POJ3784 Running Median

 

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 1670		Accepted: 823

Description

For this problem, you will write a program that reads in a sequence of 32-bit signed integers. After each odd-indexed value is read, output the median (middle value) of the elements received so far.

Input

The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. The first line of each data set contains the data set number, followed by a space, followed by an odd decimal integer M, (1 ≤ M ≤ 9999), giving the total number of signed integers to be processed. The remaining line(s) in the dataset consists of the values, 10 per line, separated by a single space. The last line in the dataset may contain less than 10 values.

Output

For each data set the first line of output contains the data set number, a single space and the number of medians output (which should be one-half the number of input values plus one). The output medians will be on the following lines, 10 per line separated by a single space. The last line may have less than 10 elements, but at least 1 element. There should be no blank lines in the output.

Sample Input

3 
1 9 
1 2 3 4 5 6 7 8 9 
2 9 
9 8 7 6 5 4 3 2 1 
3 23 
23 41 13 22 -3 24 -31 -11 -8 -7 
3 5 103 211 -311 -45 -67 -73 -81 -99 
-33 24 56

Sample Output

1 5
1 2 3 4 5
2 5
9 8 7 6 5
3 12
23 23 22 22 13 3 5 5 3 -3 
-7 -3

Source

Greater New York Regional 2009

对于每个奇数次读入，输出当前已有序列的中位数

 

维护两个堆，一个大根堆，一个小根堆。大根堆里存较小的数，小根堆里存较大的数。维护好以后，小根堆顶就是中位数。

每次新加入一个数，若该数比中位数大，存入小根堆，否则存入大根堆。

限制小根堆里的数最多比大根堆大1，若不满足，就把小根堆的堆顶弹到大根堆。

 

以下是代码，基本是抄的233。

结构体里写的是小根堆，为了缩减代码长度，把大根堆取负，也按照小根堆的算法算，就能维护出大根堆。

注意输出格式。mod20==19是为了输出10个中位数就换一行。

 

/*by SilverN*/
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
const int mxn=5000;
struct pile{
    int h[6000];
    int cnt;
    void insert(int x){//插入 
        h[++cnt]=x;
        int k=cnt;
        while(k>1 && h[k]<h[k>>1]){//维护 
            swap(h[k],h[k>>1]);
            k>>=1;
        }
    }
    void pop(){
        int k=2;
        h[1]=h[cnt];//把末尾元素顶上来 
        h[cnt--]=0;
        while(k<=cnt){
            if(h[k]>h[k+1] && k<cnt)k++;//在两个子节点中找较小的 
            if(h[k]<h[k>>1])swap(h[k],h[k>>1]),k<<=1;//把较小的顶上去 
            else break;//满足性质，退出 
        }
    }
}big,small,empty;
void ins(int x){
    if(x<=-big.h[1])
        big.insert(-x);
    else small.insert(x);
    while(small.cnt>big.cnt) big.insert(-small.h[1]),small.pop();
    while(big.cnt>small.cnt+1) small.insert(-big.h[1]),big.pop();
}
int n,m;
int main(){
    int T;
    scanf("%d",&T);
    int i,j;
    while(T--){
        big=small=empty;//初始化 
        scanf("%d%d",&n,&m);
        int num;
        printf("%d %d\n",n,(m+1)>>1);
        for(i=1;i<=m;i++){
            scanf("%d",&num);
            ins(num);
            if(i&1){//奇数
                printf("%d",-big.h[1]);
                if(i==m)printf("\n");else printf(" ");
                if(i%20==19)printf("\n");
            }
        }
    }
    return 0;
}