Question

This might be a weird question but I’m trying to figure out why the following code works.

It seems as though this code should be used where the heap elements index starts at 1 but it’s starting at 0 and the sort is completed correctly.

I say that because the left child is calculated as (element*2) and the right child is (element*2 + 1). This would make the left child for the element with index 0 also have index 0.

#include <iostream>
using namespace std;

void siftDown(int numbers[], int root, int bottom) {
    int done, maxChild, temp;
    done = 0;
    while ((root*2 <= bottom) && (!done)) {
        if (root*2 == bottom)
            maxChild = root * 2;
        else if (numbers[root*2] > numbers[root*2 + 1])
            maxChild = root * 2;
        else
            maxChild = root * 2 + 1;

        if (numbers[root] < numbers[maxChild]) {
            temp = numbers[root];
            numbers[root] = numbers[maxChild];
            numbers[maxChild] = temp;
            root = maxChild;
        } else {
            done = 1;
        }
    }
}

void heapSort(int numbers[], int n) {
    int i, temp;

    for (i = n/2; i >= 0; i--) {
        siftDown(numbers, i, n - 1);
    }

    for (i = n-1; i >= 1; i--) {
        temp = numbers[0];
        numbers[0] = numbers [i];
        numbers [i] = temp;
        siftDown(numbers, 0, i-1);
    }
}

int main() {
    int cases;
    int n;
    int count;

    cin >> cases;

    for (int i=0; i < cases; i++) {
        cin >> n;
        int array[n];
        for (int j=0; j < n; j++) {
            cin >> array[j];
        }

        heapSort(array, n);
        for (int k=0; k < n; k++) {
            cout << array[k];
        }    
        cout << endl;
    }
}

Answer 1

For the case when root = 0, there are two sub-cases: numbers[0] > numbers[1], or not. In the first, maxchild is set to 0. The next “if” clause – effectively “numbers[0] < numbers[0]” – necessarily evaluates to false, and so “done” is set to 1 and the loop terminates.

If numbers[1] >= numbers[0], then maxchild is set to 1. The next clause becomes “numbers[0] < numbers[1]” which may be true or may be false if numbers[0] == numbers[1]. If it is false, the loop terminates as before. If it is true, numbers[0] and numbers[1] are swapped – thus the larger number correctly moves to the top of the heap – and root becomes 1, the loop continues and in this case you understand how it works.

I think it’s easiest to consider this case as a heap where the root only has one child (and all other nodes have two children as normal).