libreoj 101.最大流

最新推荐文章于 2025-06-25 09:33:11 发布

原创最新推荐文章于 2025-06-25 09:33:11 发布 · 304 阅读

0 ·

CC 4.0 BY-SA版权

图论专栏收录该内容

51 篇文章

订阅专栏

本文介绍了一种解决最大流问题的有效算法——ISAP网络流算法，并提供了完整的C++实现代码。该算法通过反向BFS预处理和间隙法则来优化寻路过程，适用于解决复杂的流量分配问题。

模板题，直接上网络流ISAP板子。

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#define clear(A, X) memset (A, X, sizeof A)
#define copy(A, B) memcpy (A, B, sizeof A)
using namespace std;

const int maxE = 4000005*2;
const int maxN = 1000008;
const int maxQ = 1000000;
const long long oo = 0x3f3f3f3f3f;

struct Edge {
   int v;
   long long c;
   int n;
} edge[maxE];


int adj[maxN], cntE;//Ç°ÏòÐÇµÄ±íÍ·
int Q[maxQ], head, tail;//¶ÓÁÐ
int d[maxN], cur[maxN], pre[maxN], num[maxN];
int sourse, sink, nv;
int n, m;

void addedge (int u, int v, long long c) {

    edge[cntE].v = v;
    edge[cntE].c = c;
    edge[cntE].n = adj[u];
    adj[u] = cntE++;


    edge[cntE].v = u;
    edge[cntE].c = 0;
    edge[cntE].n = adj[v];
    adj[v] = cntE++;
}

void rev_bfs () {//·´ÏòBFS±êºÅ
    clear (num, 0);
    clear (d, -1);//Ã»±ê¹ýºÅÔòÎª-1
    d[sink] = 0;//»ãµãÄ¬ÈÏÎª±ê¹ýºÅ
    num[0] = 1;
    head = tail = 0;
    Q[tail++] = sink;

    while (head != tail) {
        int u = Q[head++];
        for (int i = adj[u]; ~i; i = edge[i].n) {
            int v = edge[i].v;
            if (~d[v]) continue;//ÒÑ¾±ê¹ýºÅ
            d[v] = d[u] + 1;//±êºÅ
            Q[tail++] = v;
            num[d[v]]++;
        }
    }
}

long long ISAP() {
    copy (cur, adj);
    rev_bfs ();
    int  u = pre[sourse] = sourse, i;
    long long flow = 0;
    while (d[sink] < nv) {
        if (u == sink) {
            long long f = oo, neck;
            for (i = sourse; i != sink; i = edge[cur[i]].v) {
                if (f > edge[cur[i]].c){
                    f = edge[cur[i]].c;
                    neck = i;
                }
            }
            for (i = sourse; i != sink; i = edge[cur[i]].v) {
                edge[cur[i]].c -= f;
                edge[cur[i] ^ 1].c += f;
            }
            flow += f;
            u = neck;
        }
        for (i = cur[u]; ~i; i = edge[i].n) if (d[edge[i].v] + 1 == d[u] && edge[i].c) break;
        if (~i) {
            cur[u] = i;
            pre[edge[i].v] = u;
            u = edge[i].v;
        }
        else {
            if (0 == (--num[d[u]])) break;
            int mind = nv;
            for (i = adj[u]; ~i; i = edge[i].n) {
                if (edge[i].c && mind > d[edge[i].v]) {
                    cur[u] = i;
                    mind = d[edge[i].v];
                }
            }
            d[u] = mind + 1;
            num[d[u]]++;
            u = pre[u];
        }
    }

    return flow;
}

void init () {
    clear (adj, -1);
    cntE = 0;
}

int main()
{
    int n,m,s,t;
    int u,v;
    long long w;
    scanf("%d%d%d%d",&n,&m,&s,&t);
    init();
    for(int i=0;i<m;i++)
    {
        scanf("%d%d",&u,&v);
        cin>>w;
        addedge(u,v,w);
    }
    sourse = s; sink = t; nv = n;
    cout<<ISAP()<<endl;
    return 0;
}