poj_1459，sap的三种写法

第一种是BFS的SAP

#include<cstdio>
#include<cstring>
using namespace std;


const int inf = 100000000;//不要开太大
int n, np, nc, m;
const int maxn = 105;
int c[maxn][maxn];//残留网络
int s, t;
int level[maxn], gap[maxn];//层次网络， 层结点数（用于间隙优化）
int q[maxn], pre[maxn];//队列， 前驱
void init_sap(){
    memset(level, 10, sizeof level);
    //for(int i = 0; i <= n ;i ++) level[i] = n + 1;
    memset(gap, 0, sizeof gap);
    int qs = 0, qe = 0;
    q[qe++] = t;
    level[t] = 0;
    gap[ level[t] ] ++;
    while(qs < qe){
        int hd = q[qs++];
        for(int i = 0; i < n; i ++){
            if(level[i] > n && c[i][hd] > 0){
                q[qe++] = i;
                level[i] = level[hd] + 1;
                gap[ level[i] ] ++;
            }
        }
    }
}
int find_path(int u){
    for(int i = 0; i < n; i ++)
      if(c[u][i] > 0 && level[u] == level[i] + 1) return i;
    return -1;
}
int relabel(int u){
    int tmp = inf;
    for(int i = 0; i < n; i ++)
      if(c[u][i] > 0 && tmp > level[i] + 1)
        tmp = level[i] + 1;
    if(tmp == inf) tmp = n;
    return tmp;
}
int sap(){
    init_sap();
    int flow = 0;
    int u = s;
    memset(pre, -1, sizeof pre);
    while(level[s] < n){
        int v = find_path(u);//寻找允许弧
        if(v >= 0){
            pre[v] = u;
            u = v;
            if(u == t){//找到完整增广路
                int min_flow = inf;
                for(int i = t; i != s; i = pre[i])
                  if(min_flow > c[ pre[i] ][i]) min_flow = c[ pre[i] ][i];
                for(int i = t; i != s; i = pre[i]){
                    c[ pre[i] ][i] -= min_flow;//正向减
                    c[i][ pre[i] ] += min_flow;
                }
                flow += min_flow;
                u = s;//重新从源点找
            }
        }else{//找不到弧
            if( -- gap[ level[u] ] == 0) return flow;//更新断层 + 判断是否断层
            v = relabel(u);
            gap[v] ++;
            level[u] = v;//重新标号
            if(u != s)
              u = pre[u];//当前弧优化
        }
    }
    return flow;
}
int main(){
    while(~scanf("%d%d%d%d", &n, &np, &nc, &m)){
        memset(c, 0, sizeof c);
        s = n, t = n + 1, n += 2;
        for(int i = 0; i < m; i ++){
            int u, v, w;
            scanf(" (%d,%d)%d", &u, &v, &w);
            c[u][v] = w;
        }
        for(int i = 0; i < np; i ++){
            int v, w;
            scanf(" (%d)%d", &v, &w);
            c[s][v] = w;
        }
        for(int i = 0; i < nc; i ++){
            int u, w;
            scanf(" (%d)%d", &u, &w);
            c[u][t] = w;
        }
        int flow = sap();
        printf("%d\n", flow);
    }
    return 0;
}

第二种就是普通的矩阵SAP，看着HH博客里的写的。。

#include<cstdio>
#include<cstring>
using namespace std;


const int inf = 100000000;//不要开太大
int n, np, nc, m;
const int maxn = 105;
int c[maxn][maxn];//残留网络
int s, t;
int level[maxn], gap[maxn];//层次网络， 层结点数（用于间隙优化）
int cur[maxn], pre[maxn];

int sap(){
    memset(cur, 0, sizeof cur);
    memset(level, 0, sizeof level);
    memset(gap, 0, sizeof gap);
    int u = pre[s] = s, v;
    int flow = 0;
    int aug = inf;
    gap[s] = t;// gap[0] = n, gap[s] = t
    while(level[s] < n){
        for(v = cur[u]; v < n; v ++){
            if(c[u][v] > 0 && level[u] == level[v] + 1)
            break;
        }
        if(v < n){
            pre[v] = u;
            if(aug > c[u][v]) aug = c[u][v];
            u = cur[u] = v;
            if(u == t){
                flow += aug;
                for(v = t; v != s; v = pre[v]){
                    c[ pre[v] ][v] -= aug;
                    c[v][ pre[v] ] += aug;
                }
                aug = inf, u = s;
            }
        }else{
            int min_label = n;
            for(v = 0; v < n; v ++){
                if(c[u][v] > 0 && min_label > level[v]){
                    cur[u] = v;
                    min_label = level[v];
                }
            }
            if(--gap[level[u]] == 0) return flow;
            level[u] = min_label + 1;
            gap[ level[u] ] ++;
            u = pre[u];
        }
    }
    return flow;
}
int main(){
    while(~scanf("%d%d%d%d", &n, &np, &nc, &m)){
        memset(c, 0, sizeof c);
        s = n, t = n + 1, n += 2;
        for(int i = 0; i < m; i ++){
            int u, v, w;
            scanf(" (%d,%d)%d", &u, &v, &w);
            c[u][v] = w;
        }
        for(int i = 0; i < np; i ++){
            int v, w;
            scanf(" (%d)%d", &v, &w);
            c[s][v] = w;
        }
        for(int i = 0; i < nc; i ++){
            int u, w;
            scanf(" (%d)%d", &u, &w);
            c[u][t] = w;
        }
        int flow = sap();
        printf("%d\n", flow);
    }
    return 0;
}

最后一种就是邻接表的SAP，也是看HH博客写的。。。

注意引用的用法。。。

不过我不明白gap初始化的情况啊。。。

还有relabel的过程也不是很理解。。。。

再理解理解吧