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HDU 3572 Task Schedule（拆点+最大流dinic）

2024-08-26 07:43:48   223人阅读

Task Schedule

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7753    Accepted Submission(s): 2381

Problem Description
Our geometry princess XMM has stoped her study in computational geometry to concentrate on her newly opened factory. Her factory has introduced M new machines in order to process the coming N tasks. For the i-th task, the factory has to start processing it at or after day Si, process it for Pi days, and finish the task before or at day Ei. A machine can only work on one task at a time, and each task can be processed by at most one machine at a time. However, a task can be interrupted and processed on different machines on different days. 
Now she wonders whether he has a feasible schedule to finish all the tasks in time. She turns to you for help.
 

 

Input
On the first line comes an integer T(T<=20), indicating the number of test cases.

You are given two integer N(N<=500) and M(M<=200) on the first line of each test case. Then on each of next N lines are three integers Pi, Si and Ei (1<=Pi, Si, Ei<=500), which have the meaning described in the description. It is guaranteed that in a feasible schedule every task that can be finished will be done before or at its end day.
 

 

Output
For each test case, print “Case x: ” first, where x is the case number. If there exists a feasible schedule to finish all the tasks, print “Yes”, otherwise print “No”.

Print a blank line after each test case.
 

 

Sample Input
2
4 3
1 3 5
1 1 4
2 3 7
3 5 9
 
2 2
2 1 3
1 2 2
 

 

Sample Output
Case 1: Yes
Case 2: Yes
 

 

题目链接：HDU 3572

拆点的最大流判断是否满流的题目，点怎么拆呢？从源点S连向每一个任务i一条容量为p的边，说明每一个任务一开始要p个流量流入，然后每一个任务i向时间点[s,e]连一条容量为1的边，说明一个任务只能在一个机器上被工作，即不能既在机器A上加工又在机器B上加工，然后每一个时间点向T连一条容量为m个边，说明一个时间点只能最多同时有m个机器在工作。最后你就是要判断从S流出的$n*p$个流量能否全部流入T中就好了

空间复杂度大概是$（500+500^2+500）*2$条边，$500+500$个点，原本只会最辣鸡的FF想低空卡过这题，然而被无限TLE教做人，查查题解又膜膜dinic，发现dinic也容易理解，分层的意义就是减少没有用的搜索，因为增广一定是从最小距离距离近的到最小距离远的，那么那些d[v]!=d[u]+1的点就可以被忽略掉了

代码：

#include <stdio.h>#include <bits/stdc++.h>using namespace std;#define INF 0x3f3f3f3f#define CLR(arr,val) memset(arr,val,sizeof(arr))#define LC(x) (x<<1)#define RC(x) ((x<<1)+1)#define MID(x,y) ((x+y)>>1)typedef pair<int,int> pii;typedef long long LL;const double PI=acos(-1.0);const int N=1010;const int M=251000+7;struct edge{    int to,nxt;    int cap;};edge E[M<<1];int head[N],tot,d[N];void add(int s,int t,int cap){    E[tot].to=t;    E[tot].cap=cap;    E[tot].nxt=head[s];    head[s]=tot++;    E[tot].to=s;    E[tot].cap=0;    E[tot].nxt=head[t];    head[t]=tot++;}void init(){    CLR(head,-1);    tot=0;}int bfs(int s,int t){    CLR(d,-1);    d[s]=0;    queue<int>Q;    Q.push(s);    while (!Q.empty())    {        int now=Q.front();        Q.pop();        for (int i=head[now]; ~i; i=E[i].nxt)        {            int v=E[i].to;            if(d[v]==-1&&E[i].cap>0)            {                d[v]=d[now]+1;                if(v==t)                    return 1;                Q.push(v);            }        }    }    return d[t]!=-1;}int dfs(int s,int t,int f){    if(s==t||!f)        return f;    int r=0;    for (int i=head[s]; ~i; i=E[i].nxt)    {        int v=E[i].to;        if(d[v]==d[s]+1&&E[i].cap)        {            int d=dfs(v,t,min(f,E[i].cap));            if(d>0)            {                E[i].cap-=d;                E[i^1].cap+=d;                r+=d;                f-=d;                if(!f)                    break;            }        }    }    if(!r)        d[s]=INF;    return r;}int dinic(int s,int t){    int r=0;    while (bfs(s,t))        r+=dfs(s,t,INF);    return r;}int main(void){    int tcase,p,s,e,i,j,n,m;    scanf("%d",&tcase);    for (int q=1; q<=tcase; ++q)    {        init();        scanf("%d%d",&n,&m);        int S=0;        int tl=INF,tr=-INF;        int sump=0;        for (i=1; i<=n; ++i)        {            scanf("%d%d%d",&p,&s,&e);            add(S,i,p);            sump+=p;            if(s<tl)                tl=s;            if(e>tr)                tr=e;            for (j=s; j<=e; ++j)                add(i,n+j,1);        }        int T=n+tr+1;        for (i=tl; i<=tr; ++i)            add(n+i,T,m);        printf("Case %d: %s\n\n",q,dinic(S,T)==sump?"Yes":"No");    }    return 0;}

HDU 3572 Task Schedule（拆点+最大流dinic）


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