 10, 0]])\n",
    "\n",
    "path, dist = solve_tsp_dynamic_programming(dist_matr)\n",
    "path, dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YuP9k2MDMkHF"
   },
   "source": [
    "Решение с красотой и соседями))) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 299
    },
    "id": "nyyRvrC8HH4q",
    "outputId": "b7cf770a-a177-4b31-eb62-46c3a62bea57"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from numpy import exp,sqrt\n",
    "n=50;m=100;ib=3;way=[];a=0\n",
    "X=np.random.uniform(a,m,n)\n",
    "Y=np.random.uniform(a,m,n)\n",
    "#X=[10, 10, 100,100 ,30, 20, 20, 50, 50, 85, 85, 75, 35, 25, 30, 47, 50]\n",
    "#Y=[5, 85, 0,90,50, 55,50,75 ,25,50,20,80,25,70,10,50,100]\n",
    "#n=len(X)\n",
    "M = np.zeros([n,n]) # Шаблон матрицы относительных расстояний между пунктами\n",
    "for i in np.arange(0,n,1):\n",
    "         for j in np.arange(0,n,1):\n",
    "                  if i!=j:\n",
    "                           M[i,j]=sqrt((X[i]-X[j])**2+(Y[i]-Y[j])**2)# Заполнение матрицы\n",
    "                  else:\n",
    "                           M[i,j]=float('inf')#Заполнение главной диагонали матрицы           \n",
    "way.append(ib)\n",
    "for i in np.arange(1,n,1):\n",
    "         s=[]\n",
    "         for j in np.arange(0,n,1):                  \n",
    "                  s.append(M[way[i-1],j])\n",
    "         way.append(s.index(min(s)))# Индексы пунктов ближайших городов соседей\n",
    "         for j in np.arange(0,i,1):\n",
    "                  M[way[i],way[j]]=float('inf')\n",
    "                  M[way[i],way[j]]=float('inf')\n",
    "S=sum([sqrt((X[way[i]]-X[way[i+1]])**2+(Y[way[i]]-Y[way[i+1]])**2) for i in np.arange(0,n-1,1)])+ sqrt((X[way[n-1]]-X[way[0]])**2+(Y[way[n-1]]-Y[way[0]])**2)                      \n",
    "plt.title('Общий путь-%s.Номер города-%i.Всего городов -%i.\\n Координаты X,Y случайные числа от %i до %i'%(round(S,3),ib,n,a,m), size=14)\n",
    "X1=[X[way[i]] for i in np.arange(0,n,1)]\n",
    "Y1=[Y[way[i]] for i in np.arange(0,n,1)]    \n",
    "plt.plot(X1, Y1, color='r', linestyle=' ', marker='o')\n",
    "plt.plot(X1, Y1, color='b', linewidth=1)   \n",
    "X2=[X[way[n-1]],X[way[0]]]\n",
    "Y2=[Y[way[n-1]],Y[way[0]]]\n",
    "plt.plot(X2, Y2, color='g', linewidth=2,  linestyle='-', label='Путь от  последнего \\n к первому городу') \n",
    "plt.legend(loc='best')\n",
    "plt.grid(True)\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 563
    },
    "id": "28QkuVNjHUOO",
    "outputId": "f0768b36-6eb4-4bca-8183-74a997799c72"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hq4COzrnQDk+jmCMiSahybuOcCzWBFuZ5V6CK74l8HMM558J2CovIDLQyMCOvxzdyjlfeC51zeQ5H5z0TncJ9G0WjVsxwzo3L6/GjgWwjZ/jIHgqnkzRXeGOSqqL9MvNNaRlRyD9ZrNtM/vsbjaJlA5k7w21DW2nFmohVXM650E5rvzgFdXZIRcdMGUZU4ZyrkcW6C4pSFiP/OOfaZLEuv0EPooKINRUahmEYRjgskaRhGIYRVZjiMgzDMKIKU1xGcP6t1iHL+4jIfhG5zi/ZYgERaSqa0+zCkOWni8g+ETmsv1dE4kVkiYiMCrNumGherCqFKbdh+IUpLiMsItIHHSB6k3PusI+jUXA45xaiUd9fEpEEABGphEZKeDKcJ6vTKDZ9gKtEpFtguVf5GAxc4byINoZR3DDFZRxGkNIa5Jx7MWTdBSLyq4jsEZHVIjJEguIniUhlEXldRLaIyC4R+VI0MHFgfT8vQOc5IrLUa2lMlzDpWCR8xtROQetnSFBGZRFp5LVQFgYtGyeHZ46+SERc0PyxIjJZNAvvThH5SUTODjlPZpmkx4WTJeR8Q4NlyoTH0ajho735kegA1Psy28E5NwcNKvuaiFQSTb3zOvCKc25qJrJUFZEfRGSbiKR513pG0PosyyJou35hymJFyDaPeq3CXSKyQkQeEw1Llmm5iEhr71hJQecJm54oM0uBUfwxxWVkwFNaY4GbnXMvhKzLSf6ocWSfS6g02sLoj8ZkK4HmCcpt/qhQHkcjKOSW8mgepW5o6KF3PXkCcTELM+cacCjSfF/gdBFJQQMx93FhIqOH8CCwHo3S/hCafPT2LLbfjY5JbIOG+PkceFfS881lVxbBpJFeDg+GWb8TDaHVGM2R9X/kLc6nYWQgYsdxGb7QB/3AHEQHOYZyK/C1c+5+b36piDRATVMjvf/notFFAgFCL0cjjiSjYcJAn7tBAROYt81yNNL4l96ywId0g3NunWhU/EzxWmIne+foltW2oTjnfgZ+Dlo0XETOQePIPRRschONUL/DObcuN+fIoRzLRORxVKkPc84tyME++7zym4cXfd+FJH0N2X4nGh4qECT4D3Sgf0lgT3ZlEbS8NLA3UA4iEhwUOHCuYUGzK0TkYVSp3pvddRlGVpjiMoIZiEafrwq8KCLfOOeCI8I35vAcOjOB+yWLXEIiEppL6CAawDWwzUrRSNZNSI9en23+qADeB/hJNG1M1TCb9AgxN5UI2b8cqizORlsPJdGAyL9kd+4QBohIPzQSxXJghHNuYk539lqlvdCWTAeRDBHEM8U5t0hE3kXjA87O4bkC6W92oKHVdnjLc1oWVcnm3ohmzb4ZDY5bHi33EiGbNQ65N+GsQOW8bRzaupxCLnLDGcUPMxUawfzX69N6GE218ko22weT3Qc2dH122+ckf1SA3uiHMbPEdt+QMSHlHSHrn0BT5tyLBg5ugSrWLFPWhyGQGPFU1Nz2P9GEmjllBFqZPAmN8p6beHb7yV3i1DO9c7wIPCsilb3lOS2LemRxb0SkHRoEeiqa5+xENNNvyZBNA/noAtNlYQ6X5q1rCdyEmRxjHlNcRjDTAZxzB1CzYWcRuTpofXb5o4JzCQEZcgkF5wCKQz/OgW0S0fxRwck5O5JF/qggyqIp0we7zDMtpznnlgUmNNVE6DW84Zx71zn3C5pMMdssumHY5p3jN7TVAofnVQuLiHRGzbT9vP1vAx4VkbzIkS3OuZVOM2ffgyYQ7OKtymlZnAZ8m8UpTgHWOueGOed+dM6lAnXCbLc35N6sCS+uW+acS3XOTUFbXCfm7EqN4ogpLiMsThNcDgaeEpG63uIngY6eN1hDEUlGP7CPefukApPRdOqnikgz4C3UpPR20OH3A8+ISHvRzMyvA7+R3r/VAjVZThSRGiJSAzjK27eKaBbVAJei2ZI/yMflLgV6ikjLIJnLZLNPOEqISBlPWQ9AU6Vkm5RQRCqgDjHPOue+BXDOjUEVw1gRKbD3VERaicjZIlJPRI4TkUfQ1uqv3iZZloWIlBWRgagymxJ0fyqg11896Di1RCTZO9d1qBk0r3KX8c7dnPT0K0aMYorLyIrngdnAONGsrj+hZqQL0Q/Ho94U7AbeHzUtfej9xgM9nHPBEav3oK2kN9DcRXHABUH9OfPR/pVb0Txsf6OKDdTL7eSgY8WjyjM/3Ir2nXyLmvhmk3VrIjOuRSNzb0C9Da9wzuUkm+4zqDks1Px1JdpiGwQZ3L/75UG2APGoB+Av6P3pjCb/XOqtz64sLkU9GOPQvszA/bkPqI2Xkdc59xHq5fmMd65uZOHanw3l0HLdiXpBfonm/TNiFAuyaxQp3kf3eedc+Sy2sfxRYfDMiZ+gSQWX+yRDPzQXVL8w65LQXFBJRSqUEXNYi8uIRCx/VHjORD0VfVFaHrvQnE/hOED4YRSGUaBYi8soUnLS4jIMw8gKU1yGYRhGVGGmQsMwDCOqMMVlGIZhRBVRH/KpWrVqLikpyW8x8sXOnTspV66c32JEBFYWGbHyyIiVRzr5KYt58+ZtdM5Vz37LyCTqFVdSUhJz5871W4x8MWPGDDp16uS3GBGBlUVGrDwyYuWRTn7KQkRWFqw0RYuZCg3DMIyowhSXYRiGEVWY4jIMwzCiClNchmEYRlRRqIpLRF4TkfUisjBoWRUR+UJEUr3fyt5yEZHnRGSZiPwiIi0LUzbDMAwjOinsFtc4oEfIsjuBac65BsA0bx7gDDQjawM0JcSoQpbNMA4nJQWSkiAuTn9TUvyWyDCMEApVcTnnvkGDogZzHpp/Ce/3/KDlbzhlNnCkiNQsTPkMIwMpKTBgAKxcCc7p74ABprwMI8Lwo48rwTn3t/d/HZDg/a8FrA7abo23zDCKhiFDIC2NncSzmtq6LC1NlxuGETH4OgDZOedEJNdRfkVkAGpOJCEhgRkzZhS0aEXKjh07ov4aCgo/y6LjqlUIMIFLuZoxXMQkBjOCE1ct4GufZLJnIyNWHunEcln4obj+EZGazrm/PVPgem/5WuCYoO1qe8sOwzk3GhgN0Lp1axftI+ktGkA6vpZFYiKsXMl+juAS3qE1czmHj2ha+g8GHzyNzp1Bwqa3LDzs2ciIlUc6sVwWfpgKPwT6ev/7ApODlvfxvAvbAduCTIqGUfgMHw7x8QBU4F9u4ymWl23KJb1Lcd110LYtvPceHDzos5yGEeMUtjv8/4BZQCMRWSMiVwKPAt1EJBU43ZsHTUm+HFgGjAGuL0zZDOMwkpNh9GioUhUQqFOH0mOe58ox7Vi0CO68Ex59FJo0gVdfhT17/BbYMGKTQjUVOud6ZbKqa5htHXBDYcpjGNmSnAw7gbnA6KsPLS5RAi64AHr2hOnTYcQIuP9+uOUWdTysUME3iQ0j5rDIGYaRC0SgSxeYOhU+/BB++AHq1oV77oH167Pf3zCM/GOKyzDySMuWMGECzJ4NGzdCo0Zw443w559+S2YYxRtTXIaRT+rXh5degkWLoHx5aN1aLY6//OK3ZIZRPDHFZRgFRM2a6ryxfDmccAJ07w5nngnffKOBOAzDKBhMcRlGAVOpEgwerCbD88+HK66AU06ByZPNld4wCgJTXIZRSJQpox6HS5bAzTfDAw9A06bw+uuwd6/f0hlG9GKKyzAKmRIl4JJLYN48ePZZeOMN7Rd75hnYscNv6Qwj+jDFZRhFhAh06wbTpsG778LMmepKP3SoeiUahpEzTHEZhg+0aQOTJqnyWrsWGjSAQYNg1Sq/JTOMyMcUl2H4SKNGMGYMLFwIpUpBixbQty/89pvfkhlG5GKKyzAigFq14PHH4Y8/VJl17QrnngsLF1b0WzTDiDhMcRlGBFG5Mtx9t7rS9+gBDz/cmFNPhSlTbCyYYQQwxWUYEUjZsnD99fDmmz9w/fWqzJo3h5QU2L/fb+kMX0lJgaQkOnbpAklJOh9jmOIyjAimRAlHr16wYIFGpB8zRl3pn38e0tL8ls4oclJSdHDgypWIc7Bypc7HmPIyxWUYUYAInHEGzJgB//sffPmlutIPGwabN/stnVFkDBnCmrTKjOdSvqWDLktLgyFD/JWriDHFZRhRRvv28MEHmhds+XJtgd12G6xZ47dkRkFz8CD8+qsGce7dG5JWzuBE5nMZb/MjbdI3jLFxFKa4DCNKadIExo6Fn39Wx40TTtC4iL//7rdkRl7ZvRu+/RYeeQTOOguqVoULL4Q5c6BzZ5h69BU8zS2cwC8MZGT6jomJ/gntA4WaAdkwjMLnmGPgqafUWvTCC3DaadChgwb6bdvWb+mMrNi0Cb77Tgeif/ed9mUef7zevyuvhNdeg4SE9O037L2e268/lY85i5J4Xjrx8TB8uD8X4BOmuAyjmFC1Ktx3n5oNX3tN4yPWqwd33gn/+Y/2kxn+4ZwOc5g5M31auxbatVNFNWyYVjTKlcv8GLd8dxG9z1xE69824lYJkpioSis5ueguJAIwxWUYxYxy5WDgQLj2Whg/XhVZyZLaArvoIjjC3voiYf9+NeMGK6q4OFVSHTrAdddBs2Y5vx+ffgrffw+//toEyq3g6xkz6NSpU6FeQ6Rij7BhFFNKloTLL9fK+CefaJLLIUPgjjs0rFTZsn5LWLzYsQNmz043+82Zo11PHTrAeedpZJQ6dfLW8t2xQxXdK69k3SKLFUxxGUYxJy4Ozj5bp5kzdTzY0KEa1Pe66+DII/2WMDr5++/0/qmZM2HxYmjZUpOGDhoEJ58MVaoUzLmGDFHnjNNPL5jjRTuxqbhSUvRJWLVKq0QxaCM2YpOAmWrhQnjsMTj2WHUCuPlmOPpov6WLXJxTb81gs9+WLaqkOnTQPGutWmny0IJm9mx45x29Z4YSe4orMPI8EHYgMPIcTHkZMUPTpprQcsUK9Ug8/ni4+GI1IzZo4Ld0/rNnjyb+DCip77+HihXTFf9//wuNG2trtjDZuxeuukqTjlatWrjniiZiT3ENGQJpabxHT36iJQ1IpUFaKg3vfIKqlyWb55URUyQlwXPPwb33ahipk0+GTp3UkaN1a7+lKzq2bIFZs9IV1U8/QcOGqqR694ZRozSCf1EzYoRGSLnkkqI/dyQTe4rLG2Feg3VM5GKW0oiqbGT/miOQKvqwNmiQ/huYKlXyWW7DKESqV4cHHtAW15gx0LMnHHecKrCuXYuXK71z+hkINvutWAEnnaSK6t571UW9QgV/5Vy8WCsV8+cXr/IvCGJPcSUmwsqVnMwsfqUZIxnII9zF1RUncN28a1i3DpYuhdRUeO89/V22TD15gpVZ4H/9+jr+zzCKA+XLwy23wA03wNtvq1t9uXI6FqxnTyhRwm8Jc8+BAxo2KaCkvvsO9u1LN/tdcYUm8CxZ0m9J0zl4EK6+WisTtWv7LU3kEXuKa/jwQ31cpdjHbTxFctn3uav5F3TooKFW+vTJaLt2Dv76S5VYQKm9+ab+//NPqFYtozIL/Narp1ltDSPaKFUK+vXTd+HDD9WV/u67tUXWpw+ULu23hJmTlgY//JCuqGbNgpo1VUn16AEPPaROKZHcinnpJf3uXHut35JEJrGnuAIOGEFehTWGD2Ns8rHMmQM33QQvvggjR6rpAPQBr1VLp9DxfgcO6GFSU9MV27Rp+rt6tdaWQk2PDRvqeI5orL0asUVcHJx/vo5D+uYbVWD336+tsmuuUYcFv1m/PqNb+sKFGrcxMMj3zTfVFBotrF6tZfz114Xv/BGtxJ7iAlVeYTwI27bV2tkbb+jLqhlooUaNzA9VooR2ntatq2F1gtm7V1tkAaW2aBFMnqxKbf163adBAyhb9liWLElXakcfbQ+sEVmIQMeOOi1YoK709eqp8WLQoIzx9AoT5/T9CZj8Zs6Ef/7RiPkdOqhcbdpEr/neOU0gOnCgBlE2whObiisL4uLURHLBBRo7rGlTuOsufZBya/YrVQoaNdIplF274I8/9CWcOnUvP/ygnvqpqbB9u/adhfanNWyoNcdINnEYxZ8WLbT/a/lyePJJdeLo1Qtuv12VWUGyb586JwRaU9Onn0z58nDqqaqoBg1SV/7iYr145x2t7L77rt+SRDa+KS4RuQW4CnDAr0B/oCYwHqgKzAMud87t9UO+ip9Y5FYAACAASURBVBU1RMtVV+ngzDFjdCxFjx4Fc/yyZVUpNm0KVaqsplOnYw+t275dHUIC/WnTp8PLL+v8gQPh+9MaNIDKlQtGNsPICfXqaTT6++5T77eTToJu3dQTsUWLvB1z+/aMbulz5+p5OnTQOIuXXjqPSy9tX7AXEiFs2qTfmvfft77x7PBFcYlILeAmoIlzbpeIvAP8H3Am8LRzbryIvARcCYzyQ8YAjRppnLcpU7TV1bixDtisX7/wzlmxooaOadny8HWbNmXsT/voo3QFV6ZMeKVWv756ixlGYZCQoD5PgwfD6NGaR6pZM/VE7NgR5O3MI9WsWZPR7JeaqhEoAoN827fPGJJqxow9Pl1l4XP77Tpeq107vyWJfPw0FR4BlBWRfUA88DfQBbjMW/86MBSfFReoae7ss7U2+cwz+mBdfbW+i0WtEKpW1Sn04XZObf0BJbZ0qaZ4X7pUTZJVqoR3Ejn22Mj2EDOih4oV9eM7cKA6RFxzDVQ+sJHBqz/ivL06fnLRyvLM7D+HmS+ezMy1ddmxI90tPTlZK2ux2Nr48ku1rFhYp5zhi+Jyzq0VkSeAVcAu4HPUNLjVOedlR2MN4MNY9cwpXVprlZdfrrXJ445TL6vkZP/7nUTUiaRGDU0kGMzBg1qzDVZqX3+tvytXqjNIuP60pCRLgWHkntKl1cTevz98UOMeHt57G7fyCNuoRFU20WHfTDr9/hL3fDeCRo38f3f8ZudOVfKjRpllJKeIc67oTypSGXgXuBTYCkwEJgFDnXP1vW2OAT51zjUNs/8AYABAQkJCq/HjxxeV6Bn47beKPPdcA0qWPMjAgak0arQjT8fZsWMH5X16YvfvF/75pwyrV5dlzZqyrFkTz9q1+n/TptLUqLGbWrV2Ubt2GrVr7/KmNKpX31Mono9+lkWAjz6qyZIlFbj99qW+ygGRUR75oWOXLuAc8zmRo/mLGvwDgBPh66++yvXxor08wjFq1LFs3lyKIUMW52q//JRF586d5znnojaol1+K62Kgh3PuSm++D9AeuBio4ZzbLyLtUUXWPatjtW7d2s2dO7fQZc6Mgwdh7Fg1G55zjprvjzoqd8eYEaEJ4XbvVs+xQEsteAD2li3aaR7OSaRGjbzXoiOhLEaPVqeA0aN9FQOIjPLIF0lJ2qwPpU4djbOUS6K+PEKYO1e7IX79NfdjzfJTFiIS1YrLL0PQKqCdiMSjpsKuwFxgOnAR6lnYF5jsk3w5Ji5O00JceCE8+KC65t5zj47FiKQQMnmhTBkdSxJuPMmOHer5GFBm334Lr76q87t3h+9Pa9DAIlzHHEGRag4RH6/LY5x9+9Sk+sQT0TVAOhLwq49rjohMAn4C9gPzgdHAFGC8iDzkLXvVD/nywpFHqrdhwH1+9GjN0VNcE7+VL68uz+HcnrdsydhC++wzjUSydKn2mWWm1PwOamoUAmEi1Vj+O+WJJzQUlRVF7vGt6905dz9wf8ji5cBJPohTYDRpAlOnany3AQP0w/7kkxolI1aoXFnH9JwUciedgw0bMjqJTJqUruQqVYKjjmpB69YZTZDHHmtp5qOaTCLVxDJLl+p3Yd48c07JC+YzVgiIaGy37t21FdamjcZMu/NOjbQdq4ho/99RR6n7czAHD2og43feWUG5ci1ITdWxPampGkngqKMO709r2FArBNFukjVii4MHtVJ7773a1WfkHlNchUiZMhpRu0+f9Iypjz0Gl15qtaxQ4uI0IHHLllsPC2S8f396IONAa23qVP1du1b3C+ckkphYfEIBGcWHV1/VkG833ui3JNGLKa4ioHZtje327bfp0eefey7vYXFijSOOUA/GevW0FRvM3r3q+RhQar/+qnnUli6FjRu1RRauP+3oozOpPKSkwF0LYXM9+Hy49ccYBcpff2l337RpVqnKD6a4ipBTT1X311de0Q9wIJCvkXdKldKB4Mcdd/i6tLR0z8fUVJg9Oz2P2s6d6YGMD7XW/pxKg8fvxu3qAdRVN+4BA/RgpryMAuDGGzXHVrNmfksS3ZjiKmJKlNBR8pdcojl3mjSBXr1q0aGDRakoaOLjNS/TCSccvm7btnSFlpqqIXdGTUxg6d4F7KA81/CybpiWplVkU1xGPnnvPVi8WEOxGfnDPpU+UbmymgsHDIA+fapx4ok637mz35LFBpUqQevWOh3i7ZY4HJuoShl2py9ftarI5TOKF1u3agzHCRMsNmhBYOkKfaZpU3jyyZ8ZOlRju118cfhAA0YRkJiIANXYRHl2ZlhuGPnhjjvU0zjUm9bIG6a4IgARjbyxeLHavlu2hKFDMwYbMIqA4cMPT51rUR6MfDJ9ug7Cf/RRvyUpPpjiiiDKltWkfPPnqxJr0kQH6PoQTjI2SU7WkCd16mhtok4dnbf+LSOP7Nql3QEvvKBpX4yCwRRXBJKYqLbwceM0/mGXLurmbRQBycka/PXgQf01pWXkgwcfVAvKuef6LUnxwhRXBNOpE/z0k/Z7de2qnbubN/stlWEYOWH+fHjtNXW6MgoWU1wRzhFHaKT5xYu1EdC4Mbz0Ehw44LdkhmFkxv79GnB7xAhISPBbmuKHKa4ooWpVtZN//rmOA2nVCr75Bo30kJSkMZOSknTeMAxfeeYZHfLSt6/fkhRPbBxXlNG8OcyYARMnQu8LdnLK1lI8duAAx+As0oNhRAB//KEehHPmWEzSwsJaXFGIiEbe+D2+FTUPrKY5P3MQ7w0JRHowDKPIcU7rjnfeqel4jMLBFFcUE79mKQeJ4/8YTxxBPvMW6cEwfGHcOA0ndvPNfktSvDFTYRTze83OpPyVzCKaZFxhkR4Mo8hZtw4GD9Z+aIs7WrhYiyuKuf2oN7ir5JNUZ2P6Qov0YBi+MGgQXHmlpSsqCkxxRSlTp8KSHbW4cUxzi/RgGD7z4Yc65vK++/yWJDawBm0Usn8/3HorPPkklDq3F/Tt5bdIhhGzbNsGN9ygud7KlvVbmtjAWlxRyOjRULMmnHOO35IYhnHXXXDGGRrpxigarMUVZWzZAg88AF98YWNEDMNvZs6EyZPht9/8liS2sBZXlDFsGPTsGT6rr2EYRcfu3XD11TByJBx5pN/SxBbW4ooili5VO7rV7gzDf4YP19ihF1