Java heapsort program error during runtime

Question

My code is working during compilation but the runtime error points to an if condition in my MaxHeapify function. I marked it out. Any help would be simply lovely, and would make me stop banging my head against the wall.

public class HeapSort {

    public static void main(String[] args) {
        int A[] = {-100, 1, 2, 5, 7, 2, 9};
        Heapsort(A);
        //System.out.println(A.length);
        for (int x = 1; x < A.length; x++) {
            System.out.println(A[x] + " ");
        }
    }

    public static void Build_MAX_heap(int A[]) {
        int n = A.length;
        for (int i = n / 2; i >= 1; i--) {
            MAX_heapify(A, i);
        }
    }

    public static void MAX_heapify(int A[], int i) {
        int heapsize = A.length;
        int l = 2 * i;
        int r = 2 * i + 1;
        //find the largest of A[i].A[l],A[r]
        int largest = i;
        if (A[l] > A[largest]) {
            largest = l;
            if (A[l] > A[largest] && l <= heapsize) {
                largest = l;
            }
            if (A[r] > A[largest] && r <= heapsize) {     //runtime error here
                largest = r;
            }
            if (largest != i) {
                int temp = A[i];
                A[i] = A[largest];
                A[largest] = temp;
                MAX_heapify(A, largest);
            }
        }
    }

    public static void Heapsort(int A[]) {

        Build_MAX_heap(A);
        int heapsize = A.length;
        for (int last = heapsize; last >= 2; last--) {   
            int temp = A[1];
            A[1] = A[last];
            A[last] = temp;
            heapsize--;
            MAX_heapify(A,1);
        }
    }
}

Answer 1

Variable r is set to:

int r = 2 * i + 1;

In first case of loop:

for (int i = n / 2; i >= 1; i--) {
    MAX_heapify(A, i);
}

i is n/2

so to function is passed:

MAX_heapify(A,n/2);

and r is 2 * (n/2) + 1 which is n+1

when you want to do this line

if (A[r] > A[largest] && r <= heapsize) {

then A[r] is A[n+1]=A[A.length+1] - this causes IndexOutOfBoundsException