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lines(最大区间和)

时间:2015-11-07 23:13:15      阅读:289      评论:0      收藏:0      [点我收藏+]

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lines

Time Limit: 5000/2500 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1350    Accepted Submission(s): 558


Problem Description
John has several lines. The lines are covered on the X axis. Let A is a point which is covered by the most lines. John wants to know how many lines cover A.
 

 

Input
The first line contains a single integer T(1T100)(the data for N>100 less than 11 cases),indicating the number of test cases.
Each test case begins with an integer N(1N105),indicating the number of lines.
Next N lines contains two integers Xi and Yi(1XiYi109),describing a line.
 

 

Output
For each case, output an integer means how many lines cover A.
 

 

Sample Input
2 5 1 2 2 2 2 4 3 4 5 1000 5 1 1 2 2 3 3 4 4 5 5
 

 

Sample Output
3 1
 
官方题解:
我们可以将一条线段[xi,yi]分为两个端点xi(yi)+1
xi时该点会新加入一条线段,同样的,在(yi)+1时该点会减少一条线段,
因此对于2n个端点进行排序,令xi为价值1,yi为价值-1,问题转化成了最大区间和,
因为1一定在-1之前,因此问题变成最大前缀和,我们寻找最大值就是答案,另外的,
这题可以用离散化后线段树来做。复杂度为排序的复杂度即nlgn
另外如果用第一种做法数组应是2n,而不是n,由于各种非确定性因素我在小数据就已
经设了n=10W的点。

题解:
 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<cmath>
 5 #include<algorithm>
 6 #define mem(x,y) memset(x,y,sizeof(x))
 7 using namespace std;
 8 typedef long long LL;
 9 const int INF=0x3f3f3f3f;
10 const int MAXN=1e5+100;
11 pair<int,int>pa[MAXN<<1];
12 int main(){
13     int T,N;
14     scanf("%d",&T);
15     while(T--){int a,b;
16         scanf("%d",&N);
17         for(int i=0;i<N;i++){
18             scanf("%d%d",&a,&b);
19             pa[i<<1]=make_pair(a,1);
20             pa[i<<1|1]=make_pair(b+1,-1);
21         }
22         sort(pa,pa+N*2);
23         int ans=0,cnt=0;
24         for(int i=0;i<2*N;i++)
25             cnt+=pa[i].second,ans=max(ans,cnt);
26         printf("%d\n",ans);
27     }
28     return 0;
29 }

 

lines(最大区间和)

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原文地址:http://www.cnblogs.com/handsomecui/p/4946174.html

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