zgtySxhymuKOL223WcyFFH+S2JYcQ2v/6qwa5//tlvSWITU1xRwhdfwKJFGqPQMAz/OHBAI78//DAcfbTf0sQm1scVBQTc3594AkqX9lsaw4htnn9e3d6vvNJvSWIXa3FFAa+8AtWrw3nn+S2JYcQ2K1aog9T332smIcMfTHFFOFu3wtChGinD3N8Nwz+cg2uvhdtug4YN/ZYmtrE6Q4Tz0ENw7rmah8swDP9ISdFAurff7rckhm8tLhE5EngFaAo44ApgCTABSAJWAJc457b4JKLvpKZqmgRzfzcMf9mwQRXWxx9DyZJ+S2P42eJ6FvjMOXcc0BxYDNwJTHPONQCmefMxyx13wH//CwkJfktiGLHNzTdD797QurXfkhjgU4tLRCoBpwH9AJxze4G9InIe0Mnb7HVgBjC46CX0n2nTdKzIhAl+S2IYsc0nn8Ds2fDLL35LYgTwq8VVF9gAjBWR+SLyioiUAxKcc39726wDYrKtceAA3HILPP64ub8bhp/8+y9cdx28/DKUK+e3NEYAcc5lv1VBn1SkNTAbOMU5N0dEngW2AwOdc0cGbbfFOVc5zP4DgAEACQkJrcaPH19EkhcOO3bsoHz58ofmP/qoJtOmJfD00wtizpMwtCxiHSuPjBR1eYwcWZ+0tBIMHrykyM6ZU/JTFp07d57nnItew6dzrsgnoAawImj+VGAK6pxR01tWE1iS3bFatWrlop3p06cf+r91q3MJCc799JN/8vhJcFkYVh6hFGV5fP+9czVqOLdxY5GdMlfkpyyAuc6Hb39BTb6YCp1z64DVItLIW9QVWAR8CPT1lvUFJvsgnq8MHw5nnw0nnui3JIYRu+zdq2GdnnkGqlb1WxojFD8HIA8EUkSkFLAc6I/2ub0jIlcCK4FLfJSvyFm2DF57DRYu9FsSw4htHn0U6tWDS2LqCxQ9+Ka4nHMLgHA21q5FLUuk8N//6liRGjX8lsQwYpdFizTH1vz5Fq0mUrGQTxHC9On6orz9tt+SGEbscvCgJod84AGoXdtvaYzMsJBPEUCw+3uZMn5LYxixy6hR+nvttf7KYWSNKS4/SUmBpCSWn55Cxd/ncOHuFL8lMoyYZfVquP9+zcZgkd8jGzMV+kVKCgwYwPa0EtzHg3y852zkmt9BgORkv6UzjJjCObj+ehg0CBo39lsaIzusXuEXQ4ZAWhoPczdn8Cmt+AnS0nS5YRhFyoQJ8OefMDgmA8xFH9bi8otVqwB4n55M5OLDlhuGUTRs2qR9zO+/D6VK+S2NkROsxeUXiYkAOIQy7D5suWEYRcNtt+l4rXbt/JbEyCmmuPxi+HCIj8+4LD5elxuGUSR88QXMmGGvXbRhpkK/CDhg9DsCt1+gTh19e8wxwzCKhJ074Zpr1AXe4hhHF9bi8pPkZKhbjx/eeANWrDClZRhFyH33wcknwxln+C2JkVusxWUYRszx44/w1lsWFzRasRaXYRgxxb59Gvn9ySehenW/pTHygikuP0lJgT+Xc1KfPpCUpPN+yJCUpKEC/JKhKIiV6zTCE3T/nzjqMY7mL7PMRzGmuPzCi5zB/v0IDlau1Pmi/KAGZFi5UkMH+CFDURAr12mEJ+j+L3ENeHLrFby0tAvytt3/aMX6uPzCi5wB8Ba9OYr1kAYMXAJbikiG+5ZAWn8GDn0haGEaLOsND/QuIiHC8HUhHPO/6X/dUNKjlFi1u/jjvWsOGMBo7mUYdXYvsfsfxZji8gsvQsZNPMfvHMdmqujyLQK/F5EMWxKAo4roZBGIRSmJDbz7vIfSzKI9X9Elw3Ij+jDF5ReJibByJTfyQsblderA8zcUjQwfPw4rV/L80JDldeqoe74PzJgxg06dOhXY8ZYvh+TGP1Fh70bG0Y+j+Tt9pUUpiQ28dw0gjoOU4GD6ciMqsT4uv4iEyBmRIEMh4Ry88Qa0bQuXXOz4rOwFGZVWMblOIwcU4+c8VjHF5RfJyTB6NNSpgxMvcsbo0UVrcw+SAb9kKAS2bIFevWDECPjyS7jlrVbEjXm52F2nkUMCz3liHZ23+x/1mKnQT5KTITmZrwvYPJYXGYoLX38NffrAuefC3LlQtqy3ophdp5FLkpPhwmQ4Et/M4EbBYYrLKBbs3QtDh8LYsfDqq3DmmX5LZBhGYWGKy4h6lizRCnVCAixYoL+GYRRfrI/LiFqcgzFj4JRT4Ior4OOPTWkZRixgLS4jKtm4Ea6+WtOtf/MNNGnit0SGYRQV1uIyoo4vvoAWLeDYY2HOHFNahhFrWIvLiBr27IG774YJE9QJo1s3vyUyDMMPTHEZUcGiRXDZZVC3rjpgVKvmt0SGYfiFmQqNiMY5ePFFOO00uOEGeO89U1qGEetYi8uIWNavV2/Bdevgu++gUSO/JTIMIxKwFpcRkXz6qTpgNGsG339vSsswjHSsxWVEFHv2xDFwIHz4Ibz9NvgVCcswjMjF1xaXiJQQkfki8rE3X1dE5ojIMhGZICKl/JTPKFp+/hmuuaYV69erA4YpLcMwwuG3qXAQsDhofgTwtHOuPpoH+EpfpDKKlIMH4emn4fTToVevVYwfD5Ur+y2VYRiRim+KS0RqA2cBr3jzAnQBJnmbvA6c7490RlHx11/Qowe88w7Mng3du/+DiN9SGYYRyfjZ4noG+C8E0pFSFdjqnNvvza8BavkhmFE0fPABtGwJJ58M336rkTAMwzCywxfnDBE5G1jvnJsnIp3ysP8AYABAQkICM2bMKFgBi5gdO3ZE/TXkhl274njxxfrMm1eZIUMW06zZdmbO1HWxVhbZYeWRkfyUx969cRw82IEZM74pWKF8IqafDedckU/AI2iLagWwDkgDUoCNwBHeNu2Bqdkdq1WrVi7amT59ut8iFBlz5zrXsKFzl1/u3Nath6+PpbLICVYeGclPeeza5Vzp0gUni9/kpyyAuc6Hb39BTb6YCp1zdznnajvnkoD/A75yziUD04GLvM36ApP9kM8oeA4cgBEj4IwzNOHjG29ApUp+S2UYRjQSaeO4BgPjReQhYD7wqs/yGAXA6tXQp48qrx9/hDp1/JbIMIxoxm93eJxzM5xzZ3v/lzvnTnLO1XfOXeyc2+O3fEb+mDgRWrXSSO7Tp5vSMgwj/0Rai8soJvz7L9x0E8ycqZmJTzrJb4kMwygu+N7iMoofs2fDiSdCiRIwf74pLcMwChZrcRkFxv798Mgj8Pzzmorkwgv9lsgwjOKIKS6jQFixAnr3htKlYd48qF3bb4kMwyiumKnQyDcpKdCmDZx/PnzxhSktwzAKF2txGXlm2za4/nr46Sf4/HPt1zIMwyhsrMVl5ImZM6F5cx1EPG+eKS3DMIoOa3EZuWLfPnjwQRgzRqdzzvFbIsMwYg1TXEaOWbYMkpM1V9aCBVCjht8SGYYRi5ip0MgW52DsWGjfXhXXJ5+Y0jIMwz+sxWVkyebNcM018Pvv8NVX0KyZ3xIZhhHrWIvLyJTp09UBo1YtDY5rSsswjEjAWlzGYezdC/feC2++Ca+9Bj16+C2RYRhGOqa4jAz8/rv2Y9WqBT//DNWr+y2RYRhGRsxUaADqgPHyy9ChA1x9NUyebErLMIzIxFpcBhs2wFVXwapV8O230Lix3xIZhmFkjrW4YpzPP4cWLaBRI01HYkrLMIxIx1pcMcru3XDXXTBpErzxBnTt6rdEhmEYOcMUVwyycCFcdhk0bKgRMKpW9VsiwzCMnGOmwhjCORg5Ejp1gptvhokTTWkZhhF9WIsrRli3Dvr3h02bYNYsaNDAb4kMwzDyhrW4YoCPP9a0I61awXffFYLSSkmBpCSIi9PflJQCPkERUpyuxTCKKdbiKsakpcEdd8CUKTBhApx2WiGcJCUFBgzQkwGsXKnzoCOZo4nidC2GUYyxFlcxZcECaN1ag+QuWFBISgtgyJD0D32AtDRdHm0Up2sxjGKMtbiKGQcPwtNPw6OP6m9yMogU4glXrQLgR1rTka/ZRbwuXwnk6bydCkiwvLDi0L8a/M0ZfMpZTKHbyi+p6J9QhmGEYC2uYsTatfCf/8B778EPP0Dv3oWstAASE3HAIJ7leW7EITrVScI5cj1Nnz4jT/sVyFQn6ZD8M+lACxYwmgHUkrV07QpPPQVLlui2hmH4hymuYsL770PLltCxI3z9NdStW0QnHj6cCaX6sJsy9OV1XRYfD8OHF5EABcjw4So7cCzLuYmRTI2/gHVjPmbQIFVaXbtC/fpw000wdaoO5DYMo2gxU2GUs2MH3HKLJnmcPBnatSva8++6IJnBg87njSOuoMR6B4l1VAFEozNDQOYhQ9QEmpgIw4dTLvn/OBc491xtbf3yi2aBHjYMLrlEx8WdeSacdRbUru3nBRhGbGCKK4r58Uf91p58sjpgVKhQ9DI8+SS06VSOjpMmABOKXoCCJjk5S6Urosk1mzfXkFmbNmnLa8oU1Xe1aqkCO+ssaNsWjrA3zDAKHHutopADB+Cxx9T5YuRIuPRSf+T46y+V4ccf/Tl/JFC1qobPuuwyvS9z5qgSu+EGWL0aundXJdajh0UpMYyCwhRXlLFqFVx+udb8585Va5Zf3H235u6qV88/GSKJEiW09XvyyWotXbNGTYoTJ8L110PTpqrEzjxTW2yF7jhjGMUUX5wzROQYEZkuIotE5DcRGeQtryIiX4hIqvdb2Q/5IpUJE3Rs1hlnwLRp/iqtuXPVRHb33f7JEOnUrq3jlz/4ANavh/vvh3/+gYsugmOO0XWTJ2s/pVHIpKRo7p49uy0iSjHAL6/C/cBtzrkmQDvgBhFpAtwJTHPONQCmefMxz/bt0Lcv3Huv1uDvvFNr937hnAbpHTYMKtoApxxRurQOVXj2WUhNVWeaxo3V1FuzZvq6Zcv8lrQYEoiIsmqlzgciopjyilp8UVzOub+dcz95//8FFgO1gPMg4FPN68D5fsgXScyapYkeS5eG+fO1xeU3EydqK6F/f78liU5ENKXMLbfAl1/q+Ltrr1VvxVNP1YbBrbfqun37zJ6YbywiSrFDnM+jKUUkCfgGaAqscs4d6S0XYEtgPmSfAcAAgISEhFbjx48vMnkLgx07dlC+fPkMyw4cEN56K5HJk2txyy1LOfXUjT5Jl5E9e+Lo2/ckBg/+nRNP3Frgxw9XFrHEwYOwbFl5Zs+uyuzZVVm1qiwtW26lbdtNtGu3mapV9/otoq/k5fno2KUL4hz7KcExrOZ2nuBWngIRvv7qq0KStPDJz7vSuXPnec65CKgG5xHnnG8TUB6YB1zgzW8NWb8lu2O0atXKRTvTp0/PMP/HH861b+9ct27OrV3rj0yZMXy4cz17Ft7xQ8si1nn//ZnujTecu/RS5ypXdq5lS+fuuce5WbOc27/fb+mKnjw9H3XqHAqOsoJE15of3EW847Yf06SgxStS8vOuAHOdj9/+/E6+Rc4QkZLAu0CKc+49b/E/IlLTW18TWO+XfH7gHLzxho7/ufhi+OwzOPpov6VK5++/ddzW44/7LUnscOSR+7j8chg/Xh08nn4a9u5Vb86aNaFPH3Xa2bLFb0kjmKCIKHVYxbecSuUS/3LSge9ZvNhn2Yw84ZdXoQCvAoudc08FrfoQ6Ov97wtMLmrZ/GLLFujVC0aM0L6NW27RlFCRxJAhcOWVcOyxfksSmxxxhEb5HzECfv1Vx8+1bw9vvgl16qSvW7jQ4ilmIDkZRo/WQhKhTJ0ajH69NHcMq8Rpp8E77/gtoJFb/BrHdQpwOfCriCzwlt0NPAq8IyJXovHFL/FJviJlwYJK9O2rIYXmzoWyZf2W6HDmzVOPxiVL/JbECFCnDlx3nU67dsH06XqPzjlH+8oCYai6dDnU4IhdwkREuQJ1fLroIpg9W5V+yZL+iGfkDr+8Cmc658Q5d4JzroU3feKc2+Sc6+qca+CcO905t9kP+YqKffu0FTNsWBNefFFdoyNRaTmnLcAHH4RKlfyWxghH2bKqqJ5/HpYvh08/1YHhTzwBNWrouhdegBUr/JY0smjZUiuLixdrAOV16/yWyMgJEWaMih1SUzXCwvz5MGbMXM46y2+JMufdd2HbNjUTGpGPCDRpotmvZ8zQaCv9+6tpsW3bjOv27fNbWv+pUkXDdHXpAq1awcyZfktkZIcpriLGOXj1Ve2b6NtXX5gqVSL367F7t37knn7a30HPRt458kh19hk3Th1sxo2DcuX0vh51lEa4HzdOo3rEKnFxMHQovPIKXHihDga3fsLIxWIVFiGbNumA/WXLNGfW8cf7LVH2PPOMxtXr0sVvSYyCIC4OTjpJp6FD1TT26afw8ccaDaVhw/To9i1bRp6DUGFzxhna33XhhTr4/5VXIIaHFUYsMfZY+se0adoRXKeORhCPBqW1bp26vpv7e/GlRg01I06apO72I0bAv/9qIOejj05ft22b35IWHXXrwnffqUNL27bmkBSJmOIqZPbsUZNM377w2mua/r1MGb+lyhn33KMfrgYN/JbEKApKlYLOndWhY/Fi+P57bXW9+qoGBe7SRcfxLV5c/M1oZcvqdd98M3ToAO+9l/0+RtFhpsJCZPFizdNUp44meqxWzW+Jcs78+fDRR1bbjGXq1YOBA3XauVMDA0+ZogGBS5ZMNyl26hQ9lbHcIKIDvVu00D7C2bPh4YctOWgkYC2uQsA5ePFFDZh6/fXw/vvRpbQC7u8PPKAd+4ZRrpyOD3vpJfVSnDxZsz0PH64OHoF1q1f7LWnB06aNuswvWADdusW2E0ukYIqrgFm/Xl/i115TO/nVV0dfwsD331dHkquu8lsSIxIRgWbNNL3Ot9/q2LDLLlM38hNPhBNOgLvu0vn9+/2WtmCoVk2dWDp00AwNs2b5LVFsY4qrAPn0UzUrNGum/QONGvktUe4J9Mk99ZSZRIycUaWKhit76y1tjbz8sg6dGDgQEhLS122MjAQHeaZECc1B9+KLcN55Oti7uPf1RSr2aSoAdu2CwYM10+3bb6vNP1p59ln1eOzWLevt9u3bx5o1a9i9e3eBnr9SpUostsinh4jG8jjyyPQIS/v36/uxa5eGDStVSh0fypaFihXLULt2bUpGWZylc87RiumFF2q/18svqynVKDpMceWTX39VM0njxvDzz1C5st8S5Z1//oHHHtOXMjvWrFlDhQoVSEpKQgrQFvrvv/9SoUKFAjtetFOcyuPgQU1AunUrbN3q2LRpEz//vAaoy+mnR9d4qfr11Vx47bXQrp16HZr3bdFhpsI8cvCgtk66dIHbbtPUElGptFJSICkJ4uK4t/7b9GmzmIYNs99t9+7dVK1atUCVllG8iYuDihUhMRFOOEE4/viq1Ky5mxde0DFj//mPDnhPTfVb0pwRHw+vv64OWKecog4rRtFgLa488PffOr5p61Y1FURtmo+UFA3lkZbGApozeUdXfv+6JaQ8dlgk7XCY0jLyQ9myQsWK8MUXOuj5yy81uv3jj6vpLeBuf+qpULq039KGR0Sj87dsqS7zc+ZoP5iFRytcrMWVSz78UD2n2rZVj6qoVVoAQ4awOa00cziJgYzkfh6g8q6/NGR9FFCiRAlatGhxaEpMTOTGG2/0WywjD1SoAD17wpgxsGaNWjCqVoV771V3+549NfzSxo2l/BY1LG3bah/enDnQowds2OC3RMUba3HlkJ071SQ4dapGSz/lFL8lyjn//qvml8C0dKn3u3Ie+zmCBqTShh8ZwGjdYdUqfwXOIWXLlmXBggWH5seNG8fcuXN9lMgoCES0cnjiiRq9ZeNGzQY+ZQp88kkbHn44PdfYSSdFTuumenX9Ptx7r7rMEvC1oAAAFc9JREFUT5yo8hkFj7W4csBPP2m6g507dRBiJCqtXbs08+3772u8uauugo4dNb17IB7dxIl6DZ07qzlmce3/sJUjmUsbRnE9R3BAD5aY6O/F