Stars（树状数组基础）

最新推荐文章于 2022-08-09 21:39:29 发布

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本文介绍了一个天文学领域的算法问题，该问题关注如何计算二维平面上星星的分布级别，并通过一个具体的示例说明了如何利用离线BIT树进行高效计算。

E - Stars

Time Limit: 1000 MS Memory Limit: 32768 KB

64-bit integer IO format: %I64d , %I64u Java class name: Main

[Submit] [Status]

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

Sample Output

#include<stdio.h>
#include<iostream>
#include<string.h>
using namespace std;

int n,x,y;
int a[32010];
int val[32005];

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

void update(int x,int num)
{
    while(x<=32005)
    {
        a[x] += num;
        x += lowbit(x);
    }
}

int getsum(int x)
{
    int ans = 0;
    while(x>0)
    {
        ans += a[x];
        x -= lowbit(x);
    }
    return ans;
}

int main()
{
    while(~scanf("%d",&n))
    {
        memset(a,0,sizeof(a));
        memset(val,0,sizeof(val));
        int x,y;
        for(int i=0; i<n; i++)
        {
            scanf("%d%d",&x,&y);
            x++;
            update(x,1);
            val[getsum(x)]++;
        }

        for(int i=1; i<=n; i++)
        {
            printf("%d\n",val[i]);
        }
    }
    return 0;
}