[LeetCode] 322. Coin Change.py

DP/[LeetCode] 322. Coin Change.py

@@ -0,0 +1,122 @@
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        dp = [0] + [math.inf for _ in range(amount)]
+        for i in range(1, len(dp)):
+            for c in coins:
+                if i-c >= 0:
+                    dp[i] = min(dp[i], dp[i-c]+1)
+        return dp[-1] if dp[-1] != math.inf else -1
+
+'''
+
+    amount  : 3
+    
+    res     : 2     (2+1), (1+1+1)
+    
+    
+                  c
+    coins   : [1, 2]
+                        i
+               0. 1. 2. 3
+    dp      : [0, 1, 1, 2]
+    
+            
+            
+1. DP
+    => 4 ways
+    a) fibonacci
+    - 
+    
+    
+    b) state machine
+    c) 2 strings
+    d) merge intervals (gaps)\
+    
+    
+1. Problem is
+    - coins
+    - amount
+    - total amount of money
+    - impossible        : -1
+    
+2. TC
+    tc1)
+    conis   : [1, 2]
+    amo     : 5
+    res     : 3     (2 + 2 + 1)
+    
+    
+    tc2)
+    coins   : [1]
+    amo     : 5
+    res     : 5
+    
+    tc3)
+    coins   : [2]
+    amo     : 3
+    res     : -1
+    
+    
+    tc4)
+    coins   : [1, 2]
+    amo     : 3
+    res     : 2
+    
+    tc5)
+    coins   : [2, 3]
+    amo     : 5
+    res     : 2
+    
+    
+3. Brain Storming
+    
+    amo     : 5
+    res     : 2
+    
+    
+    coins   : [1, 2, 3]
+    0       : 0
+    1       : 1
+    2       : 1
+                (1 + 1)
+                (2)
+    3       : 1
+    4       : 2
+                           c
+    5       : 2         <= 1 + (4)      : (4) + 1
+                           2 + (3)      : (3) + 1
+                           3 + (2)      : (2) + 1       => 2
+                           
+                           
+                           
+        
+    
+    a) dp   <= [0 for _ in range(amount)]?
+    b) for c in coins:
+         
+    
+    
+    for i in range(1, amoun+1) ??
+        for c in coins:
+            if i-c is possiblE
+            dp[i] = min(dp[i], dp[i-c]+1)
+            
+            
+            
+                  c
+    coins   : [2, 3]
+    amo     : 5
+    res     : 2
+    
+                              i
+               0. 1. 2. 3. 4  5
+    dp      : [0, i, 1, 1, 2, 2]
+                              \
+                               \-------dp[3] + 1
+                                       dp[2] + 1
+                             
+    amount      4
+                2 + amount(2)
+    
+
+'''