Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Maximum Heap

A binary heap which satisfies max-heap property is called max-heap. In a max-heap, for every node $i$ other than the root, $A[i] \leq A[parent(i)]$, that is, the value of a node is at most the value of its parent. The largest element in a max-heap is stored at the root, and the subtree rooted at a node contains values no larger than that contained at the node itself.

Here is an example of a max-heap.

Write a program which reads an array and constructs a max-heap from the array based on the following pseudo code.

$maxHeapify(A, i)$ move the value of $A[i]$ down to leaves to make a sub-tree of node $i$ a max-heap. Here, $H$ is the size of the heap.

1 maxHeapify(A, i)
2 l = left(i)
3 r = right(i)
4 // select the node which has the maximum value
5 if l ≤ H and A[l] > A[i]
6 largest = l
7 else
8 largest = i
9 if r ≤ H and A[r] > A[largest]
10 largest = r
11
12 if largest ≠ i　// value of children is larger than that of i
13 swap A[i] and A[largest]
14 maxHeapify(A, largest) // call recursively

The following procedure buildMaxHeap(A) makes $A$ a max-heap by performing maxHeapify in a bottom-up manner.

1 buildMaxHeap(A)
2 for i = H/2 downto 1
3 maxHeapify(A, i)

Input

In the first line, an integer $H$ is given. In the second line, $H$ integers which represent elements in the binary heap are given in order of node id (from $1$ to $H$).

Output

Print values of nodes in the max-heap in order of their id (from $1$ to $H$). Print a single space character before each value.

Constraint

$1 \leq H \leq 500,000$

$-2,000,000,000 \leq$ value of a node $\leq 2,000,000,000$

Sample Input 1

10
4 1 3 2 16 9 10 14 8 7

Sample Output 1

16 14 10 8 7 9 3 2 4 1

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JAVA (judge verdict: WA: Presentation Error)

import java.util.Scanner;

public class Main {
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt(); 
		int[] nums = new int[n];
		for(int i=0;i<n;i++){
			nums[i] = sc.nextInt();
		}
		for(int i=n/2-1;i>=0;i--){
			heapify(nums,n,i);
		}
		printArr(nums);

	}
	public static void heapify(int[] A,int n,int i){
		int largest = i; 
		int l = 2*i+1;
		int r = 2*i+2;
		if(l<n && A[l]>A[largest]){
			largest = l; 
		}
		if(r<n && A[r]>A[largest]){
			largest = r; 
		}
		if(largest!=i){
			swap(A,i,largest);
			heapify(A,n,largest);
		}
	}
	public static void swap(int[] A,int i,int j){
		int t = A[i];
		A[i] = A[j];
		A[j] = t; 
	}
	public static void printArr(int[] A){
		for(int i=0;i<A.length;i++){
			if(i!=0) System.out.print(" "+A[i]);
			else System.out.print(A[i]);
		}
	}
}