5JN///2XunXrss/L2bF9+3bq1q3Lt99+S4sWLWjSpAlly5Y91FIDSEpKYmM2/trTpk3jxBNPpFmzZlxxxRXs2bOHCRMm0KJFC+rXr0+lSpVo0aIFZ555ZpbH6dSpE40aNTp0/hLel9c5xx133EHTpk1p1qwZEyZMOLTPiBEjaNasGc2bN+fOO+8Me6zynnfDgQMHuOOOO2jTpg0nnHACL7/88qHt586dS/ny5Q9roY4bNy5Da/XGG29k3LhxAMybN4+OHTvSqlUrunfvzt9//x32OlasWMHmzZs5//zzOeGEE2jXrh2//PJLlmWRE6pVg9694X//g/fe+55nn1VvxWuu0Wf78sth/HjNIu43RxwBjzyi/d9nn62Dss1lvhBwzkX11KpVK1dYHDjg3IgRzlWr5lxKSqGdxk2fPj1H2+3d69ySJc59/LFzTz3l3HXXOde1q3OJic6VLu3cccc5d845zt16q3MvveTctGnOrV6t1xGWt95yLj7eOX23dIqP1+XZsGjRopxfYC7Yvn17jrctV65chvmxY8e6G264wTnnXL9+/dz777/vnHPu5Zdfdrfeeuuh7f788093/PHHZ9i3Tp06bsOGDZmea9euXa527dpuyZIlzjnnLr/8cvf0008fWj99+nR31lln5Ujujh07uh9//PGw65g0aZI7/fTT3f79+926devcMccc45YuXeo++eQT1759e7dz507nnHObNm06tG+HDh3cvHnzMhzn5ZdfdsOGDXPOObd7927XqlUrt3z5cuecc7Nnz3adO3c+rLyC/zvn3A033ODGjh3r9u7d69q3b+/Wr1/vnHNu/Pjxrn///mGvwznnbrzxRjd06FDnnHPTpk1zzZs3z7Iscvschb4rK1c6N2qUc2ef7VyFCs516ODcI48498svzh08mKtDFzhLlzrXtKlzffs65926AiWn341wAHNdBHy/8zqZqTAT1qyBPn000d6PP6rjXVFw4ICGzQmY84JNe6tWQe3a6nbbsKG64J97rv5PTMzDgOGAA8aQIXrwxESN4ZMDx4xI56qrruKxxx7j/PPPZ+zYsYwZMybbfTp37kxcXBzNmjVjzJgxlA1KR71kyRLq1q1LQ8/lsm/fvrzwwgvcfPPNBSbzzJkz6dWrFyVKlCAhIYGOHTvy008/8cMPP9C/f3/i4+MBqFKlyqF9du3aRZmQQIGff/45v/zyC5MmTQJg27ZtpKamUrduXXbs2JFh/2AmTJjATC+L4tq1a2ndujVLlixh4cKFdPMG9h04cICaNWtmeQ3vvvsuAF26dGHTpk1s376dihUr5rFUsiYxUV3Sr71WrQ5ff60mxfPO01bZWWepWbFrV/UCLEoaNFDnrQEDNGnsu+9GeZ94BGGKKwyTJqmL66BBGtamoG3ozqlnYkAhTZtW75Ab8PLlahoJKKcGDfSla9BA0y0UuHdVYKRoMeOUU05hxYoVzJgxgwMHDtC0adNs95k+fTpVq1alT58+vPnmmwwYMKAIJM0ff//992GKxDnHyJEj6d69+2Hb//nnn9SuXTvssS699FKef/55gENmQ+ccxx9/PLOiIMZR2bLqGNGjBzz3HPz+uyqxp5/WR/yUU9I9FevWLRqZypXTqCEvvKDK67XXiOhs59GC9XEF8e+/cMUVqqw++kgbInlVWs6pZ9H33+tYjyFDNNNsixbqQXXiidqJO2sWVKiwn8svVxv+pk3a4vrqK7WP33abjtQ/7rjIdQmOVPr06cNll11G//79c7yPiFClShX27t2bYXmjRo1YsWIFy5YtA+DNN9+kY8eOBSrvqaeeyoQJEzhw4AAbNmzgm2++oVWrVnTr1o2xY8eSlpYGwObNmwFt3Rx55JFUDhlA2L17d0aNGnWoj2/p0qXs3LkT5xzvvvsuZ599do5latSoERs2bDikuPbt28dvv/2W5TWkpKQAMGPGDKpVq1Zora2sEFGLxO2367u0ejVceaV6/rVvn75u+nS1qhS2LDfeqP3P114L992nlhUj71iLy2POHK2VdeyoKT1yGqxg27Yw3npL0wdRBlpNDRuqS2+DBjpVqpR+jBkzVtGpU72Cv6gYJzk5mXvuuYdevXrlaPuzzz6buLg4ypcvz4MPPphhXZkyZRg7diwXX3wx+/fvp02bNlx77bUFKm/Pnj2ZNWsWzZs3R0R47LHHSEhIoH79+ixYsIDWrVtTqlQpzjzzTHr27MlNN93Ea6+9dthxrrrqKlasWEHLli1xzlG9enU++OADBg8ezGeffcbatWuJi4tj8+bN7Nq1i379+mUqU6lSpZg0aRI33XQT27ZtY//+/dx8880cn0km1KFDh3LFFVdwwgknEB8fz+uvv15QxZMvKlWCiy7S6eBBVWCffKKh2lJT4fTTtSV0xhkaX7EwOPlkjTJ/6aV6rpQUdfk38oDfnWz5nfLknPHWW87VqeOciNufWNcNu2iBO+oo5yZODL/5zp3O/fyzrn/4Yef693fulFOcO+oo58qVc65FC+cuvti5IUOcGzfOue+/d27Dhpx3Duenk9UvIsE5IzsmTpzoevfuXWDH84OCLI++ffu6P//8M8OykSNH+vr85dc5oyBYt865sWOdu+gi54480rnWrZ27/37nfvghC8emfLBvn3N33OFcUpJzIb4tucKcM2KJoGgRK0mk96rXKblmK7OemMzepufx4YcZW02pqTqOpF699NZT+/aa0bhBA3U3twASkcfAgQP59NNP+eSTT/wWJWK47rrrqF69eoZl3bt3p1Jw8z8GSUiAfv102rdP0xFNmaLv+KZN2go76ywNSVUQRXXEERoTtG1bPfYjj1gKodwSe4pryBBIS+MTzqAX/+NfKpB4cBVNbm3HMS+mK6fmzdWs0KCBpi2PlEGORs4YOXKk3yJEHG3btj1sWQOLDJuBkiU1u0OnTjrW8c8/1aQ4dqz2kbVqle6p2Lhx/iqtF16omRguuED7up9/Xh1MjOyJPcXlRYUowQEe4H4akEoDUqnLCkqm7s1mZyMc8kDhNDnd/TZy0/CXunXhhht0SktTR48pU9RzsUSJdC/FTp3ypnSOOw5++EFbXB06qMt8UQ29iWZiz6vQiwrRnc+5mWc5i09oSCol6xzts2CGYUQy8fEaDWPUKFi5Uj2PjzlGTX0JCer9O2pU7iOmlS+vHsWXX64pUj77rHDkL07EXotr+PBDfVyHiI/X5UaeKMiWUXHKP2UUX0SgaVOdBg/WcFNTp6pZ8b7/b+/+Y6sqzwCOfx/50UpJGDKto7D+SAu2tK6t2GK0ik4RAq4rNWqtQtEGDWMOM7PosoyxxMwZgro4fzBcFTSoMKnVzA0UqjRkKihuaieIZQix0hZBoK1Q+uyP9/Q3l9JS7o+e55M09Nx7zr1PX97bp+e873ne37pSVG1nY5dd1ntxABFYtMhdirzlFlfO6je/cUvBmJ781yzFxbB8OcTHu94SH++2B+FNuH7SVqevtraWrKwsPvroox77JCQkkJGRQWZmJhkZGSR412QC1farrKzkyiuvZObMmUycOJG7776b1tZWoKMyfXJyMkVFRbiJWrBs2TLS09NJT0/n0UcfBWD37t2ICE899VT7+8XFxVFSUhKwruLxbjcXlZSUkJiY2F4XcMuWLTQ3NzNv3jwyMjLIyspi06ZNgKs7mJ+fz9SpU0lJSWHJkiXtr3Oy+ADq6+sZPnx4+8/Udq/XnDlzKC8vb9+vuLiYV23hqR5Gj3YJZ+VKqK11Ve6HDXNFDC64wD23alXvVePz8tyU+TffdGdw4VB/MSyFelrjmX6dzVqFwWLT4Tv0d/p3TEyMHjp0SHNzc3Xjxo0n3adzPcK6ujqNj49X1cC1/TZt2qRRUVG6a9cubWlp0WuvvVbXePdMtNUFbGxs1NjYWD1w4IBu3bpV09PT9ciRI3r48GFNS0vTDz74QGtqajQ5OVmvv/56