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最新推荐文章于 2017-09-25 22:31:16 发布

原创最新推荐文章于 2017-09-25 22:31:16 发布 · 365 阅读

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#acm #hdu #Network Flow #SAP

本文介绍了一种解决网络最大流问题的方法，通过构建特定的图结构，并使用SAP算法求解最大流，最终判断是否能达成给定条件。适用于竞赛编程及实际网络流问题求解。

It's a network max_flow problem. Make edges from start_point to Task_i. the capacity of this edge is ni * ti ,from Task_i to every time_points,the capacity of this edge is INF,from every time_points to end_point,the capacity of the edge is m.

And then run SAP,You must get answer.

The portal:http://acm.hdu.edu.cn/showproblem.php?pid=2883

#include <cstdio>
#include <cstring>
#include <memory.h>
#include <cstdlib>
#include <cmath>

const int MAXN = 100010;
const int MAXE = 400010;
const int INF = 0x3f3f3f3f;

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

int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],pre[MAXN],cur[MAXN];

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

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 ++;
}

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 flag[1000005];

void Deal_with(){
    int n,m,numtot,t_max,si,ni,ei,ti,ans;
    while(~scanf("%d %d ",&n,&m)){
        init();
        memset(flag,0,sizeof(flag));
        int start_point = 0,t_ans = 0;
        numtot = n;
        for(int i=1;i<=n;i++){
            scanf("%d %d %d %d",&si,&ni,&ei,&ti);
            addedge(start_point,i,ni*ti);
            t_ans += ni * ti;
            si ++;
            for(int j = si ;j <= ei; j++){
                if(!flag[j]) flag[j] = ++ numtot;
                addedge(i,flag[j],INF);
            }
        }
        numtot ++;
        int end_point = numtot;
        for(int i=1;i<=1000000;i++){
            if(flag[i]){
                addedge(flag[i],end_point,m);
            }
        }
        ans = sap(start_point,end_point,numtot+1);
        //printf("ans : %d t_ ans : %d\n",ans,t_ans);
        if(ans == t_ans){
            puts("Yes");
        }
        else{
            puts("No");
        }
    }
}

int main(void){
    //freopen("a.in","r",stdin);
    Deal_with();
    return 0;
}