isap sap 模板

拖拖欠欠终于学了isap。但是最近一直变量名打错是shenmegui，一周打错三次，，三个晚上就没了。

模板抄自yyn- -详细的注释http://blog.csdn.net/u013368721/article/details/30490255，另外isap的大体思路来自这位大牛http://blog.sina.com.cn/s/blog_7c62590b0100qs7z.html

如果之前已经有了dinic的基础，那么学isap真的超快，如果没有也没有关系，看完上面两篇的就会了

大体思路如下

algorithm Improved-Shortest-Augmenting-Path
1 f<-- 0
2 从终点t 开始进行一遍反向 BFS 求得所有顶点的起始距离标号 d(i)
3 i<-- s
4 while d(s) <n do
5 if i =t then // 找到增广路
6 Augment
7 i<-- s // 从源点 s开始下次寻找
8 if Gf 包含从i 出发的一条允许弧 (i,j)
9 then Advance(i)
10 else Retreat(i) //没有从 i 出发的允许弧则回退
11 return f

procedure Advance(i)     //寻找允许弧，避免从头开始找
1 设 (i,j) 为从i 出发的一条允许弧
2 pi(j) <--i //保存一条反向路径，为回退时准备
3 i<-- j // 前进一步，使 j成为当前结点

procedure Retreat(i)    //回退
1 d(i) <-- 1 +min{d(j):(i,j)属于残量网络Gf} //称为重标号的操作
2 if i != s
3 then i<-- pi(i) // 回退一步

procedure Augment     //寻找增广轨
1 pi中记录为当前找到的增广路 P
2 delta<-- min{rij:(i,j)属于P}
3 沿路径P 增广 delta 的流量
4 更新残量网络Gf

关于cur当前弧的优化：避免多次走到重复的位置上，比如走过x->y这条边后，下次再从x为起点开始走是就不再走x->y的边了

关于gap的优化：首先有int num[max_nodes]; // 离 sink 的最短距离等于 i 的节点数量，即  表示里sink距离为i的路还有num[i]条,那么如果num[i] = 0时,表示这样距离的路已经没了,那么比i更长的路上的点显然也到不了sink,所以直接跳出（也就是所谓的断链，不明白的纸上画画就出来了）

#include <map>#include <set>#include <queue>#include <stack>#include <vector>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iostream>#include <algorithm>using namespace std;#define lson l, mid, rt << 1#define rson mid + 1, r, rt << 1 | 1#define ls rt << 1#define rs rt << 1 | 1#define pi acos(-1.0)#define eps 1e-8typedef long long ll;const int inf = 0x3f3f3f3f;const int N = 204;struct node{int v, nxt;ll w;}e[N<<1];int head[N];int d[N];int cur[N];int pre[N];int num[N];int st, ed, cnt, nn;int n, m;void init(){cnt = 0;memset( head, -1, sizeof( head ) );}void add( int u, int v, ll w ){e[cnt].v = v;e[cnt].w = w;e[cnt].nxt = head[u];head[u] = cnt++;e[cnt].v = u;e[cnt].w = 0;e[cnt].nxt = head[v];head[v] = cnt++;}void rev_bfs( ){memset( num, 0, sizeof( num ) );memset( d, -1, sizeof( d ) );d[ed] = 0;num[0] = 1;queue <int> q;while ( !q.empty() )q.pop();q.push( ed );while( !q.empty() ){int u = q.front();q.pop();for( int i = head[u]; ~i; i = e[i].nxt ){int v = e[i].v;if( ~d[v] )continue;d[v] = d[u]+1;q.push(v);num[ d[v] ]++;}}}ll isap(){memcpy( cur, head, sizeof head );rev_bfs();ll flow = 0;int u = pre[st] = st, i;while( d[ed] < nn ){if( u == ed ){int f = inf, tmp;for( i = st; i != ed; i = e[ cur[i] ].v ){if( f > e[ cur[i] ].w ){f = e[ cur[i] ].w;tmp = i;}}for( i = st; i != ed; i = e[ cur[i] ].v ){e[cur[i]].w -= f;e[cur[i]^1].w += f;}flow += f;u = tmp;}for( i = cur[u]; ~i; i = e[i].nxt ){int v = e[i].v;if( d[v]+1 == d[u] && e[i].w )break;}if( ~i ){cur[u] = i;pre[ e[i].v ] = u;u = e[i].v;}else{if( (--num[ d[u] ]) == 0 )break;int minn = nn;for( i = head[u]; ~i; i = e[i].nxt ){if( e[i].w && minn > d[e[i].v] ){cur[u] = i;minn = d[ e[i].v ];}}d[u] = minn + 1;num[ d[u] ]++;u = pre[u];}}return flow;}int main(){while( ~scanf("%d%d", &n, &m) ){init();int u, v; ll w;for( int i = 1; i <= n; ++i ){scanf("%d%d%lld", &u, &v, &w);add( u, v, w );}st = 1, ed = m, nn = m+1;ll ans = isap();printf("%lld\n", ans);}return 0;}

sap:

