Java: check if array is heap

问题

I am trying to implement that checks whether a given array is a heap.

public static boolean Heap(int[] A)
{
    for (int i = 1; i <= (A.length - 2) / 2; i++) {
        if (A[i] < A[2 * i] || A[i] < A[2 * i + 1]) {
            return false;
        }
    }
    return true;
}

A = {50, 45, 40, 35, 20, 25, 20};
B = {45, 50, 40, 35, 20, 25, 20};

    if (Heap(A)) {
        System.out.println("Heap");
    } else {
        System.out.println("Not a heap");
    }

When I call the function for the arrays above, they both return true, while B should have been caught in the if statement if (A[i] < A[2 * i]...

What am I doing wrong?

回答1:

Perhaps this is what you want:

public static void main(String... args) {
    int[] A = {50, 45, 40, 35, 20, 25, 20};
    int[] B = {45, 50, 40, 35, 20, 25, 20};
    System.out.println(isMaxHeap(A));
    System.out.println(isMaxHeap(B));
}

private static boolean isMaxHeap(int[] arr) {
    int N = arr.length;
    for (int i = (N - 2) / 2; i > -1; --i) { // start from the first internal node who has children;
        int j = 2 * i + 1; // the left child;
        if (j < N - 1 && arr[i] < arr[j+1]) j++; // select the bigger child;
        if (arr[i] < arr[j]) return false; // if parent is smaller than the child;
    }
    return true;
}

But do please show some efforts next time before asking.

回答2:

The bottom-up solution is simple: check each node to see that it's not greater than its parent. For a min-heap, change the > to <:

for (int i = a.length-1; i > 0; --i)
{
    int parent = (i-1)/2;
    if (a[i] > a[parent]) return false;
}
return true;

You'll often see the recursive solution:

bool isMaxHeap(int[] a)
{
    return isMaxHeap(a, 0);
}

bool isMaxHeap(int[] a, int ix)
{
    int leftChild = (ix*2)+1;
    if (leftChild < a.length)
    {
        if (a[leftChild] > a[ix]) return false;
        if (!isMaxHeap(a, leftChild) return false;
    }

    int rightChild = leftChild+1;
    if (rightChild < a.length)
    {
        if (a[rightChild] > a[ix]) return false;
        if (!isMaxHeap(a, rightChild) return false;
    }
    return true;
}

The idea here is that in a heap, every subtree is also a heap. So we check the top level, then check each branch of the tree. We apply that recursively.

来源：https://stackoverflow.com/questions/51584921/java-check-if-array-is-heap

标签

java

algorithm

heap