27. Possible Bipartition.cpp

/*

Given a set of N people (numbered 1, 2, ..., N), we would like to split everyone into two groups of any size.

Each person may dislike some other people, and they should not go into the same group. 

Formally, if dislikes[i] = [a, b], it means it is not allowed to put the people numbered a and b into the same group.

Return true if and only if it is possible to split everyone into two groups in this way.

Example 1:
Input: N = 4, dislikes = [[1,2],[1,3],[2,4]]
Output: true
Explanation: group1 [1,4], group2 [2,3]

Example 2:
Input: N = 3, dislikes = [[1,2],[1,3],[2,3]]
Output: false

Example 3:
Input: N = 5, dislikes = [[1,2],[2,3],[3,4],[4,5],[1,5]]
Output: false

*/

class Solution {
public:
    
    bool dfs(vector<vector<int>> &graph, int i, int col, vector<int> &color)
    {
        color[i]=col;
        
        for(auto x:graph[i])
        {   //if color of adjacent nodes is same return false
            if(color[x]==color[i])
                return false;
            //if node is not visited, color connected components with alternate colors
            if(color[x]==0 && !dfs(graph,x,-col,color))
                return false;
        }
    return true;
    }
    
    bool possibleBipartition(int N, vector<vector<int>>& dislikes) 
    {
        vector<vector<int>>graph(N+1); //adj list
        vector<int>color(N+1,0);       //marks the color for nodes
        
        for(auto i:dislikes)           //creating the adj list
        {
            graph[i[0]].push_back(i[1]);
            graph[i[1]].push_back(i[0]);
        }
        
        for(int i=1;i<=N;i++)
        {
            //if node not visited and dfs of connected components is false return false, else continue to next component
            if( color[i]==0 && !dfs(graph,i,1,color) )
                return false;
        }
    return true;
    }
};