Problem

Given an integer array, heapify it into a min-heap array.

For a heap array A, A[0] is the root of heap, and for each A[i], A[i * 2 + 1] is the left child of A[i] and A[i * 2 + 2] is the right child of A[i].

Clarification

What is heap?

• Heap is a data structure, which usually have three methods: push, pop and top. where “push” add a new element the heap, “pop” delete the minimum/maximum element in the heap, “top” return the minimum/maximum element.

What is heapify?

• Convert an unordered integer array into a heap array. If it is min-heap, for each element A[i], we will get A[i * 2 + 1] >= A[i] and A[i * 2 + 2] >= A[i].

What if there is a lot of solutions?

• Return any of them.

Example

Given [3,2,1,4,5], return [1,2,3,4,5] or any legal heap array.

Solution

class Solution {
public:
    /**
     * @param A: Given an integer array
     * @return: void
     */
    void heapify(vector<int> &A) {
        for(int i = 1; i < A.size(); i++) {
            heapify(A, i);
        }
    }
    
    void heapify(vector<int> &a, int n) {
        int father = (n - 1) / 2;
        int current = n;
        while (current > 0 && a[current] < a[father]) {
            swap(a[current], a[father]);
            current = father;
            father = (current - 1) / 2;
        }
    }
};