网络流最大流——ISAP算法

ISAP 时间复杂度最坏 O(n*n*m)  与dinic都是增广路算法，但是ISAP只需要bfs一次所以基本上要比dinic要快不少。

code

#include <iostream>
#include <string>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <queue>
#include <functional>
#include <map>
#include <set>
#include <stack>
#define FT(a, b) memset(a, b, sizeof(a))
#define FAT(a) memset(a, 0, sizeof(a))
using namespace std;
typedef long long ll;
const int M = 3e5 + 10;
const int N = 2e4 + 10;
const int INF = 0x3f3f3f3f;
const int mod = 1e9 + 7;
int n, m, s, t;
int h[N], e[M], ne[M], w[M], idx;
int deepth[N], gap[N];
void add(int a, int b, int c)
{
    e[idx] = b, ne[idx] = h[a], w[idx] = c, h[a] = idx++;
}
void bfs()
{
    FT(deepth, -1);
    FAT(gap);
    queue<int> q;
    q.push(t);
    deepth[t] = 0;
    gap[0] = 1;
    while (q.size())
    {
        int a = q.front();
        q.pop();
        for (int i = h[a]; ~i; i = ne[i])
        {
            int j = e[i];
            if (deepth[j] == -1)
            {
                deepth[j] = deepth[a] + 1;
                gap[deepth[j]]++;
                q.push(j);
            }
        }
    }
}
// int ans;
int dfs(int now, int flow)
{
    if (now == t)
    {
        // ans += flow;
        return flow;
    }
    int nowflow = 0;
    for (int i = h[now]; ~i; i = ne[i])
    {
        int j = e[i];
        if (w[i] && deepth[j] + 1 == deepth[now])
        {
            int k = dfs(j, min(flow - nowflow, w[i]));
            w[i] -= k, w[i ^ 1] += k, nowflow += k;
            if (nowflow == flow)
                return nowflow;
        }
    }
    --gap[deepth[now]];
    if (!gap[deepth[now]])
        gap[s] = n + 2;
    ++deepth[now];
    ++gap[deepth[now]];
    return nowflow;
}

int ISAP()
{
    int ans = 0;
    bfs();
    while (gap[s] < n)
        ans += dfs(s, INF);
    return ans;
}
int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("D://code//c++//in.txt", "r", stdin);
#endif
    scanf("%d%d%d%d", &n, &m, &s, &t);
    FT(h, -1);
    idx = 0;
    for (int i = 0; i < m; i++)
    {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        add(a, b, c), add(b, a, 0);
    }
    printf("%d\n", ISAP());

    return 0;
}