《算法基础》 二分图

《算法基础》 二分图

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1.染色法判断二分图

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;

const int N = 100010, M = 200010;
int h[N], e[M], ne[M], idx;
int color[N];
int n, m;

void add(int a, int b)
{
	e[idx] = b; ne[idx] = h[a]; h[a] = idx ++;
}

int dfs(int u, int c)   //将第u个顶点染成颜色i
{
	color[u] = c;

	for (int i = h[u]; i != -1; i = ne[i]) {
		int j = e[i];
		if (!color[j]) {
			if (!dfs(j, 3 - c)) return false;
		}
		else if (color[j] == c) return false;
	}
	return true;
}


int main()
{
	cin >> n >> m;

	memset(h, -1, sizeof h);

	while (m --) {
		int a, b;
		scanf("%d%d", &a, &b);
		add(a, b);
		add(b, a);
	}

	bool flag = true;
	for (int i = 1; i <= n; i ++) {
		if (!color[i]) {
			if (!dfs(i, 1)) {
				flag = false;
				break;
			}
		}
	}

	if (flag == true) cout << "Yes" << endl;
	else cout << "No" << endl;
	return 0;
}

2.匈牙利算法

#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;

const int N = 510, M = 100010;
int h[N], e[M], ne[M], idx;
int match[N];    //每个妹子匹配到的男生
bool st[N];
int n1, n2, m;

void add(int a, int b)
{
	e[idx] = b; ne[idx] = h[a]; h[a] = idx ++;
}

bool find(int x)
{
	for (int i = h[x]; i != -1; i = ne[i]) {
		int j = e[i];
		if (!st[j]) {
			st[j] = 1;
			if (match[j] == 0 || find(match[j])) {
				match[j] = x;
				return true;
			}
		}
	}
	return false;
}

int main()
{
	cin >> n1 >> n2 >> m;
	
	memset(h, -1, sizeof h);
	
	while (m --) {
		int a, b;
		scanf("%d%d", &a, &b);
		add(a, b);
	}
	
	int res = 0;
	for (int i = 1; i <= n1; i ++) {
		memset(st, 0, sizeof st);
		if (find(i)) res ++;
	}
	cout << res << endl;
	return 0;
}