Marriage Match IV

3
7 8
1 2 1
1 3 1
2 4 1
3 4 1
4 5 1
4 6 1
5 7 1
6 7 1
1 7

6 7
1 2 1
2 3 1
1 3 3
3 4 1
3 5 1
4 6 1
5 6 1
1 6

2 2
1 2 1
1 2 2
1 2

2
1
1

题意：有n个城市m条边，告诉起点和终点，问从起点到终点不走重复边的最短路有多少条。

思路：求最短路的条数可以用最大流，建图时要去掉不是最短路上的边，判断某条边是不是最短路上的边：如果满足dist1[u]  + dist2[v] + E1[i].len = dist1[End]则可以说明该边是最短路上的边，其中 dist1[]  为各点到起点的最短距离，dist2[] 为各点到终点的最短距离。

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <stack>
#include <vector>
#include <set>
#include <queue>
#pragma comment (linker,"/STACK:102400000,102400000")
#define MAXN 1005
#define MAXM 300005
#define mod 1000000009
#define INF 0x3f3f3f3f
#define pi acos(-1.0)
#define eps 1e-6
#define lson rt<<1,l,mid
#define rson rt<<1|1,mid+1,r
#define FRE(i,a,b)  for(i = a; i <= b; i++)
#define FREE(i,a,b) for(i = a; i >= b; i--)
#define FRL(i,a,b)  for(i = a; i < b; i++)
#define FRLL(i,a,b) for(i = a; i > b; i--)
#define mem(t, v)   memset ((t) , v, sizeof(t))
#define sf(n)       scanf("%d", &n)
#define sff(a,b)    scanf("%d %d", &a, &b)
#define sfff(a,b,c) scanf("%d %d %d", &a, &b, &c)
#define pf          printf
#define DBG         pf("Hi\n")
typedef long long ll;
using namespace std;

struct Edge
{
    int to,next,cap,flow;
}edge[MAXM];

int n,m,start,End;
int tol,tol1,tol2;
int head[MAXN];
int gap[MAXN],dep[MAXN],pre[MAXN],cur[MAXN];

struct EDGE
{
    int u,v,len,next;
}E1[MAXM],E2[MAXM];

int head1[MAXN],dist1[MAXN],inq[MAXN];
int head2[MAXN],dist2[MAXN];

void init()
{
    tol=0;tol1=0;tol2=0;
    memset(head,-1,sizeof(head));
    memset(head1,-1,sizeof(head1));
    memset(head2,-1,sizeof(head2));
}

void add1(int u,int v,int w)
{
    E1[tol1].u=u; E1[tol1].v=v; E1[tol1].len=w; E1[tol1].next=head1[u]; head1[u]=tol1++;
}

void add2(int u,int v,int w)
{
    E2[tol2].u=u; E2[tol2].v=v; E2[tol2].len=w; E2[tol2].next=head2[u]; head2[u]=tol2++;
}

//加边，单向图三个参数，双向图四个参数
void addedge(int u,int v,int w,int rw=0)
{
    edge[tol].to=v; edge[tol].cap=w; edge[tol].next=head[u];
    edge[tol].flow=0; head[u]=tol++;
    edge[tol].to=u; edge[tol].cap=rw; edge[tol].next=head[v];
    edge[tol].flow=0; head[v]=tol++;
}

void spfa(int s,int *dist,int *head,EDGE *E)  //spfa求最短路
{
    memset(inq,0,sizeof(inq));
    queue<int>Q;
    Q.push(s);
    inq[s]=1;
    dist[s]=0;
    while (!Q.empty())
    {
        int u=Q.front(); Q.pop();
        inq[u]=0;
        for (int i=head[u];i+1;i=E[i].next)
        {
            int v=E[i].v;
            if (dist[v]>dist[u]+E[i].len)
            {
                dist[v]=dist[u]+E[i].len;
                if (!inq[v])
                {
                    inq[v]=1;
                    Q.push(v);
                }
            }
        }
    }
}

//输入参数：起点，终点，点的总数
//点的编号没有影响，只要输入点的总数
int sap(int start,int End,int N)
{
    memset(gap,0,sizeof(gap));
    memset(dep,0,sizeof(dep));
    memcpy(cur,head,sizeof(head));
    int u=start;
    pre[u]=-1;
    gap[0]=N;
    int ans=0;
    while (dep[start]<N)
    {
        if (u==End)
        {
            int Min=INF;
            for (int i=pre[u];i!=-1;i=pre[edge[i^1].to])
                if (Min>edge[i].cap-edge[i].flow)
                    Min=edge[i].cap-edge[i].flow;
            for (int i=pre[u];i!=-1;i=pre[edge[i^1].to])
            {
                edge[i].flow+=Min;
                edge[i^1].flow-=Min;
            }
            u=start;
            ans+=Min;
            continue;
        }
        bool flag=false;
        int v;
        for (int i=cur[u];i!=-1;i=edge[i].next)
        {
            v=edge[i].to;
            if (edge[i].cap-edge[i].flow && dep[v]+1==dep[u])
            {
                flag=true;
                cur[u]=pre[v]=i;
                break;
            }
        }
        if (flag)
        {
            u=v;
            continue;
        }
        int Min=N;
        for (int i=head[u];i!=-1;i=edge[i].next)
            if (edge[i].cap-edge[i].flow && dep[edge[i].to]<Min)
            {
                Min=dep[edge[i].to];
                cur[u]=i;
            }
        gap[dep[u]]--;
        if (!gap[dep[u]]) return ans;
        dep[u]=Min+1;
        gap[dep[u]]++;
        if (u!=start) u=edge[pre[u]^1].to;
    }
    return ans;
}


int main()
{
    int i,j,t,u,v,w;
    scanf("%d",&t);
    while (t--)
    {
        init();
        scanf("%d%d",&n,&m);
        for (i=0;i<m;i++)
        {
            scanf("%d%d%d",&u,&v,&w);
            if (u==v) continue;  //去自环
            add1(u,v,w);
            add2(v,u,w);
        }
        scanf("%d%d",&start,&End);
        memset(dist1,INF,sizeof(dist1));
        memset(dist2,INF,sizeof(dist2));
        spfa(start,dist1,head1,E1);
        spfa(End,dist2,head2,E2);
        for (i=0;i<tol1;i++)  //建图
        {
            if (dist1[E1[i].u]+dist2[E1[i].v]+E1[i].len==dist1[End])
                addedge(E1[i].u,E1[i].v,1);
        }
        printf("%d\n",sap(start,End,n));
    }
    return 0;
}

Marriage Match IV (hdu 3416 网络流+spfa最短路)

原文：http://blog.csdn.net/u014422052/article/details/45268595