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: Wrong Answer)

import java.util.Scanner;
public class Main{
	static int[]heap;
    static int MAXHEAP=500000;
    static int n;
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int i;
		heap=new int[MAXHEAP+1];
       Scanner sca= new Scanner(System.in);
       n=sca.nextInt();
       for(i=1;i<=n;i++){
    	   heap[i]=sca.nextInt();
    	   heap[i*2]=heap[i*2+1]=-1;
       }
       buildMaxHeap();
       for(i=1;i<=n;i++){
      System.out.print(" "+heap[i]);
      if(i==n)System.out.println("");
       }
	}
	public static void maxHeapify(int i){
		int l=i*2,r=i*2+1,largest,hz;
		if(i<=n&&heap[l]>heap[i]){
			largest=l;
		}else{
			largest=i;
		}
		if(r<=n&&heap[r]>heap[largest])largest=r;
		if(largest!=i){
			hz=heap[largest];
			heap[largest]=heap[i];
			heap[i]=hz;
			maxHeapify(largest);
		}
	}
	public static void buildMaxHeap(){
		int i;
		for(i=n/2;i>=1;i--){
			maxHeapify(i);
		}
	}

}