is it a Heap Max?

Question

For a project, am i working with heaps. In this project i have to "investigate" whether an array is a max heap.

These 2 rules apply for a max heap:

1. The parent shall be bigger or equal to its child / children
2. Each node, in a heap, shall contain an element

Therefore have i created 2 for loops checking whether these rules apply. Unfortunately for me, my code doesn't work.

I have 2 for loops:

 //Checks if there's a 0 value in the array. If so: Return false

    for (int i = 1; i <= A.length; i++) {
        System.out.println("A.length: " + A[i]);
        if (A[i] == 0) {
            System.out.println("weweh: "+ A[i]);
            return false;
        }

//Checks if either left or right child have a bigger value than itself

    for (int i = 1; i <= (A.length - 2) / 2; i++) {
        System.out.println("A: " + i);
        if (A[i] < A[2 * i] || A[i] < A[2 * i + 1]) {
            return false;
        }
    }


 //the array


 int A[] = {0, 40, 35, 30, 25, 15, 10, 5};

The last for loop works, but for some reason i get a mistake in the first for loop. The loop can find a number. Lets say that i picked 15 to be equal with A[i], then it would work and return false, but when the selected number 0 isn't there, then it sends me the error, and it wont go further for the second loop.

 //Error:

 A.length: 40
A.length: 35
Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 8
A.length: 30
A.length: 25
A.length: 15
A.length: 10
A.length: 5
    at ismaxheap.IsMaxHeap.MaxHeap(IsMaxHeap.java:24)
    at ismaxheap.IsMaxHeap.main(IsMaxHeap.java:15)
/Users/yusuf/Library/Caches/NetBeans/8.2/executor-snippets/run.xml:53: Java returned: 1
BUILD FAILED (total time: 0 seconds)

THE WHOLE CODE:

public class IsMaxHeap {

public static void main(String[] args) {
    MaxHeap();
    System.out.println("Max Heap:  " + MaxHeap());
}

public static boolean MaxHeap() {

    int A[] = {0, 40, 35, 30, 25, 15, 10, 5};

    for (int i = 1; i <= A.length; i++) {
        System.out.println("A.length: " + A[i]);
        if (A[i] == 0) {
            System.out.println("weweh: "+ A[i]);
            return false;
        }
    } 

    for (int i = 1; i <= (A.length - 2) / 2; i++) {
        System.out.println("A: " + i);
        if (A[i] < A[2 * i] || A[i] < A[2 * i + 1]) {
            return false;
        }
    }
    return true;
}

}

Answer 1

In your first loop you are looping one more than possible by using <=

for (int i = 1; i <= A.length; i++) 

Since you are trying to access A[i] and if i == A.length then you are out of bounds.

Should be:

for (int i = 1; i < A.length; i++) 

Now I don't know why are you starting at index 1 since indexing in Java start with 0.

Dealing with special case of one child

This is the case when you array length is 3 (Since the zero index is ignored)

All you have to check is if A[2] < A[1] to be a Max heap, otherwise return false immediately.

Otherwise do the normal loop.