1301 - Monitoring Processes

1301 - Monitoring Processes

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Time Limit: 3 second(s)

Memory Limit: 32 MB

We have planned to design a new operating system. Like other OS we will use the techniques of processes, schedulers, locks etc. The basic plan is to use the OS in hardwires that have low configurations. So, efficiency matters. That's why we want to minimize the cost as well as the power consumption. To be more specific, there are n processes, and each process starts its execution in timestamp s_i, and ends its execution in timestamp t_i. For simplicity assume that the timestamps are represented as integers. Now when a process is being executed, we need a wrapper program to look after the process. The reason behind using wrapper programs is that, they will continuously check the processes and if any process tries to harm the system or wants to take hold of some restricted resources or even tries to invoke some forbidden methods, the wrapper will halt the process and generate appropriate error signals. But the problem is that a wrapper program cannot monitor more than one process in any timestamp and when it's been assigned to a process, it will have to wait until the process finishes. But after this, the same wrapper program can be used for monitoring another process. So, a wrapper program can be used for multiple processes but not more than one in any timestamp.

So, we have the process schedules and we want to find the number of wrapper programs to monitor them according to the given restrictions. As you are the leading programmer of this project, you are asked to find the minimum number of wrapper programs to monitor all the processes.

Input

Input starts with an integer T (≤ 20), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 50000). Each of the next n lines contains two integers s_i t_i (1 ≤ s_i ≤ t_i ≤ 10⁹).

Output

For each case, print the case number and the minimum number of wrapper programs to monitor all the processes.

Sample Input	Output for Sample Input
2 2 1 3 3 5 4 1 10 10 20 11 21 3 5	Case 1: 2 Case 2: 2

Note

Dataset is huge, use faster I/O methods.

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PROBLEM SETTER: JANE ALAM JAN

思路：离散化+线段树；

转换为求重复次数最多的点，因为重复处必须要分开，那么只要找到那个重复最多次数的点将这些段分成重复最多次数段即可。

  1 #include<stdio.h>
  2 #include<algorithm>
  3 #include<iostream>
  4 #include<string.h>
  5 #include<stdlib.h>
  6 #include<queue>
  7 #include<set>
  8 using namespace std;
  9 typedef long long LL;
 10 typedef struct pp
 11 {
 12     int x;
 13     int y;
 14     int id;
 15 } ss;int maxx;
 16 ss ans[50005];
 17 int ak[200000];
 18 int tree[200000*4];
 19 void in(int n,int m,int l,int r,int k)
 20 {
 21     if(l>m||r<n)
 22     {
 23         return ;
 24     }
 25     else if(l<=n&&r>=m)
 26     {
 27         tree[k]+=1;
 28         return ;
 29     }
 30     else
 31     {
 32         in(n,(n+m)/2,l,r,2*k+1);
 33         in((n+m)/2+1,m,l,r,2*k+2);
 34     }
 35 }
 36 void fang(int n,int m,int k)
 37 {
 38     if(n==m)
 39     {   if(tree[k]>maxx)
 40          maxx=tree[k];
 41         return ;
 42     }
 43     else
 44     {
 45         tree[2*k+1]+=tree[k];
 46         tree[2*k+2]+=tree[k];
 47         fang(n,(n+m)/2,2*k+1);
 48         fang((n+m)/2+1,m,2*k+2);
 49     }
 50 }
 51 int main(void)
 52 {
 53     int i,j,k;
 54     scanf("%d",&k);
 55     int s;
 56     int n,m;
 57     for(s=1; s<=k; s++)
 58     {   maxx=0;
 59         scanf("%d",&n);
 60         int vv=0;
 61         for(i=0; i<n; i++)
 62         {
 63             scanf("%d %d",&ans[i].x,&ans[i].y);
 64             ak[vv++]=ans[i].x;
 65             ak[vv++]=ans[i].y;
 66         }
 67         sort(ak,ak+vv);
 68         for(i=0; i<n; i++)
 69         {
 70             int l=0;
 71             int r=vv-1;
 72             int id=0;
 73             while(l<=r)
 74             {
 75                 int mid=(l+r)/2;
 76                 if(ak[mid]<=ans[i].x)
 77                 {
 78                     id=mid;
 79                     l=mid+1;
 80                 }
 81                 else r=mid-1;
 82             }
 83             ans[i].x=id;
 84             l=0;
 85             r=vv-1;
 86             while(l<=r)
 87             {
 88                 int mid=(l+r)/2;
 89                 if(ak[mid]<=ans[i].y)
 90                 {
 91                     id=mid;
 92                     l=mid+1;
 93                 }
 94                 else r=mid-1;
 95             }
 96             ans[i].y=id;
 97         }
 98         memset(tree,0,sizeof(tree));
 99         for(i=0; i<n; i++)
100         {
101             in(0,200000,ans[i].x,ans[i].y,0);
102
103         }
104         fang(0,200000,0);
105         printf("Case %d: %d\n",s,maxx);
106     }
107     return 0;
108 }