Task Schedule
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4617 Accepted Submission(s): 1513
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
最大流。这个题的建图算是经典,因为限定每个时刻每台机器只能处理一个任务,所以可以把时间点分配给各个合法的机器...具体是先设定一个超级源点S,连向各个任务,容量为该任务所需时间,各个任务连向在范围内的时间点,容量为1(保证每个时刻xxx这个条件),所有时间点连向超级汇点T,容量为机器台数,最后求最大流,等于所有机器所需时间和的就是yes
代码:
#include <cstdio> #include <cstring> #include <queue> #define SIZE 1100 #define INF 1000000000 using namespace std ; struct Edge{ int to , w , next ; }edge[SIZE*SIZE]; int n , m , start , ends , index = 0; int head[SIZE] , level[SIZE] , cur[SIZE]; bool visited[SIZE] ; bool bfs() { queue<int> que ; que.push(start) ; memset(level,-1,sizeof(level)) ; level[start] = 0 ; while(!que.empty()) { int pos = que.front() ; que.pop() ; for(int next = head[pos] ; next != -1 ; next = edge[next].next) { if(level[edge[next].to]<0 && edge[next].w>0) { level[edge[next].to] = level[pos]+1 ; que.push(edge[next].to) ; } } } return level[ends] != -1 ; } int min(int a , int b) { return a>b?b:a ; } int dfs(int pos , int flow) { int deta = 0 , tmp = 0; if(pos == ends) return flow ; for(int next = head[pos] ; next != -1 ; next = edge[next].next) { if(edge[next].w > 0 && level[pos] == level[edge[next].to]-1) { tmp = dfs(edge[next].to,min(flow-deta,edge[next].w)) ; if(tmp>0) { edge[next].w -= tmp ; edge[next^1].w += tmp ; deta += tmp ; if(deta == flow) break ; } else level[edge[next].to] = -1 ; //不加这个,,超时。。。 } } return deta ; } int dinic() { int ans = 0 , flow = 0 ; while(bfs()) { int deta = 0 ; ans += dfs(0,INF) ; } return ans ; } void add(int s , int d , int w) { edge[index].next = head[s] ; edge[index].to = d ; edge[index].w = w ; head[s] = index ++ ; edge[index].next = head[d] ; edge[index].to = s ; edge[index].w = 0 ; head[d] = index ++ ; } int main() { int t , c = 1 ; scanf("%d",&t) ; while(t--) { scanf("%d%d",&n,&m) ; memset(head,-1,sizeof(head)) ; index = 0 ; int sum = 0 , max = -1; start = 0; for(int i = 1 ; i <= n ; ++i) { int x , y , z ; scanf("%d%d%d",&x,&y,&z) ; sum += x ; max = max>z?max:z ; add(start,i,x) ; for(int j = y ; j <= z ; ++j) { add(i,j+n,1) ; } } ends = n+max+1 ; for(int i = 1 ; i <= max ; ++i) add(i+n,ends,m) ; int ans = dinic() ; printf("Case %d: ",c++) ; if(ans != sum) puts("No\n") ; else puts("Yes\n"); } return 0 ; }
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