Flow Problem 最大流 最小增廣路 SAP算法 從EK算法的753MS降到了46MS

EK 算法的鏈接：http://blog.csdn.net/ipqhjjybj/article/details/9171181

SAP算法果然對這個優化了好多。。時間直接從753MS降到46MS呀。。

題目描述

Network flow is a well-known difficult problem for ACMers. Given a graph, your task is to find out the maximum flow for the weighted directed graph.

Input:

The first line of input contains an integer T, denoting the number of test cases.
For each test case, the first line contains two integers N and M, denoting the number of vertexes and edges in the graph. (2 <= N <= 15, 0 <= M <= 1000)
Next M lines, each line contains three integers X, Y and C, there is an edge from X to Y and the capacity of it is C. (1 <= X, Y <= N, 1 <= C <= 1000)

#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>

#include <iostream>
#include <cmath>
#include <algorithm>
#include <numeric>
#include <utility>

#include <cstring>
#include <vector>
#include <stack>
#include <queue>
#include <map>
#include <string>
using namespace std;

#define inf 0x3f3f3f3f
#define MAXN 20
#define MAXM 1005
#define clr(x,k) memset((x),(k),sizeof(x))
#define cpy(x,k) memcpy((x),(k),sizeof(x))
#define Base 10000

typedef vector<int> vi;
typedef stack<int> si;
typedef vector<string> vs;
#define sz(a) int((a).size())
#define pb push_back
#define all(c) (c).begin(),(c).end()
#define rep(i,n) for(int i = 0;i < n;++i)
#define foreach(it,c) for(vi::iterator it = (c).begin();it != (c).end();++it)

#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))

struct node{
    int c,next,to;
}edges[MAXM];
int box[MAXN],n,m,tot;
void add(int a,int b,int c){
    edges[tot].to=b;
    edges[tot].c=c;
    edges[tot].next=box[a];
    box[a]=tot++;
}
int Map[MAXN][MAXN]; //map:鄰接數組 因爲可能有重邊情況。優化下，再用SAP算法
void init(){
    clr(Map,0);
    for(int i = 0,a,b,c;i < m;i++){
        scanf("%d %d %d",&a,&b,&c);
        Map[a][b] += c;
    }
    tot=2;
    clr(box,-1);
    for(int i = 1;i <= n;i++)
        for(int j = 1;j <= n;j++)
            if(Map[i][j])
                add(i,j,Map[i][j]),add(j,i,0);
}
int SAP_Max_Flow(int start,int end,int N){
    int numh[MAXN],h[MAXN],curedges[MAXN],pre[MAXN];
    //numh: 用於GAP優化的統計高度數量數組；h:距離標號數組;curedges;當前弧數組,pre,前驅數組
    int cur_flow,flow_ans=0,u,tmp,neck,i;
    clr(h,0);
    clr(numh,0);
    clr(pre,-1);
    for(i = 1;i <= n;i++)
        curedges[i]=box[i];
    numh[0]=N;
    u=start;
    while(h[start]<N){
        if(u==end){
            cur_flow=inf;
            for(i=start;i!=end;i=edges[curedges[i]].to){
                if(cur_flow>edges[curedges[i]].c){
                    neck=i;
                    cur_flow=edges[curedges[i]].c;
                }
            }
            for(i=start;i!=end;i=edges[curedges[i]].to){
                tmp=curedges[i];
                edges[tmp].c-=cur_flow;
                edges[tmp^1].c+=cur_flow;
            }
            flow_ans+=cur_flow;
            u=neck;
        }
        for(i=curedges[u];i!=-1;i=edges[i].next){
            if(edges[i].c&&h[u]==h[edges[i].to]+1)
                break;
        }
        if(i!=-1){
            curedges[u]=i;
            pre[edges[i].to]=u;
            u=edges[i].to;
        }
        else{
            if(0==--numh[h[u]])break;
            curedges[u]=box[u];
            for(tmp=N,i=box[u];i!=-1;i=edges[i].next)
                if(edges[i].c)
                    tmp=min(tmp,h[edges[i].to]);
            h[u]=tmp+1;
            ++numh[h[u]];
            if(u!=start) u=pre[u];
        }
    }
    return flow_ans;
}
int main(){
    //freopen("3549.in","r",stdin);
    int t,tt=0;
    scanf("%d",&t);
    while(t--){
        scanf("%d %d",&n,&m);
        init();
        printf("Case %d: %d\n",++tt,SAP_Max_Flow(1,n,n));
    }
    return 0;
}