Heaps: Find the Running Median

The median of a dataset of integers is the midpoint value of the dataset for which an equal number of integers are less than and greater than the value. To find the median, you must first sort your dataset of integers in non-decreasing order, then:

• If your dataset contains an odd number of elements, the median is the middle element of the sorted sample. In the sorted dataset ,  is the median.
• If your dataset contains an even number of elements, the median is the average of the two middle elements of the sorted sample. In the sorted dataset ,  is the median.

Given an input stream of  integers, you must perform the following task for each  integer:

1. Add the  integer to a running list of integers.
2. Find the median of the updated list (i.e., for the first element through the  element).
3. Print the list's updated median on a new line. The printed value must be a double-precision number scaled to  decimal place (i.e.,  format).

Input Format

The first line contains a single integer, , denoting the number of integers in the data stream. 
Each line  of the  subsequent lines contains an integer, , to be added to your list.

Constraints

Output Format

After each new integer is added to the list, print the list's updated median on a new line as a single double-precision number scaled to  decimal place (i.e.,  format).

Sample Input

6
12
4
5
3
8
7

Sample Output

12.0
8.0
5.0
4.5
5.0
6.0

Explanation

There are  integers, so we must print the new median on a new line as each integer is added to the list:

풀이

배열의 경우 사이즈를 정해서 하는데 해당 문제는 하나씩 입력 받을 때마다 내부 아이템이 늘어나고 거기에 따른 median을 구하는 문제이다.

따라서 배열을 list로 바꿔고 Collection을 sort 하는 방향으로 우선 생각했다.

코드 작성 후 제출했더니 3문제를 제외하고 전부 timeout 문제에 접하게 되었는데

Trick을 써줄려고 sort 대신에 binarySearch를 사용한다.

discussion에 보니 binarySearch 의 경우 O(logN) 이기 때문에 time out에 걸리지 않는다고 나와있다.

package datastructure;

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class FindTheRunningMedian {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        List<Integer> data = new ArrayList<>();
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; i++) {
            int a_i = in.nextInt();
            int pos = Collections.binarySearch(data, a_i);
            if (pos < 0) pos = Math.abs(pos)-1;
            data.add(pos, a_i);
            sb.append(median(data)).append(System.lineSeparator());
        }
        System.out.println(sb.toString());
    }
    public static double median(List<Integer> data) {
        if ((data.size() & 1) == 1) {
            return data.get(data.size()/2);
        } else {
            int midSize = data.size()/2;
            return (data.get(midSize-1) + data.get(midSize)) / 2.0;
        }
    }
}