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最短路记录路径,同时求出最短的路径上最少要有多少条边,

然后用在最短路上的边重新构图后求最小割.

Tricks Device

8 9
1 2 2
2 3 2
2 4 1
3 5 3
4 5 4
5 8 1
1 6 2
6 7 5
7 8 1

2 6

/* ***********************************************
Author        :CKboss
Created Time  :2015年07月24日 星期五 10时07分09秒
File Name     :HDOJ5294.cpp
************************************************ */

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;

typedef pair<int,int> pII;

const int INF=0x3f3f3f3f;
const int maxn=2200;

int n,m;

/*************EDGE********************/

struct Edge
{
	int to,next,cost,cap,flow;
}edge[maxn*60],edge2[maxn*60];

int Adj[maxn],Size;
int Adj2[maxn],Size2;

void Add_Edge(int u,int v,int c)
{
	edge[Size].to=v;
	edge[Size].next=Adj[u];
	edge[Size].cost=c;
	Adj[u]=Size++;
}

/********spfa************/

int dist[maxn];
bool inQ[maxn];

vector<int> Pre[maxn];

int spfa(Edge* edge,int* Adj)
{
    memset(dist,63,sizeof(dist));
    memset(inQ,false,sizeof(inQ));
    dist[1]=0;
    queue<int> q;
    inQ[1]=true;q.push(1);

    while(!q.empty())
    {
        int u=q.front();q.pop();

        for(int i=Adj[u];~i;i=edge[i].next)
        {
            int v=edge[i].to;
            if(dist[v]>dist[u]+edge[i].cost)
            {
				Pre[v].clear();
				Pre[v].push_back(u);

                dist[v]=dist[u]+edge[i].cost;

                if(!inQ[v])
                {
                    inQ[v]=true;
                    q.push(v);
                }
            }
			else if(dist[v]==dist[u]+edge[i].cost)
			{
				Pre[v].push_back(u);
			}
        }

        inQ[u]=false;

    }
    return dist[n];
}

/********************rebuild************************/

void Add_Edge2(int u,int v,int w,int rw=0)
{
	edge2[Size2].cost=1;
	edge2[Size2].to=v; edge2[Size2].cap=w; edge2[Size2].next=Adj2[u];
	edge2[Size2].flow=0; Adj2[u]=Size2++;

	edge2[Size2].cost=1;
	edge2[Size2].to=u; edge2[Size2].cap=w; edge2[Size2].next=Adj2[v];
	edge2[Size2].flow=0; Adj2[v]=Size2++;
}

bool used[maxn];
int edges;

void rebuild()
{
	memset(used,false,sizeof(used));
	queue<int> q;
	q.push(n); used[n]=true;
	edges=0;

	while(!q.empty())
	{
		int v=q.front(); q.pop();
		for(int i=0,sz=Pre[v].size();i<sz;i++)
		{
			int u=Pre[v][i];
			/// u--->v
			//cout<<u<<" ---> "<<v<<endl;
			edges++;
			Add_Edge2(u,v,1);

			if(used[u]==false)
			{
				used[u]=true; q.push(u);
			}
		}
	}
}


/************************max_flow*******************************/

int gap[maxn],dep[maxn],pre[maxn],cur[maxn];

int sap(int start,int end,int N,Edge* edge=edge2)
{
	memset(gap,0,sizeof(gap));
	memset(dep,0,sizeof(dep));
	memcpy(cur,Adj2,sizeof(Adj2));

	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;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;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;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=Adj2[u];~i;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;
}

void init()
{
	memset(Adj,-1,sizeof(Adj)); Size=0;
	memset(Adj2,-1,sizeof(Adj2)); Size2=0;
	for(int i=1;i<=n;i++) Pre[i].clear();
}


int main()
{
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);

	while(scanf("%d%d",&n,&m)!=EOF)
	{
		init();
		for(int i=0,u,v,c;i<m;i++)
		{
			scanf("%d%d%d",&u,&v,&c);
			Add_Edge(u,v,c); Add_Edge(v,u,c);
		}
		spfa(edge,Adj);
		rebuild();
		int max_flow=sap(1,n,n);
		int min_short_path=spfa(edge2,Adj2);
		printf("%d %d\n",max_flow,m-min_short_path);
	}
    
    return 0;
}

HDOJ 5294 Tricks Device 最短路(记录路径)+最小割

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原文地址：http://blog.csdn.net/ck_boss/article/details/47041537