Possible Bipartition

第22天

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

Note:

1 <= N <= 2000
0 <= dislikes.length <= 10000
1 <= dislikes[i][j] <= N
dislikes[i][0] < dislikes[i][1]
There does not exist i != j for which dislikes[i] == dislikes[j].

又是一道图的题目，而且和昨天的题目思路是一样的，先遍历染色，然后再判断是否满足即可。

这里有些不同的是，这道题给出的输入是边的列表，然后我们需要手动建个图。同时，这道题还可以用在遍历时判断是否已经不符合了，进而可以提前退出。代码如下：

bool possibleBipartition(int N, vector<vector<int>>& dislikes) {
    vector<vector<int>> graph(N);
    for(int i = 0;i < dislikes.size(); i++) {
        graph[dislikes[i][0]-1].push_back(dislikes[i][1]-1);
        graph[dislikes[i][1]-1].push_back(dislikes[i][0]-1);
    }
    char color = 'b';
    vector<char> visited(N, 'w');
    for(int i = 0;i < N;i++) {
        if (visited[i] == 'w' && dfs(graph, visited ,i, color) == false) {
            return false;
        }
    }
    return true;
}

bool dfs(vector<vector<int>> &graph, vector<char> &visited, int index, char color) {
    visited[index] = color;

    for(int i = 0;i < graph[index].size(); i++) {
        int j = graph[index][i];
        if ((visited[j] == 'w' && !dfs(graph, visited, j, ~color)) || visited[j] == color){
            return false;
        }
    }

    return true;
}