hdu 1541 Stars（树状数组）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1541

Stars

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 7144    Accepted Submission(s): 2802

Problem 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

51 15 17 13 35 5

 

Sample Output

12110

 

Source

Ural Collegiate Programming Contest 1999

 

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题目大意：求出0~n-1的每个等级有多少个星星。开始输入一个n，表示共有n颗星星，接下来n行，每行输入一个x，y表示星星的坐标，最后求各个阶段星星的等级（阶段分为0~n-1）有多少个星星。

特别注意：1、星星坐标中的y是递增输入的。

    2、星星等级的计算方法是：该颗星星的左边及其下方有多少个星星，等级就为多少。

解题思路：先看一排的星星坐标，也就是先不管y，只看y值相同的星星坐标的x。设a[i]表示x轴坐标为i的点的个数。所以这里的求a[0]+a[1]+.....+a[x]的和刚好又用到的是树状数组的另一个最基本的应用-区间求和。

详见代码。

#include <iostream>#include <cstring>#include <cstdio>#include <algorithm>using namespace std;int c[32010];int lowbit(int k){    return k&((k)xor(k-1));}void add(int num,int k){    while (k<=32009)    {        c[k]+=num;        k+=lowbit(k);    }}int sum(int k){    int s=0;    while (k)    {        s+=c[k];        k-=lowbit(k);    }    return s;}int main(){    int n;    int a[32000+10],w[32000+10];    while (~scanf("%d",&n))    {        memset(c,0,sizeof(c));        memset(w,0,sizeof(w));        for (int i=0; i<n; i++)        {            int x,y;            scanf("%d%d",&x,&y);            //a[x]++;//表示相同x有几个星星            int s=sum(x+1);//求出等级            w[s]++;//这个等级的星星有多少个            add(1,x+1);//变化一个星星，加上1        }        for (int i=0; i<n; i++)            printf ("%d\n",w[i]);    }    return 0;}