HDU 1533.Going Home(费用流模板)

最新推荐文章于 2019-10-12 19:59:01 发布

原创最新推荐文章于 2019-10-12 19:59:01 发布 · 358 阅读

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本文介绍了一种基于最小费用最大流算法的具体实现方法，并通过一个具体的实例来展示如何使用该算法解决特定的问题。该算法适用于寻找从源点到汇点的路径中，既能够达到最大流量又具有最小总成本的方案。

#include <map>
#include <set>
#include <stack>
#include <queue>
#include <cmath>
#include <ctime>
#include <vector>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 0x3f3f3f3f
#define inf -0x3f3f3f3f
#define lson k<<1, L, mid
#define rson k<<1|1, mid+1, R
#define mem0(a) memset(a,0,sizeof(a))
#define mem1(a) memset(a,-1,sizeof(a))
#define mem(a, b) memset(a, b, sizeof(a))
typedef long long ll;
const int maxn=11000;

struct Edge{
    int from,to,cap,flow,cost;
    Edge(int u,int v,int c,int f,int w):from(u),to(v),cap(c),flow(f),cost(w) {}
};

struct MCMF{
    int n,m,s,t;
    vector<Edge>edges;
    vector<int>G[maxn];
    int inq[maxn];
    int d[maxn];
    int p[maxn];
    int a[maxn];

    void init(int n){
        this->n=n;
        for(int i=0;i<=n;i++)
            G[i].clear();
        edges.clear();
    }

    void AddEdge(int from,int to,int cap,int cost){
        edges.push_back(Edge(from,to,cap,0,cost));
        edges.push_back(Edge(to,from,0,0,-cost));
        m=edges.size();
        G[from].push_back(m-2);
        G[to].push_back(m-1);
    }
    bool spfa(int s,int t,int &flow,int& cost){
        for(int i=0;i<=n;i++)
            d[i]=INF;
        mem0(inq);
        d[s]=0;
        inq[s]=1;
        p[s]=0;
        a[s]=INF;
        queue<int>Q;
        Q.push(s);
        while(!Q.empty()){
            int u=Q.front();
            Q.pop();
            inq[u]=0;
            for(int i=0;i<G[u].size();i++){
                Edge& e=edges[G[u][i]];
                if(e.cap>e.flow&&d[e.to]>d[u]+e.cost){
                    d[e.to]=d[u]+e.cost;
                    p[e.to]=G[u][i];
                    a[e.to]=min(a[u],e.cap-e.flow);
                    if(!inq[e.to]){
                        Q.push(e.to);
                        inq[e.to]=1;
                    }
                }
            }
        }
        if(d[t]==INF)
            return false;
        flow+=a[t];
        cost+=d[t]*a[t];
        int u=t;
        while(u!=s){
            edges[p[u]].flow+=a[t];
            edges[p[u]^1].flow-=a[t];
            u=edges[p[u]].from;
        }
        return true;
    }

    int Mincost(int s,int t){
        int flow=0;
        int cost=0;
        while(spfa(s,t,flow,cost));
        return cost;
    }
};
MCMF  ZYC;
char mp[101][101];
struct node{
    int x;
    int y;
}line1[maxn],line2[maxn];

int main(){
    int n,m;
    while(scanf("%d%d",&n,&m)!=EOF){
        if(n==0&&m==0)
            break;
        int num=0;
        ZYC.init(maxn);
        int s=0;
        int t=m*n+1;
        int cnt1=0,cnt2=0;
        getchar();
        for(int i=1;i<=n;i++){
            scanf("%s",mp[i]+1);
            for(int j=1;j<=m;j++){
                //printf("%c\n",mp[i][j]);
                if(mp[i][j]=='m'){
                    line1[cnt1].x=i;
                    line1[cnt1].y=j;
                    ZYC.AddEdge(0,(i-1)*m+j,1,0);
                    cnt1++;
                }
                if(mp[i][j]=='H'){
                    line2[cnt2].x=i;
                    line2[cnt2].y=j;
                    ZYC.AddEdge((i-1)*m+j,t,1,0);
                    cnt2++;
                }
            }
        }
         for(int i=0;i<cnt1;i++)
             for(int j=0;j<cnt2;j++){
                int cost=fabs(line1[i].x-line2[j].x)+fabs(line1[i].y-line2[j].y);
                ZYC.AddEdge((line1[i].x-1)*m+line1[i].y,(line2[j].x-1)*m+line2[j].y,1,cost);
             }
        printf("%d\n",ZYC.Mincost(0,t));
    }
    return 0;
}