Median

Median

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

Challenge

O(n) time.

---------------------------- thinking -----------------------------------
quick sort idea
http://codeanytime.blogspot.com/2014/12/median.html
http://www.shuati.info/blog/2014/07/01/Median-in-stream-of-integers/
http://algs4.cs.princeton.edu/23quicksort/
---------------------------- codes ------------------------------------
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 kth = (1 + nums.size()) / 2 - 1;
        return medianHelper(nums, 0, nums.size()-1, kth);
    }
    void swap(vector<int> &nums, int i, int j) {
        int temp = nums[i];
        nums[i] = nums[j];
        nums[j] = temp;
    }
    int medianHelper(vector<int> &nums, int start, int end, int kth) {
        int s = start + 1;
        int e = end;
        while (s <= e) {
            if (nums[s] < nums[start]) {
                s++;
            } else if (nums[e] > nums[start]) {
                e--;
            } else {
                swap(nums, s, e);
                s++;
                e--;
            }
        }
        swap(nums, start, e);
        if (e == kth) {
            return nums[e];
        } else if (e < kth) {
            //BUG here, the start val should be e+1 instead of e -> the same reason as binary search
            return medianHelper(nums, e+1, end, kth);
        } else {
            return medianHelper(nums, start, e-1, kth);
        }
    }
};