Weird Behaviour of Merge Sort Algorithm in C++

Question

I have implemented a merge sort algorithm, but it has a very weird bug which is hard to explain so please look at the code and output.

CODE:-

#include <bits/stdc++.h>

using namespace std;

int merge(int *ar, int l, int r) {
    int aux[r - l + 1], s1 = 0, s2 = (r - l) / 2 + 1;

    for (int i = 0; i < r - l + 1; i++)
        aux[i] = ar[l + i];
    for (int k = 0; k < r - l + 1; k++) {
        if (s1 > ((r - l) / 2))
            ar[l + k] = aux[s2++];
        else
        if (s2 > r)
            ar[l + k] = aux[s1++];
        else
        if (aux[s1] <= aux[s2])
            ar[l + k] = aux[s1++];
        else
            ar[l + k] = aux[s2++];
    }
    //for (int i = 0; i < 17; i++) cout << ar[i] << " ";
    //cout << endl;
    return 0;
}

void  mergesort(int *ar, int l, int r) {
    if (l >= r)
        return;
    int mid = (l + r) / 2;
    mergesort(ar, l, mid);
    mergesort(ar, mid + 1, r);
    merge(ar, l, r);
}

int main() {
    int ar[] ={ 34, 54, 56, 42, 32, 46, 99, 85, 5, 45, 34, 54, 6, 56, 54, 64, 5 },
        l = 0, r = sizeof(ar) / sizeof(int) - 1;
    mergesort(ar, l, r);
    for (int i = 0; i < r + 1; i++)
        cout << ar[i] << " ";
    return 0;
}

OUTPUT:-

5 5 6 16 16 16 32 16 34 34 16 46 54 54 16 56 99

I don't know where are these 16 are coming from, this does not happen for array of single digit numbers of any length and small arrays of 2 digit numbers. Also, if I cout anything in the merge function (like spaces, tabs, new lines or any number) I get the correct output i.e,

        5 5 6 32 34 34 42 45 46 54 54 54 56 56 56 64 99

[I have printed spaces here.]

I tried changing function parameters but it does not help. Please help I cannot figure this out on my own.

Answer 1

In the merge function, the test if (s2 > r) is incorrect. It should be if (s2 > r - l).

It is very confusing to pass r as the index of the last element. In C and C++, it is more idiomatic to pass the index of the element after the last one, so r - l be the length of the array. With this approach, there are no error-prone +1/-1 adjustments.

Here is a modified version:

#include <iostream>

using namespace std;

void merge(int *ar, int l, int r) {
    int len = r - l;
    int mid = len / 2;
    int s1 = 0, s2 = mid;
    int aux[len];

    for (int i = 0; i < len; i++)
        aux[i] = ar[l + i];
    for (int k = l; k < r; k++) {
        if (s1 >= mid)
            ar[k] = aux[s2++];
        else
        if (s2 >= len)
            ar[k] = aux[s1++];
        else
        if (aux[s1] <= aux[s2])
            ar[k] = aux[s1++];
        else
            ar[k] = aux[s2++];
    }
}

void mergesort(int *ar, int l, int r) {
    if (r - l >= 2)
        return;
    int mid = l + (r - l) / 2;
    mergesort(ar, l, mid);
    mergesort(ar, mid, r);
    merge(ar, l, r);
}

int main() {
    int ar[] = { 34, 54, 56, 42, 32, 46, 99, 85, 5, 45, 34, 54, 6, 56, 54, 64, 5 };
    int len = sizeof(ar) / sizeof(ar[0]);
    mergesort(ar, 0, len);
    for (int i = 0; i < len; i++)
        cout << ar[i] << " ";
    cout << endl;
    return 0;
}