Median

Description:

Given a unsorted array with integers, find the median of it.

A median is the middle number of the array after it is sorted.

If there are even numbers in the array, return the N/2-th number after sorted.

Example：

Given [4, 5, 1, 2, 3], return 3.

Given [7, 9, 4, 5], return 5.

分析：

思路：

参考：

  1. What is the most efficient algorithm to find the kth smallest element in an array having n unordered elements?
  2. Quickselect
  3. Median - C++

Code:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51

class Solution {
public:
    /**
     * @param nums: A list of integers.
     * @return: An integer denotes the middle number of the array.
     */
    int median(vector<int> &nums) {
        // write your code here
        int left = 0;
        int right = nums.size();
        
        int k = -1;
        if (right % 2 ==1) k = right / 2;
        else k = right / 2 - 1;
        
        return select_kth(nums, left, right - 1, k);
    }
    
    int select_kth(vector<int> &nums, int left, int right, int k) {
        if (left == right) return nums[left];
        int pivot = left + floor(rand() % (right - left + 1));
        
        pivot = partition(nums, left, right, pivot);
        if (pivot == k) return nums[k];
        else if (pivot < k) return select_kth(nums, pivot+1, right, k);
        else return select_kth(nums, left, pivot-1, k);
    }
    
    int partition(vector<int> &nums, int left, int right, int pivot) {
        int val = nums[pivot];
        swap(nums, pivot, right);
        int currIndex = left;
        
        for (int i = left;i < right;i++) {
            if (nums[i] < val) {
                swap(nums, currIndex, i);
                currIndex++;
            }
        }
        swap(nums, currIndex, right);
        
        return currIndex;
    }
    
    void swap(vector<int> &nums, int left, int right) {
        int tem = nums[left];
        nums[left] = nums[right];
        nums[right] = tem;
    }
};