VVV9/fXXNTc3V+fOnauqp66r2NYec+fObX/vNkuXLm2vG1hdXa3jx4/XpqYmLSsr0wsvvFDr6+u1sbFRJ02apO+//37A+FRVa2trNTExUVW71l2srKzU/Px8VVU9ePCgJiQk6PHjx/v8/xNIOEyHP9v27VNdsUK1oEB11CjVKVNUf/971W3bAt8yc+yY6r33qiYlqXr/RT34eTq8/864zKDU2tpKQUEBsbGxXH311X06dv369axcuZLMzExyc3NpaGhgp3cHeU5ODklJSQwZMoSioqL2Wn5NTU1kZmYyfvx4Zs2axejRo6mqqqKgoICYmBhGjhzJ7Nmz2bx5MwBRUVEkJyfzySefsGrVKm6//fb29y8tLaWsrAyAsrKy0670UVVVxW233QbARRddRHx8PDt27ADguuuuY8yYMZx77rnMnj2bqqqqU8YXqIbhVVddxc6dO6mrq2P16tUUFhYytM9FMf1t7Fg3I/GVV+Drr91CkwcOQFERxMW5iRnr1rnKPW2GDYNly9z42bRp4BXqN56wS1wiMl1EPhORz0Xk/t6PMMYlkhtuuIFvv/2WjRs39ulYVVfbb/v27Wzfvp2amhqmTZsG9FzluW27bS2w2tpadu3axZYtW3p9n3nz5vHwww/T0tJCbKfyDP2pq9ibQHEHcqoahnPmzOH555+nrKyMO+6444xj87OoKFel45FH4LPP4J13ICPDTeoYO7bjOe/vD266yRUOfughN+713XehjT9chFXiEpEhwJ+BGUAaUCQiaaGNykSCmJgYFi1axNNPP80999xDU1PTaR8bqLYfwHvvvUdNTQ2tra289NJLXHHFFV2OHTp0KCNGjKC+vp68vDzKy8tpbGzk6NGjrFu3jry8vPZ9L7nkEvbv33/SM6r+1FXsXBdwx44d7Nmzh4kTJwKwYcOG9pJO5eXlXH755aeMb82aNQFrGJaUlLSPh6Wl2cdxICUnu3Gw9etd4e2f/xyqq92aeSkpbsLG3r1QVeVuhs7Lgz2PrYOEBK665ho3d97rA34SVokLyAE+V9UvVPUY8CKQH+KYTASZMGECt956K4sXLz7tY0pLS0lLSyM7O5v09HTuuusuWlpaALj00ktZuHAhqampJCYmUlBQAHRcKpw0aRIxMTFMnz6d7OxsSkpKyMnJITc3l9LSUrKysrq81xtvvMHMk5QHLy4u5ptvvjntuooACxYsoLW1lYyMDG6++WaeffZZorxKzDk5ORQWFnLxxRdTWFjI5MmTA8b3xBNPsHz5cpYuXUpmZialpaVs3ryZiooKAGJjY0lNTe1TUjV9N3KkW45l+XKXrNascasqL1nilkM5fhyO7DtE9qI8NvwvBVF18/Lnz/df8gr1IFvnL+BGYEWn7duBx091jE3OCI1wm5xxNvRlccgzFaiuYn/ao/uikL1ZvHhxjz742muvaVlZmaqqHj16VJOSkvTgwYN9jqU3fpicMRDq6lyJ1aIR5TqaBhVO6F+4U9sXgPUmGp0uInxyRkSOsorIfGA+uL8GKysrQxvQGTpy5EjE/QyjRo3icOfR5AFy4sSJs/K6/dHY2EhLS8tZj+e+++5jw4YNrF27tsd79ac9mpubOXbs2GkfN2PGDM4///wu+0+YMIH4+HgqKipYuHAhCxYs4Jxzzhnwtmhubu5T34/Ez8pAiYuDF5oKOME5vEsuUXQMeOmePbzto3YRl3zDg4hcBvxOVa/3th8AUNU/BDpm8uTJunXr1iBFeHZUVlYyderUUIfRJ9XV1aSmpg7469oNyF0N9vboaz+KxM/KgEpIcJcHu4uPh927T/tlRGSbqk4esLiCLNzGuN4HUkQkUUSGA7cAFSGOyRhjwsODD7pKP535sPJPWCUuVW0BFgL/BKqBl1U18HKrJqTC6WzdRB7rP/3QqfKP+rjyT9iNcanq3wFbRCnMRUdH09DQwJgxY3q9R8iY7lSVhoYGoqOjQx1K5CkuhuJi3vbxZdOwS1wmMowbN469e/dS11vxtT5qbm62X2adDOb2iI6ODnjTszGnYonL9MuwYcNITEwc8NetrKzsce+Tn1l7GNNTWI1xGWOMMb2xxGWMMSaiWOIyxhgTUcLqBuT+EJE64CR35EWU7wP1oQ4iTFhbdGXt0ZW1R4czaYt4VT1/IIMJpohPXIOBiGyN5LvYB5K1RVfWHl1Ze3Twc1vYpUJjjDERxRKXMcaYiGKJKzwsD3UAYcTaoitrj66sPTr4ti1sjMsYY0xEsTMuY4wxEcUSVxCJyHgR2SQin4rIJyLyC+/x80Rkg4js9P4dHepYg0VEhojIhyLyuredKCLvisjnIvKSt7yNL4jI90RkrYj8V0SqReQyn/eNe73PyccislpEov3UP0TkryKyX0Q+7vTYSfuDOH/y2uXfIpIdusjPPktcwdUC/FJV04ApwM9EJA24H3hLVVOAt7xtv/gFbgmbNn8EHlHVZOAb4M6QRBUajwH/UNWLgB/h2sWXfUNE4oB7gMmqmg4Mwa3P56f+8SwwvdtjgfrDDCDF+5oPPBmkGEPCElcQqepXqvqB9/1h3C+mOCAfeM7b7Tngp6GJMLhEZBwwE1jhbQtwDbDW28VPbTEKuBJ4BkBVj6nqQXzaNzxDgXNFZCgwAvgKH/UPVX0HONDt4UD9IR9Yqc6/gO+JyA+CE2nwWeIKERFJALKAd4FYVf3Ke6oWiA1RWMH2KPAroNXbHgMc9BYUBdiLS+x+kAjUAWXepdMVIhKDT/uGqu4DlgJ7cAnrELAN//aPNoH6QxzwZaf9BnXbWOIKAREZCfwNWKSq33Z+Tt00z0E/1VNEZgH7VXVbqGMJE0OBbOBJVc0CjtLtsqBf+gaAN3aTj0voY4EYel428zU/9YfuLHEFmYgMwyWtF1T1Fe/hr9tO671/94cqviC6HPiJiOwGXsRdAnoMd4mjbZ24ccC+0IQXdHuBvar6rre9FpfI/Ng3AK4FalS1TlWPA6/g+oxf+0ebQP1hHzC+036Dum0scQWRN4bzDFCtqss6PVUBzPW+nwu8GuzYgk1VH1DVcaqagBt036iqxcAm4EZvN1+0BYCq1gJfishE76EfA5/iw77h2QNMEZER3uemrT182T86CdQfKoA53uzCKcChTpcUBx27ATmIROQKYDPwHzrGdX6NG+d6GfghrtL9TarafVB20BKRqcB9qjpLRJJwZ2DnAR8Ct6nqd6GML1hEJBM3UWU48AUwD/fHpS/7hogsAW7Gzcb9ECjFjdv4on+IyGpgKq4K/NfAYqCck/QHL7k/jruc2gjMU9WtoYg7GCxxGWOMiSh2qdAYY0xEscRljDEmoljiMsYYE1EscRljjIkolriMMcZEFEtcxhhjIoolLmOMMRHFEpcxxpiI8n+8BPyx1QRJaQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from numpy import exp,sqrt\n",
    "n=50;m=100;way=[];a=0\n",
    "X=np.random.uniform(a,m,n)\n",
    "Y=np.random.uniform(a,m,n)\n",
    "X=[10, 10, 100,100 ,30, 20, 20, 50, 50, 85, 85, 75, 35, 25, 30, 47, 50]\n",
    "Y=[5, 85, 0,90,50, 55,50,75 ,25,50,20,80,25,70,10,50,100]\n",
    "n=len(X)\n",
    "RS=[];RW=[];RIB=[]\n",
    "s=[]\n",
    "for ib in np.arange(0,n,1):\n",
    "         M = np.zeros([n,n])\n",
    "         for i in np.arange(0,n,1):\n",
    "                  for j in np.arange(0,n,1):\n",
