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
#include
#include
#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
#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 ;
}