poj2352(线段树或树状数组)

Stars

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 26238		Accepted: 11448

Description

Astronomers often examine star maps where stars are represented by points on a plane and each star has Cartesian coordinates. Let the level of a star be an amount of the stars that are not higher and not to the right of the given star. Astronomers want to know the distribution of the levels of the stars.

For example, look at the map shown on the figure above. Level of the star number 5 is equal to 3 (it's formed by three stars with a numbers 1, 2 and 4). And the levels of the stars numbered by 2 and 4 are 1. At this map there are only one star of the level 0, two stars of the level 1, one star of the level 2, and one star of the level 3.

You are to write a program that will count the amounts of the stars of each level on a given map.

Input

The first line of the input file contains a number of stars N (1<=N<=15000). The following N lines describe coordinates of stars (two integers X and Y per line separated by a space, 0<=X,Y<=32000). There can be only one star at one point of the plane. Stars are listed in ascending order of Y coordinate. Stars with equal Y coordinates are listed in ascending order of X coordinate.

Output

The output should contain N lines, one number per line. The first line contains amount of stars of the level 0, the second does amount of stars of the level 1 and so on, the last line contains amount of stars of the level N-1.

Sample Input

5
1 1
5 1
7 1
3 3
5 5

Sample Output

1
2
1
1
0

Hint

This problem has huge input data,use scanf() instead of cin to read data to avoid time limit exceed.

 

题目是在引导我们用线段树或树状数组，因为在反复地进行加与查询操作

注意此题不能先求出lowbit[]，这样可能超时

这告诉我们即使在时间复杂度相同的情况下，运行时间可能存在很大差别。

#include<iostream>
#include<cstdio>
#include<string>
#include<cstring>
const int MAX=32000+10;

int n;
//int lowbit[MAX];
int C[MAX];
int ans[15002];

int lowbit(int i)
{
	return i&(-i);
}

int QuerySum(int p)
//查询原数组中下标1-p的元素的和 
{ 
   int nSum = 0; 
   while( p > 0 ) 
   {  
      nSum += C[p]; 
      p -= lowbit(p); 
   } 
    return nSum; 
} 

void Modify( int p,int val) 
//原数组中下表为p的元素+val，导致C[]数组中部分元素值的改变
{ 
    while( p <=MAX) 
   { 
      C[p] += val; 
      p += lowbit(p); 
    } 
} 

int main()
{
	int i;
	int x,y;
	scanf("%d",&n);
		memset(C,0,sizeof(C));
		memset(ans,0,sizeof(ans));
	//	for(i=1;i<=n;i++)
	//		lowbit[i]=i&(-i);
		for(i=1;i<=n;i++)
		{
			scanf("%d%d",&x,&y);
			ans[QuerySum(x+1)]++;
			Modify( x+1,1) ;
		}
		for(i=0;i<=n-1;i++)
			printf("%d\n",ans[i]);
	return 0;
}