Heap Sort

• Time : O(nlogn)
• Space : O(n)

#include <vector>
using namespace std;

void push(vector<int>& heap, int v) {
	heap.push_back(v);
	int i = heap.size() - 1;
	while(i) {
		if(heap[i] < heap[i / 2])
			swap(heap[i], heap[i / 2]);
		else break;
		i /= 2;
	}
}

int pop(vector<int>& heap) {
	int res = heap[0];
	heap[0] = heap.back();
	heap.pop_back();
	int i = 0;
	while(true) {
		if(i * 2 + 1 < heap.size()) {
			int mi = min(heap[i * 2], heap[i * 2 + 1]);
			if(mi >= heap[i]) break;
			if(heap[i * 2] == mi) {
				swap(heap[i], heap[i * 2]);
				i = i * 2;
			} else {
				swap(heap[i], heap[i * 2 + 1]);
				i = i * 2 + 1;
			}
		} else if(i * 2 < heap.size()) {
			if(heap[i * 2] >= heap[i]) break;
			swap(heap[i], heap[i * 2]);
			i = i * 2;
		} else break;
	}
	
	return res;
}

vector<int> heapSort(vector<int> array) {
  vector<int> heap;
	for(auto& n : array)
		push(heap, n);
	int idx = 0;
	while(!heap.empty()) {
		array[idx++] = pop(heap);
	}
  return array;
}