Question: at least one endpoint of each side needs to be colored. If you want to paint at least a few points
Idea: minimum vertex coverage: associate each edge with at least one of the vertices with the least vertex. This is obviously the minimum vertex coverage problem of the bare path;
Reference: Bipartite Graph
Code:
#include<iostream>#include<algorithm>#include<cstdio>#include<stdio.h>#include<string.h>#include<queue>#include<cmath>#include<map>#include<set>#include<vector>using namespace std;typedef unsigned long long ull;const int maxn = 500 + 10;const ull seed = 131;struct Edge{ int v, next;}edge[maxn * maxn * 2];int head[maxn], match[maxn], vis[maxn], tot;void addEdge(int u, int v){ edge[tot].v = v; edge[tot].next = head[u]; head[u] = tot++;}bool dfs(int u){ for(int i = head[u]; i != -1; i = edge[i].next){ int v = edge[i].v; if(!vis[v]){ vis[v] = 1; if(match[v] == -1 || dfs(match[v])){ match[v] = u; match[u] = v; return true; } } } return false;}int solve(int n){ int ans = 0; memset(match, -1, sizeof(match)); for(int i = 1; i <= n; i++){ if(match[i] == -1){ memset(vis, 0, sizeof(vis)); if(dfs(i)) ans++; } } return ans;}int main(){ int n, m; while(~scanf("%d%d", &n, &m)){ memset(head, -1, sizeof(head)); tot = 0; for(int i = 1; i <= m; i++){ int u, v; scanf("%d%d", &u, &v); addEdge(u, v); addEdge(v, u); } printf("%d\n", solve(n)); } return 0;}
SCU 4439 vertex cover (minimum coverage of a bipartite graph)