Data Stream Median

Description:

Numbers keep coming, return the median of numbers at every time a new number added.

Example

For numbers coming list: [1, 2, 3, 4, 5], return [1, 1, 2, 2, 3].

For numbers coming list: [4, 5, 1, 3, 2, 6, 0], return [4, 4, 4, 3, 3, 3, 3].

For numbers coming list: [2, 20, 100], return [2, 2, 20].

Challenge

Total run time in O(nlogn).

Clarification

What's the definition of Median? - Median is the number that in the middle of a sorted array. If there are n numbers in a sorted array A, the median is A[(n - 1) / 2]. For example, if A=[1,2,3], median is 2. If A=[1,19], median is 1.

Solution:

class Solution {
public:
	/**
	 * @param nums: A list of integers.
	 * @return: The median of numbers
	 */
	vector<int> medianII(vector<int> &nums) {
		vector<int> rc;
		auto sz = (int)nums.size();
		if (sz == 0) return rc;
		multiset<int> left, right;
		for (int i = 0; i < sz; ++i) {
			if (left.size() == right.size()) {
				if (!right.empty() && nums[i] > *right.begin()) {
					left.insert(*right.begin());
					right.erase(right.begin());
					right.insert(nums[i]);
				} else
					left.insert(nums[i]);
			} else {
				if (nums[i] < *left.rbegin()) {
					right.insert(*left.rbegin());
					left.erase(prev(end(left)));
					left.insert(nums[i]);
				} else
					right.insert(nums[i]);
			}
			rc.push_back(*left.rbegin());
		}
		return rc;
	}
};