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Marriage Match IV---hdu3416(spfa + Dinic)

2016-09-01 14:47 260 查看
题目链接:http://acm.split.hdu.edu.cn/showproblem.php?pid=3416

有一个有向图,n个点,m条边,给一个起点和终点,求出从起点到终点的最短路共有几条,每条路只能走一次,每个点可以走多次;

先用spfa求出从起点到各点的距离dist,然后根据dist的值建立新的图,边权为1,套用Dinic模板求起点到终点的最大流即可;

#include <iostream>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <queue>
#include <stack>
#include <algorithm>
#include <map>
#include <string>
typedef long long LL;
#define INF 0x3f3f3f3f
#define met(a, b) memset(a, b, sizeof(a))
#define N 200005

using namespace std;

struct node
{
int v, w, Next;
}G
, e
;

int n, m, dist
, vis
, A, B;
int l
;

int Head
, cnt;
void Add(int u, int v, int w)
{
G[cnt].v = v;
G[cnt].w = w;
G[cnt].Next = Head[u];
Head[u] = cnt++;
}

int Head1
, cnt1;
void Add1(int u, int v, int w)
{
e[cnt1].v = v;
e[cnt1].w = w;
e[cnt1].Next = Head1[u];
Head1[u] = cnt1++;
}

void spfa()
{
for(int i=1; i<=n; i++)
dist[i] = INF;
met(vis, 0);
queue<int>Q;
Q.push(A);
vis[A] = 1;
dist[A] = 0;
while(!Q.empty())
{
int p = Q.front();Q.pop();
vis[p] = 0;
for(int i=Head[p]; i!=-1; i=G[i].Next)
{
int q = G[i].v;
if(dist[q] > dist[p]+G[i].w)
{
dist[q] = dist[p]+G[i].w;
if(!vis[q])
{
vis[q] = 1;
Q.push(q);
}
}
}
}
}

bool bfs(int s, int End)
{
met(l, 0);
queue<int>Q;
Q.push(s);
l[s] = 1;
while(!Q.empty())
{
int u = Q.front();Q.pop();
if(u == End)return true;
for(int i=Head1[u]; i!=-1; i=e[i].Next)
{
int v = e[i].v;
if(!l[v] && e[i].w)
{
l[v] = l[u]+1;
Q.push(v);
}
}
}
return false;
}

int dfs(int u, int MaxFlow, int End)
{
if(u == End)return MaxFlow;

int uflow = 0;

for(int j=Head1[u]; j!=-1; j=e[j].Next)
{
int v = e[j].v;
if(l[v]==l[u]+1 && e[j].w)
{
int flow = min(e[j].w, MaxFlow-uflow);
flow = dfs(v, flow, End);
e[j].w -= flow;
e[j^1].w += flow;
uflow += flow;
if(uflow == MaxFlow)
break;
}
}
if(uflow == 0)
l[u] = 0;
return uflow;
}

int Dinic()
{
int MaxFlow = 0;
while(bfs(A, B))
MaxFlow += dfs(A, INF, B);
return MaxFlow;
}

int main()
{
int T;
scanf("%d", &T);
while(T--)
{
met(Head, -1);
cnt = 0;
met(Head1, -1);
cnt1 = 0;

scanf("%d %d", &n, &m);

for(int i=1; i<=m; i++)
{
int u, v, w;
scanf("%d %d %d", &u, &v, &w);
if(u == v)continue;
Add(u, v, w);
}
scanf("%d %d", &A, &B);

spfa();///更新dist;

for(int i=1; i<=n; i++)
{
for(int j=Head[i]; j!=-1; j=G[j].Next)
{
int v = G[j].v;
if(dist[v] == dist[i]+G[j].w)///建立新的网络流图;
{
Add1(i, v, 1);
Add1(v, i, 0);
}
}
}

int ans = Dinic();///求最大流即可;

printf("%d\n", ans);
}
return 0;
}


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