#include <map>#include <set>#include <queue>#include <stack>#include <vector>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iostream>#include <algorithm>using namespace std;#define lson l, mid, rt << 1#define rson mid + 1, r, rt << 1 | 1#define ls rt << 1#define rs rt << 1 | 1#define pi acos(-1.0)#define eps 1e-8typedef long long ll;const int inf = 0x3f3f3f3f;const int N = 2000;const int E = 10005;struct node{    int nxt, v, cap, w;}e[E];int n, m, nn;int st, ed;int cnt;int head[N];int dep[N];int cur[N];int gap[N];int pre[N];void init(){    cnt = 0;    memset( head, -1, sizeof( head ) );    st = 1, ed = n, nn = n + 1;}void add( int u, int v, int w, int rw = 0 ){    e[cnt].v = v;    e[cnt].cap = w;    e[cnt].w = 0;    e[cnt].nxt = head[u];    head[u] = cnt++;    e[cnt].v = u;    e[cnt].cap = rw;    e[cnt].w = 0;    e[cnt].nxt = head[v];    head[v] = cnt++;}int isap(){    memset( gap, 0, sizeof( gap ) );    memset( dep, 0, sizeof( dep ) );    memcpy( cur, head, sizeof head );    int u = st;    pre[u] = -1;    gap[0] = nn;    int flow = 0;    while( dep[st] < nn )    {        if( u == ed )        {            int minn = inf, tmp;            for( int i = pre[u]; ~i; i = pre[e[i^1].v] )            {                if( minn > e[i].cap - e[i].w )                {                    minn = e[i].cap - e[i].w;                }            }            for( int i = pre[u]; ~i; i = pre[e[i^1].v] )            {                e[i].w += minn;                e[i^1].w -= minn;            }            u = st;            flow += minn;        }        bool f = 0;        int v;        for( int i = cur[u]; ~i; i = e[i].nxt )        {            v = e[i].v;            if( e[i].cap - e[i].w && dep[v]+1 == dep[u] )            {                f = 1;                cur[u] = pre[v] = i;                break;            }        }        if( f )        {            u = v;            continue;        }        int minn = nn;        for( int i = head[u]; ~i; i = e[i].nxt )        {            if( e[i].cap - e[i].w && dep[e[i].v] < minn )            {                cur[u] = i;                minn = dep[e[i].v];            }        }        gap[dep[u]]--;        if( !gap[dep[u]] )            return flow;        dep[u] = minn + 1;        gap[dep[u]]++;        if( u != st )            u = e[pre[u]^1].v;    }    return flow;}int main(){    int tot;    scanf("%d", &tot);    for( int ca = 1; ca <= tot; ++ca )    {        scanf("%d%d", &n, &m);        init();        int u, v, w;        for( int i = 1; i <= m; ++i )        {            scanf("%d%d%d", &u, &v, &w);            add( u, v, w );        }        int ans = isap();        printf("Case %d: ", ca);        printf("%d\n", ans);    }}

较为稳定的一种isap写法

const int N = 1000;struct node{    int v, w, nxt;}e[N*N];int head[N];int pre[N];int dep[N];int gap[N];int cur[N];int n, m, nn;int cnt;int st, ed;int S[N], top;void init(){    st = cnt = 0;    memset( head, -1, sizeof( head ) );}void add( int u, int v, int w ){    e[cnt].v = v;    e[cnt].w = w;    e[cnt].nxt = head[u];    head[u] = cnt++;    e[cnt].v = u;    e[cnt].w = 0;    e[cnt].nxt = head[v];    head[v] = cnt++;}void rev_bfs(){queue <int> q;while( !q.empty() )q.pop();memset( dep, -1, sizeof( dep ) );memset( gap, 0, sizeof( gap ) );q.push(ed);dep[ed] = 0;gap[0] = 1;while( !q.empty() ){int u = q.front();q.pop();for( int i = head[u]; ~i; i = e[i].nxt ){int v = e[i].v;if( ~dep[v] )continue;q.push(v);dep[v] = dep[u] + 1;gap[dep[v]]++;}}}int isap(){int flow = 0, u = st, i;memcpy( cur, head, sizeof cur );rev_bfs();top = 0;nn = ed + 1;while( dep[st] < nn ){if( u == ed ){int tmp, minn = inf;for( i = 0; i < top; ++i ){if( minn > e[S[i]].w ){tmp = i;minn = e[S[i]].w;}}for( i = 0; i < top; ++i ){e[S[i]].w -= minn; e[S[i]^1].w += minn;}flow += minn;top = tmp;u = e[S[top]^1].v;}for( i = cur[u]; ~i; i = e[i].nxt ){if( e[i].w > 0 && dep[u] == dep[e[i].v] + 1 ){cur[u] = i;break;}}if( ~i ){S[top++] = cur[u];u = e[i].v;}else{if( 0 == (gap[dep[u]]) )break;int minn = nn;for( i = head[u]; ~i; i = e[i].nxt ){if( e[i].w > 0 && minn > dep[e[i].v] ){minn = dep[e[i].v];cur[u] = i;}}dep[u] = minn + 1;gap[dep[u]]++;if( u != st )u = e[S[--top]^1].v;}}return flow;}