最大流 ISAP 模板

ISAP算法还不懂的戳这里：http://www.renfei.org/blog/isap.html

最大流入门题传送门：POJ 1273 Drainage Ditches

下面是ISAP + 当前弧优化 + GAP优化的代码：

#include <stdio.h>  
#include <string.h>  
#include <algorithm>  
#define clear(A, X) memset (A, X, sizeof A)  
#define copy(A, B) memcpy (A, B, sizeof A)  
using namespace std;  
  
const int maxE = 1000000;  
const int maxN = 100000;  
const int maxQ = 1000000;  
const int oo = 0x3f3f3f3f;  
   
struct Edge {  
   int v;//弧尾  
   int c;//容量  
   int n;//指向下一条从同一个弧头出发的弧  
} edge[maxE];//边组  
  
 
int adj[maxN], cntE;//前向星的表头  
int Q[maxQ], head, tail;//队列  
int d[maxN], cur[maxN], pre[maxN], num[maxN];  
int sourse, sink, nv;//sourse：源点，sink：汇点，nv：编号修改的上限  
int n, m;  
  
void addedge (int u, int v, int c) {//添加边  
    //正向边  
    edge[cntE].v = v;  
    edge[cntE].c = c;//正向弧的容量为c  
    edge[cntE].n = adj[u];  
    adj[u] = cntE++;  
      
    //反向边  
    edge[cntE].v = u;  
    edge[cntE].c = 0;//反向弧的容量为0  
    edge[cntE].n = adj[v];  
    adj[v] = cntE++;  
}  
   
void rev_bfs () {//反向BFS标号  
    clear (num, 0);  
    clear (d, -1);//没标过号则为-1  
    d[sink] = 0;//汇点默认为标过号  
    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;//已经标过号  
            d[v] = d[u] + 1;//标号  
            Q[tail++] = v;  
            num[d[v]]++;  
        }  
    }  
}  
  
int ISAP() {  
    copy (cur, adj);//复制，当前弧优化  
    rev_bfs ();//只用标号一次就够了，重标号在ISAP主函数中进行就行了  
    int flow = 0, u = pre[sourse] = sourse, i;  
  
    while (d[sink] < nv) {//最长也就是一条链，其中最大的标号只会是nv - 1，如果大于等于nv了说明中间已经断层了。  
        if (u == sink) {//如果已经找到了一条增广路，则沿着增广路修改流量  
            int f = oo, neck;  
            for (i = sourse; i != sink; i = edge[cur[i]].v) {  
                if (f > edge[cur[i]].c){  
                    f = edge[cur[i]].c;//不断更新需要减少的流量  
                    neck = i;//记录回退点，目的是为了不用再回到起点重新找  
                }  
            }  
            for (i = sourse; i != sink; i = edge[cur[i]].v) {//修改流量  
                edge[cur[i]].c -= f;  
                edge[cur[i] ^ 1].c += f;  
            }  
            flow += f;//更新  
            u = neck;//回退  
        }  
        for (i = cur[u]; ~i; i = edge[i].n) if (d[edge[i].v] + 1 == d[u] && edge[i].c) break;  
        if (~i) {//如果存在可行增广路，更新  
            cur[u] = i;//修改当前弧  
            pre[edge[i].v] = u;  
            u = edge[i].v;  
        }  
        else {//否则回退，重新找增广路  
            if (0 == (--num[d[u]])) break;//GAP间隙优化，如果出现断层，可以知道一定不会再有增广路了  
            int mind = nv;  
            for (i = adj[u]; ~i; i = edge[i].n) {  
                if (edge[i].c && mind > d[edge[i].v]) {//寻找可以增广的最小标号  
                    cur[u] = i;//修改当前弧  
                    mind = d[edge[i].v];  
                }  
            }  
            d[u] = mind + 1;  
            num[d[u]]++;  
            u = pre[u];//回退  
        }  
    }  
      
    return flow;  
}  
  
void init () {//初始化  
    clear (adj, -1);  
    cntE = 0;  
}  
  
void work () {  
    int u, v, c;  
    init ();  
    for (int i = 0; i < m; ++ i) scanf ("%d%d%d", &u, &v, &c), addedge (u, v, c);  
    sourse = 1; sink = n; nv = sink + 1;  
    printf ("%d\n", ISAP ());  
}    
int main() {  
    while (~scanf("%d%d", &m, &n)) work ();  
    return 0;  
}  
           

#include <bits/stdc++.h>

#define clr( a , x ) memset ( a , x , sizeof a )

const int MAXN = 100005 ;
const int MAXE = 1000005 ;
const int INF = 0x3f3f3f3f ;

struct Edge {
	int v ;
	int c ;
	int n ;
	Edge () {}
	Edge ( int v , int c , int n ) : v ( v ) , c ( c ) , n ( n ) {}
} ;

Edge E[MAXE] ;
int H[MAXN] , cntE ;
int d[MAXN] ;
int cur[MAXN] ;
int pre[MAXN] ;
int gap[MAXN] ;
int s , t , nv , flow ;
int Q[MAXN] , head , tail ;

void init () {
	cntE = 0 ;
	clr ( H , -1 ) ;
}

void addedge ( int u , int v , int c , int r = 0 ) {
	E[cntE] = Edge ( v , c , H[u] ) ;
	H[u] = cntE ++ ;
	E[cntE] = Edge ( u , r , H[v] ) ;
	H[v] = cntE ++ ;
}

void revbfs () {
	head = tail = 0 ;
	clr ( d , -1 ) ;
	clr ( gap , 0 ) ;
	Q[tail ++] = t ;
	d[t] = 0 ;
	gap[d[t]] = 1 ;
	while ( head != tail ) {
		int u = Q[head ++] ;
		for ( int i = H[u] ; ~i ; i = E[i].n ) {
			int v = E[i].v ;
			if ( ~d[v] ) continue ;
			d[v] = d[u] + 1 ;
			gap[d[v]] ++ ;
			Q[tail ++] = v ;
		}
	}
}

int isap () {
	memcpy ( cur , H , sizeof cur ) ;
	flow = 0 ;
	revbfs () ;
	int u = pre[s] = s , i ;
	while ( d[s] < nv ) {
		if ( u == t ) {
			int f = INF ;
			for ( i = s ; i != t ; i = E[cur[i]].v ) {
				if ( f > E[cur[i]].c ) {
					f = E[cur[i]].c ;
					u = i ;
				}
			}
			flow += f ;
			for ( i = s ; i != t ; i = E[cur[i]].v ) {
				E[cur[i]].c -= f ;
				E[cur[i] ^ 1].c += f ;
			}
		}
		for ( i = cur[u] ; ~i ; i = E[i].n ) {
			int v = E[i].v ;
			if ( E[i].c && d[u] == d[v] + 1 ) break ;
		}
		if ( ~i ) {
			cur[u] = i ;
			pre[E[i].v] = u ;
			u = E[i].v ;
		} else {
			if ( 0 == -- gap[d[u]] ) break ;
			int minv = nv ;
			for ( int i = H[u] ; ~i ; i = E[i].n ) {
				int v = E[i].v ;
				if ( E[i].c && minv > d[v] ) {
					minv = d[v] ;
					cur[u] = i ;
				}
			}
			d[u] = minv + 1 ;
			gap[d[u]] ++ ;
			u = pre[u] ;
		}
	}
	return flow ;
}