BestCoder Round #20 lines (模拟线段树的思想)

lines

Time Limit: 5000/2500 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 787    Accepted Submission(s): 194

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(1≤T≤100)(the data for N>100 less than 11 cases),indicating the number of test cases.
Each test case begins with an integer N(1≤N≤105),indicating the number of lines.
Next N lines contains two integers Xi and Yi(1≤Xi≤Yi≤109),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

 

 

题目意思很好懂，就是求n条线段的所覆盖的区域中，哪一个点被覆盖的次数最多。

 

一开始的思路是离散+线段树，因为这题和POJ 2528是同一个思路，只是求的值不同而已。

 

后来有一种思路，和线段树的思路很相近：

先把端点都存下来然后进行排序，这可以看成一个离散化处理。

如果在这个线段里面，b[左端点]++，b[右端点+1]--

这里可以用前缀和来解释这这种表示方法

比如一条线段的两个端点1 3

那么

b[1]=1, b[4]=-1;

b[1]=1 ,b[2]=b[1]+b[2]=1, b[3]=b[2]+b[3]=1, b[4]=b[3]+b[4]=0;

这样一来，问题就转化成了求前缀和的最大值是多少了。

 

 

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cmath>
#include<stack>
#include<queue>
#include<stack>
#include<stdlib.h>
#include<algorithm>
#define LL __int64
using namespace std;

const double EPS=1e-8;
const int MAXN=100000+5;
int a[MAXN*2],b[MAXN*2];
struct node
{
    int star,en;
}line[MAXN];

int bs(int a[],int x,int val)
{
    int l=0,r=x-1;
    while(l<=r)
    {
        int mid=(l+r)/2;
        if(a[mid]==val) return mid;
        if(val>a[mid]) l=mid+1;
        else r=mid-1;
    }
}
int main()
{
    int kase,n;
    scanf("%d",&kase);
    while(kase--)
    {
        int cnt=0;
        memset(a,0,sizeof(a));
        memset(b,0,sizeof(b));
        scanf("%d",&n);
        for(int i=0;i<n;i++)
        {
            scanf("%d %d",&line[i].star,&line[i].en);
            a[cnt++]=line[i].star;
            a[cnt++]=line[i].en;   //将端点记录在a数组中
        }
        sort(a,a+cnt);   //排序的话，可以说是一个离散化处理
        int p=1;
        for(int i=1;i<cnt;i++)
            if(a[i]!=a[i-1])
                a[p++]=a[i];   //删除重复的端点

        for(int i=0;i<n;i++)
        {
            int vis;
            vis=bs(a,p,line[i].star);
            b[vis]++;
            vis=bs(a,p,line[i].en);
            b[vis+1]--;
        }

        int maxn=b[0];
        for(int i=1;i<p;i++)
        {
            b[i]=b[i-1]+b[i];
            if(b[i]>maxn)
                maxn=b[i];
        }
        printf("%d\n",maxn);
    }
    return 0;
}