hiho1122_二分图匈牙利算法

题目

    给定一个图的N个节点和节点之间的M条边，数据保证该图可以构成一个二分图。求该二分图最大匹配。 
题目链接：二分图最大匹配 
    首先通过染色法，将图的N个节点分成两个部分；然后通过匈牙利算法求二分图的最大匹配。

实现

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#include<stdio.h> #include<string.h> #include<iostream> #include<string> #include<set> #include<map> #include<vector> #include<queue> #include<stack> #include<unordered_map> #include<unordered_set> #include<algorithm> using namespace std;   struct Edge{     int to;     int next; }; Edge gEdges[80005]; int gEdgeIndex; int gHead[10005]; int gMatch[10005]; bool gVisited[10005]; int gColor[10005]; bool conflict; void Init(){     gEdgeIndex = 0;     memset(gHead, -1, sizeof(gHead));     memset(gVisited, false, sizeof(gVisited));     memset(gMatch, -1, sizeof(gMatch));     memset(gColor, -1, sizeof(gColor));     conflict = false; } void InsertEdge(int u, int v){     int e = gEdgeIndex++;     gEdges[e].to = v;     gEdges[e].next = gHead[u];     gHead[u] = e; }   void PaintColor(int node, int c){     if (conflict)         return;     gColor[node] = c;     for (int e = gHead[node]; e != -1; e = gEdges[e].next){         int x = gEdges[e].to;         if (gColor[x] == c){             conflict = true;             return;         }         if (gColor[x] == -1)             PaintColor(x, 1 - c);     } }   bool Dfs(int node){         for (int e = gHead[node]; e != -1; e = gEdges[e].next){         int v = gEdges[e].to;         if (!gVisited[v]){              gVisited[v] = true; //置位             if (gMatch[v] == -1){             //如果对方的阵营中v点还没有匹配，则成功找到一条交错路径                 gMatch[node] = v;                 gMatch[v] = node;                 return true;             }             else if (Dfs(gMatch[v])){             //如果对方阵营中v有匹配点，匹配点肯定在己方阵营，则继续从己方阵营的点             //递归                 gMatch[node] = v;                 gMatch[v] = node;                 return true;             }         }     }     return false; } int main(){     int n, m, u, v;     Init();     scanf("%d %d", &n, &m);       for (int i = 0; i < m; i++){         scanf("%d %d", &u, &v);         InsertEdge(u, v);         InsertEdge(v, u);     }               for (int i = 1; i <= n; i++)         if (gColor[i] == -1)             PaintColor(i, 0);       int ans = 0;     for (int i = 1; i <= n; i++){         if (gColor[i] == 0 && gMatch[i] == -1){//从固定一方阵营中，不断找未匹配点         //寻找交错路，找到一条交错路，则匹配个数增加1             memset(gVisited, false, sizeof(gVisited));             if (Dfs(i))                 ans++;         }     }     printf("%d\n", ans);     return 0; }