Java heapsort program error during runtime

You're doing you bounds checking for r (and l, too, in the previous statement) after checking the element at index r. If r is out of bounds, the first half of the expression will throw an exception, and never make it to the bounds check.

Your if statements should be structured

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

so that you know you're in bounds before you start trying to access your array. In addition, since arrays are zero-indexed, the index of heapsize isn't valid, so r needs to be less than, not less than or equal to.

Your problem is that your are checking A[r] before checking if r is out of range so i would try to modify the code this way

 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 (r<=heapsize && A[r] > A[largest]) {     //modification 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);
    }
}

}