【floyd+拆点+二分答案+网络流】POJ 2391

最新推荐文章于 2019-09-05 15:07:08 发布

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最新推荐文章于 2019-09-05 15:07:08 发布

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分类专栏：网络流文章标签：网络 insert sap include c

本文链接：https://blog.youkuaiyun.com/leolin_/article/details/7207819

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本文探讨了如何使用算法来优化网络流量，包括流量控制、路径选择和资源分配等关键方面，旨在提高网络效率和用户体验。

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#include <map>
#include <set>
#include <list>
#include <queue>
#include <deque>
#include <stack>
#include <string>
#include <cstdio>
#include <math.h>
#include <iomanip>
#include <cstdlib>
#include <limits.h>
#include <string.h>
#include <iostream>
#include <fstream>
#include <algorithm>
using namespace std;

#define LL long long
#define pii pair<int ,int>
#define bug cout<<"here!!"<<endl
#define PI acos(-1.0)
#define FRE freopen("input.txt","r",stdin)
#define FF  freopen("output.txt","w",stdout)
#define eps 1e-8
#define MIN INT_MIN
const LL MAX = (1ll<<58);
const int inf = (1<<29);
#define N 410
#define M (N*N)
int n,m;//n为点数 m为边数
int h[N];
int gap[N];
int p[N],ecnt;
int source,sink;
struct edge{
    int v;
    int next;
    int val;
}e[M];

inline void init(){memset(p,-1,sizeof(p));ecnt=0;}

//有向
inline void insert1(int from,int to,int val){
    e[ecnt].v=to;
    e[ecnt].val=val;
    e[ecnt].next=p[from];
    p[from]=ecnt++;

    swap(from,to);

    e[ecnt].v=to;
    e[ecnt].val=0;
    e[ecnt].next=p[from];
    p[from]=ecnt++;
}

//无向
inline void insert2(int from,int to,int val){
    e[ecnt].v=to;
    e[ecnt].val=val;
    e[ecnt].next=p[from];
    p[from]=ecnt++;

    swap(from,to);

    e[ecnt].v=to;
    e[ecnt].val=val;
    e[ecnt].next=p[from];
    p[from]=ecnt++;
}

inline int dfs(int pos,int cost){
    if (pos==sink){
        return cost;
    }

    int j,minh=n-1,lv=cost,d;

    for (j=p[pos];j!=-1;j=e[j].next){
        int v=e[j].v,val=e[j].val;
        if(val>0){
            if (h[v]+1==h[pos]){
                if (lv<e[j].val) d=lv;
                else d=e[j].val;

                d=dfs(v,d);
                e[j].val-=d;
                e[j^1].val+=d;
                lv-=d;
                if (h[source]>=n) return cost-lv;
                if (lv==0) break;
            }

            if (h[v]<minh)   minh=h[v];
        }
    }

    if (lv==cost){
        --gap[h[pos]];
        if (gap[h[pos]]==0) h[source]=n;
        h[pos]=minh+1;
        ++gap[h[pos]];
    }
    return cost-lv;
}

int sap(int st,int ed){
    source=st;
    sink=ed;
    int ans=0;
    memset(gap,0,sizeof(gap));
    memset(h,0,sizeof(h));
    gap[st]=n;
    while (h[st]<n){
        ans+=dfs(st,INT_MAX);
    }
    return ans;
}
LL g[205][205];
int flow;
int x[205],y[205];

void floyd(int nn){
    int i,j,k;
    for(k=1;k<=nn;k++){
        for(i=1;i<=nn;i++){
            if(g[i][k] < MAX)
            for(j=1;j<=nn;j++){
                if(g[k][j] < MAX)
                if(g[i][k] + g[k][j] < g[i][j]){
                    g[i][j] = g[i][k] + g[k][j];
                }
            }
        }
    }
}
bool chk(LL mid,int nn){
    int i,j;
    init();
    for(i=1;i<=nn;i++){
        insert1(i,i+nn,inf);
        insert1(0,i,x[i]);
        insert1(i+nn,n-1,y[i]);
    }
    for(i=1;i<nn;i++){
        for(j=i+1;j<=nn;j++){
            if(g[i][j] <= mid){
                insert1(i,j+nn,inf);
                insert1(j,i+nn,inf);
            }
        }
    }
    int ans = sap(0,n-1);
    return ans == flow;
}
LL l,r,mid;
void gao(int nn){
    l = 0;
    LL ans = -1;
    while(l<=r){
        mid = (l+r)>>1;
        if(chk(mid,nn)){
            r = mid-1;
            ans = mid;
        } else l = mid+1;
    }
    if(ans==-1)puts("-1");
    else
    printf("%I64d\n",ans);
}
int main(){FRE;
    while(scanf("%d%d",&n,&m) != -1){
        int i,j;
        for(i=1;i<=n;i++){
            for(j=1;j<=n;j++){
                g[i][j] = MAX;
            }
            g[i][i] = 0;
        }
        int nn = n;
        n = 2*n+2;
        flow = 0;
        r=0;
        for(i=1;i<=nn;i++){
            scanf("%d%d",&x[i],&y[i]);
            flow += x[i];
        }
        while(m--){
            int a,b;
            LL c;
            scanf("%d%d%I64d",&a,&b,&c);
            if(g[a][b] > c) {
            g[a][b] = g[b][a] = c;
            r+=c;
            }
        }
        floyd(nn);
        gao(nn);
    }
    return 0;
}