Invalid results in merge sort application - arrays

Question

Hello I am working on an application of the merge sort algorithm however after a few hours I am unable to find a solution. Any help or hint would be appreciated. I have tried to debug my code but after many attempts I have not been successful in seeing what the mistake is.
The problem is that the algorithm gives back a wrong result. Example:
input: (10, 5, 16, 2)
output: (2, 5, 5, 10)
#include <stdio.h>
void mergesort(int A[], int l, int r);
void merge(int A[], int l, int q, int r);
int main() {
int n;
scanf("%d", &n);
int tablica[n];
for (int i = 0; i < n; i++)
scanf("%d", &tablica[i]);
mergesort(tablica, 0, n - 1);
for (int i = 0; i < n; i++)
printf("%d ", tablica[i]);
return 0;
}
void mergesort(int A[], int l, int r) {
if (l < r) {
int q = (l + r) / 2;
mergesort(A, l, q);
mergesort(A, q + 1, r);
merge(A, l, q, r);
}
}
void merge(int A[], int l, int q, int r) {
int n = q - l + 1;
int m = r - q;
int B[n];
int C[m];
for (int i = 0; i < n; i++)
B[i] = A[i];
for (int i = 0; i < m; i++)
C[i] = A[q + 1 + i];
int i = 0;
int j = 0;
for (int k = l; k <= r; k++) {
if (B[i] <= C[j] || j >= m) {
A[k] = B[i];
i++;
} else {
A[k] = C[j];
j++;
}
}
}

Answer 1

Without knowing what exactly doesn't work (Does it not compile? Do you get wrong output for some inputs?) it's hard to help. At least one error is here:
if(B[i] <= C[j] || j >= m)
Should be
if(j >= m || i < n && B[i] <= C[j])
It is both important to check j >= m before you check the inequality, and add the i < n check.
Without the latter once you fully consume the B array, B[i] will go beyond the array boundaries, and you will get undefined behavior.
Without the former once j >= m the condition B[i] <= C[j] will be checked before j >= m, also triggering undefined behavior.
UPDATE: with the actual example you provided, the second error narrows down to replacing B[i] = A[i] with B[i] = A[l + i]. With these two changes the example you provided works.

Answer 2

The function merge has several bugs.
For example the size of the array C shall be calculated like
int m = r - q + 1;
instead of
int m = r - q;
Instead of this for loop
for(int i = 0; i < n; i++)
B[i] = A[i];
you have to write
for(int i = 0; i < n; i++)
B[i] = A[l + i];
This if statement
if(B[i] <= C[j] || j >= m)
can result in undefined behavior because there is no check of the validity of the used indices i and j whether they belong to the valid ranges.
The functions can be defined the following way as it is shown in the demonstrative program below.
#include <stdio.h>
void merge( int a[], size_t left, size_t middle, size_t right )
{
size_t n1 = middle - left;
size_t n2 = right - middle;
int a1[n1];
int a2[n2];
for ( size_t i = 0; i < n1; i++ )
{
a1[i] = a[left + i];
}
for ( size_t i = 0; i < n2; i++ )
{
a2[i] = a[middle + i];
}
size_t i = left, i1 = 0, i2 = 0;
while ( i1 < n1 && i2 < n2 )
{
a[i++] = a2[i2] < a1[i1] ? a2[i2++] : a1[i1++];
}
while ( i1 < n1 ) a[i++] = a1[i1++];
while ( i2 < n2 ) a[i++] = a2[i2++];
}
void mergesort( int a[], size_t left, size_t right )
{
if ( left + 1 < right )
{
size_t middle = ( left + right ) / 2;
mergesort( a, left, middle );
mergesort( a, middle, right );
merge( a, left, middle, right );
}
}
int main(void)
{
size_t n;
if ( scanf( "%zu", &n ) == 1 && n != 0 )
{
int a[n];
for ( size_t i = 0; i < n; i++ ) scanf( "%d", a + i );
mergesort( a, 0, n );
for ( size_t i = 0; i < n; i++ )
{
printf( "%d ", a[i] );
}
putchar( '\n' );
}
return 0;
}
If the input is
4
10 5 16 2
then the output will be
2 5 10 16

Answer 3

There is a bug in the merge function:
if (B[i] <= C[j] || j >= m) accesses B[i] and C[j] before testing if i and j are below their respective boundaries. The test should be:
if (i < n && (j >= m || B[i] <= C[j])) {
A[k] = B[i++];
} else {
A[k] = C[j++];
}
Note also these remarks:
you do not need to save the second half of the array because its elements are copied before they get overwritten.
in void mergesort(int A[], int l, int r) r should be excluded, to avoid confusing and error prone +1/-1 adjustments.
similarly, in void merge(int A[], int l, int q, int r), q should be the start of the second half and r the index of the element after the end of the slice.
l looks confusingly similar to 1
Here is a modified version:
#include <stdio.h>
void mergesort(int A[], int low, int high);
void merge(int A[], int low, int mid, int high);
int main() {
int n;
if (scanf("%d", &n) != 1 || n <= 0)
return 1;
int tablica[n];
for (int i = 0; i < n; i++) {
if (scanf("%d", &tablica[i]) != 1)
return 1;
}
mergesort(tablica, 0, n);
for (int i = 0; i < n; i++)
printf("%d ", tablica[i]);
printf("\n");
return 0;
}
void mergesort(int A[], int low, int high) {
if (high - low >= 2) {
int mid = low + (high - low) / 2;
mergesort(A, low, mid);
mergesort(A, mid, high);
merge(A, low, mid, high);
}
}
void merge(int A[], int low, int mid, int high) {
int n = mid - low;
int B[n];
for (int i = 0; i < n; i++)
B[i] = A[low + i];
int i = 0;
int j = mid;
int k = low;
while (i < n) {
if (j >= high || B[i] <= A[j]) {
A[k++] = B[i++];
} else {
A[k++] = C[j++];
}
}
}