    "                           if i!=j:\n",
    "                                    M[i,j]=sqrt((X[i]-X[j])**2+(Y[i]-Y[j])**2)\n",
    "                           else:\n",
    "                                    M[i,j]=float('inf')\n",
    "         way=[]\n",
    "         way.append(ib)\n",
    "         for i in np.arange(1,n,1):\n",
    "                  s=[]\n",
    "                  for j in np.arange(0,n,1):                  \n",
    "                           s.append(M[way[i-1],j])\n",
    "                  way.append(s.index(min(s)))\n",
    "                  for j in np.arange(0,i,1):\n",
    "                           M[way[i],way[j]]=float('inf')\n",
    "                           M[way[i],way[j]]=float('inf')         \n",
    "         S=sum([sqrt((X[way[i]]-X[way[i+1]])**2+(Y[way[i]]-Y[way[i+1]])**2) for i in np.arange(0,n-1,1)])+ sqrt((X[way[n-1]]-X[way[0]])**2+(Y[way[n-1]]-Y[way[0]])**2)                      \n",
    "         RS.append(S)\n",
    "         RW.append(way)\n",
    "         RIB.append(ib)\n",
    "S=min(RS)\n",
    "way=RW[RS.index(min(RS))]\n",
    "ib=RIB[RS.index(min(RS))]       \n",
    "X1=[X[way[i]] for i in np.arange(0,n,1)]\n",
    "Y1=[Y[way[i]] for i in np.arange(0,n,1)]\n",
    "plt.title('Общий путь-%s.Номер города-%i.Всего городов -%i.\\n Координаты X,Y заданы'%(round(S,3),ib,n), size=14)\n",
    "plt.plot(X1, Y1, color='r', linestyle=' ', marker='o')\n",
    "plt.plot(X1, Y1, color='b', linewidth=1)   \n",
    "X2=[X[way[n-1]],X[way[0]]]\n",
    "Y2=[Y[way[n-1]],Y[way[0]]]\n",
    "plt.plot(X2, Y2, color='g', linewidth=2,  linestyle='-', label='Путь от  последнего \\n к первому городу')\n",
    "plt.legend(loc='best')\n",
    "plt.grid(True)\n",
    "plt.show()  \n",
    "Z=sqrt((X[way[n-1]]-X[way[0]])**2+(Y[way[n-1]]-Y[way[0]])**2)\n",
    "Y3=[sqrt((X[way[i+1]]-X[way[i]])**2+(Y[way[i+1]]-Y[way[i]])**2) for i in np.arange(0,n-1,1)]\n",
    "X3=[i for i in np.arange(0,n-1,1)]\n",
    "plt.title('Пути от города к городу')\n",
    "plt.plot(X3, Y3, color='b', linestyle=' ', marker='o')\n",
    "plt.plot(X3, Y3, color='r',  linewidth=1,  linestyle='-', label='Без учёта замыкающего пути - %s'%str(round(Z,3)))\n",
    "plt.legend(loc='best')\n",
    "plt.grid(True)\n",
    "plt.show ()         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 317
    },
    "id": "8PA_S9JdHfR1",
    "outputId": "a3e5cabe-df95-4002-824f-b6a67705688f"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "def mnkLIN(x,y):                             \n",
    "              a=round((len(x)*sum([x[i]*y[i] for i in range(0,len(x))])-sum(x)*sum(y))/(len(x)*sum([x[i]**2 for i in range(0,len(x))])-sum(x)**2),3)\n",
    "              b=round((sum(y)-a*sum(x))/len(x) ,3)\n",
    "              y1=[round(a*w+b ,3) for w in x]         \n",
    "              s=[round((y1[i]-y[i])**2,3) for i in range(0,len(x))]                          \n",
    "              sko=round((sum(s)/(len(x)-1))**0.5,3)\n",
    "              p=(sko*len(x)*100)/sum(y1)\n",
    "              plt.title('Аппроксимация методом наименьших \\n квадратов Y=%s*x+%s с погрешностью  -%i -проц.'%(str(a),str(b),int(p)), size=14)\n",
    "              plt.xlabel('Количество  городов', size=14)\n",
    "              plt.ylabel('Длина маршрутов', size=14)\n",
    "              plt.plot(x, y, color='r', linestyle=' ', marker='o', label='Данные метода ближайшего соседа')\n",
    "              plt.plot(x, y1, color='b',linewidth=1, label='Аппроксимирующая прямая')\n",
    "              plt.legend(loc='best')\n",
    "              plt.grid(True)\n",
    "              plt.show()\n",
    "y=[933.516, 1282.842, 1590.256, 1767.327 ,1949.975, 2212.668, 2433.955, 2491.954, 2549.579, 2748.672]\n",
    "x=[100,200,300,400,500,600,\t700,800, 900,1000]  \n",
    "mnkLIN(x,y)       "
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Laba 10.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}