染色法判定二分图 & 匈牙利算法

匈牙利

#include <cstring>
#include <algorithm>
#include <iostream>
using namespace std;
const int N = 510, M = 100010;
int ne[M], e[M], h[M], match[N];
int len, n1, n2, m;
bool vis[N];

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

bool find(int x)
{
    for (int i = h[x]; ~i; i = ne[i])
    {
        int y = e[i];
        if (!vis[y])
        {
            vis[y] = true;
            if (match[y] == 0 || find(match[y]))
            {
                match[y] = x;
                return true;
            }
        }
    }
    return false;
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    memset(h, -1, sizeof h);
    cin >> n1 >> n2 >> m;
    for (int i = 1; i <= m; i++)
    {
        int x, y;
        cin >> x >> y;
        add(x, y);
    }

    int ans = 0;
    for (int i = 1; i <= n1; i++)
    {
        memset(vis, false, sizeof vis);
        if (find(i))
            ans++;
    }
    cout << ans << endl;
    return 0;
}

染色法

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

const int N = 2e5 + 10;
int ne[N], e[N], h[N], color[N];
int n, m, len;

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

bool dfs(int x, int c)
{
    color[x] = c;
    for (int i = h[x]; ~i; i = ne[i])
    {
        int y = e[i];
        if (!color[y])
            if (!dfs(y, 3 - c))
                return false;
        if (color[y] == color[x])
            return false;
    }
    return true;
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    memset(h, -1, sizeof h);
    cin >> n >> m;
    for (int i = 1; i <= m; i++)
    {
        int a, b;
        cin >> 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;

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