HDU 3549 Flow Problem 最大流 最小增广路 SAP算法 从EK算法的753MS降到了46MS
2013-06-25 17:37
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EK 算法的链接:http://blog.csdn.net/ipqhjjybj/article/details/9171181
SAP算法果然对这个优化了好多。。时间直接从753MS降到46MS呀。。
题目描述
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)
SAP算法果然对这个优化了好多。。时间直接从753MS降到46MS呀。。
题目描述
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:邻接数组 因为可能有重边情况。优化下,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: 用于GAP优化的统计高度数量数组;h:距离标号数组;curedges;当前弧数组,pre,前驱数组 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; }
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