[树状数组] 树状数组基础练习题题解（一）

Time Limit: 1000MS
Memory Limit: 65536

Contents

1 Description
2 Input
3 Output
4 Sample Input
5 Sample Output
6 Hint
7 Source

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

Hint

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

Source

Ural Collegiate Programming Contest 1999

题目大意是定义一个星星的“级别”，每个星星的“级别”是横纵坐标均不大于这颗星星的星星数目，最后输出每个“级别”的星星数量。

我们可以，从左到右，从下往上，枚举每一颗星星，输出当前横坐标小于等于当前星星横坐标的星星数量，然后更新当前横坐标星星数目。

#include
#include
#include
#include
#include
#include
#define LL long long

using namespace std;

inline int read(){
    int x = 0;
    int p = 1;
    char ch = getchar();

    while(ch < '0' || ch > '9'){
        if(ch == '-')
            p = -1;
        ch = getchar();
    }

    while('0' <= ch && ch <= '9'){
        x = x*10 + ch - '0';
        ch = getchar();
    }

    return x*p;
}

const int MAXN = 32005;

int tree[MAXN + 10];

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

inline void add(int i,int x){
    while(i<=MAXN){
        tree[i] += x;
        i += lowbit(i);
    }
}

inline int query(int i){
    int ans = 0;

    while(i>0){
        ans += tree[i];
        i -= lowbit(i);
    }

    return ans;
}

int n;
int level[MAXN];

int main(){
    scanf("%d",&n);

    memset(level,0,sizeof(level));
    memset(tree,0,sizeof(tree));

    for(int i=0;i