HDU - 2444 The Accomodation of Students 染色法判断二分图+最大匹配

题意：有n个学生，有m对人是认识的，每一对认识的人能分到一间房，问能否把n个学生分成两部分，每部分内的学生互不认识，而两部分之间的学生认识。如果可以分成两部分，就算出房间最多需要多少间，否则就输出No

判断二分图后是的话求一下最大匹配

链接：hdu - 2444

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <set>
#include <map>
#include <stack>
#include <queue>
#define INF 0x3f3f3f3f

using namespace std;

const int inf = 0x3f3f3f3f;
const int maxn = 1000;
const int maxm = 1000;

int used[maxn];
int link[maxn];
int mat[maxn][maxn];
int gn, gm;

int color[maxn];

int dfs(int t) {
    for(int i = 1; i <= gm; i++) {
        if(!used[i] && mat[t][i]) {
            used[i] = 1;
            if(link[i] == -1 || dfs(link[i])) {
                link[i] = t;
                return 1;
            }
        }
    }
    return 0;
}

int maxmatch() {
    int num = 0;
    memset(link, 0xff, sizeof(link));
    for(int i = 1; i <= gn; i++) {
        memset(used, 0, sizeof(used));
        if(dfs(i)) {
            num++;
        }
    }
    return num;
}

bool judge(int x) {
    for(int i = 1; i <= gn; i++) {
        if(i != x && mat[x][i]) {
            if(color[i] == -1) {
                color[i] = (color[x] + 1) % 2;
                if(!judge(i))
                    return 0;
            }
            else if(color[i] == color[x])
                return 0;
        }
    }
    return 1;
}

int main()
{
    int n, m, k, t;
    while(~scanf("%d %d", &n, &m)) {
        gn = gm = n;
        memset(mat, 0, sizeof(mat));
        memset(color, -1, sizeof(color));
        while(m--) {
            int a, b;
            scanf("%d %d", &a, &b);
            mat[a][b] = mat[b][a] = 1;
        }
        int flag = judge(1);
        if(flag) {
            int res = maxmatch();
            printf("%d\n", res / 2);
        }
        else {
            puts("No");
        }
    }
    return 0;
}