网络流，最基础的增广路算法！-优快云博客

本文介绍了一个简单的网络流算法实现，使用C++编程语言。该算法通过Ford-Fulkerson方法寻找增广路径，并更新流量直至无法找到新的增广路径为止。代码中详细展示了如何初始化网络边、读取输入数据并执行最大流算法。

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哈哈，我的第一个网络流！

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
const int MAXN = 1005;
const int INF = 0x7ffffff;
struct edge_{
    int c, f;
}edge[MAXN][MAXN];
int n, m;
int flag[MAXN], pre[MAXN], alpha[MAXN], que[MAXN];
int h, t, v, u;

int ford(){
    while(1){
        memset(flag, -1, sizeof(flag));
        memset(pre, -1, sizeof(pre));
        memset(alpha, -1, sizeof(alpha));
        flag[0] = 0, pre[0] = 0, alpha[0] = INF;
        t = 0, h = 1;
        que[t] = 0;
        while(t < h && flag[n - 1] ==  -1){
            u = que[t], t++;
            for(v = 0; v < n; v ++){
                if(flag[v] == -1){
                    if(edge[u][v].c < INF && edge[u][v].f < edge[u][v].c){
                        flag[v] = 0, pre[v] = u;
                        alpha[v] = min(alpha[u], edge[u][v].c - edge[u][v].f);
                        que[h] = v, h++;
                    }
                    else if(edge[v][u].c < INF && edge[v][u].f > 0){
                        flag[v] = 0, pre[v] = -u;
                        alpha[v] = min(alpha[u], edge[v][u].f);
                        que[h] = v, h++;
                    }
                }
            }
            flag[u] = 1;
        }
        if(flag[n - 1] == -1 || alpha[n - 1] == 0)
            break;
        v = n - 1, u = abs(pre[v]);
        int a = alpha[v];
        while(1){
            if(edge[u][v].f < INF)
                edge[u][v].f += a;
            else
                edge[v][u].f -= a;
            if(v == 0)
                break;
            v = u, u = abs(pre[v]);
        }
    }
    int maxFord = 0;
    for(int i = 0; i < n; i++)
        for(int j = 0; j < n; j++){
            if(i == 0 && edge[i][j].f < INF)
                maxFord += edge[i][j].f;
            if(edge[i][j].f < INF)
                printf("%d -> %d : %d\n", i, j, edge[i][j].f);
    }
    return maxFord;
}

int main(){
    freopen("in.in", "r", stdin);
    int u, v, c, f;
    cin>> n >> m;
    for(int i = 0; i < n; i++)
        for(int j = 0; j < n; j++)
            edge[i][j].c = edge[i][j].f = INF;
    for(int i = 0; i < m; i++){
        cin>> u >> v >> c >> f;
        edge[u][v].c = c;
        edge[u][v].f = f;
    }
    cout<< ford() <<endl;
    return 0;
}