# Non-Recursive Merge Sort

Non-recursive merge sort works by considering window sizes of 1,2,4,8,16..2^n over the input array. For each window (‘k’ in code below), all adjacent pairs of windows are merged into a temporary space, then put back into the array.

Here is my single function, C-based, non-recursive merge sort.
Input and output are in ‘a’. Temporary storage in ‘b’.
One day, I’d like to have a version that was in-place:

``````float a[50000000],b[50000000];
void mergesort (long num)
{
int rght, wid, rend;
int i,j,m,t;

for (int k=1; k < num; k *= 2 ) {
for (int left=0; left+k < num; left += k*2 ) {
rght = left + k;
rend = rght + k;
if (rend > num) rend = num;
m = left; i = left; j = rght;
while (i < rght && j < rend) {
if (a[i] <= a[j]) {
b[m] = a[i]; i++;
} else {
b[m] = a[j]; j++;
}
m++;
}
while (i < rght) {
b[m]=a[i];
i++; m++;
}
while (j < rend) {
b[m]=a[j];
j++; m++;
}
for (m=left; m < rend; m++) {
a[m] = b[m];
}
}
}
}
``````

By the way, it is also very easy to prove this is O(n log n). The outer loop over window size grows as power of two, so k has log n iterations. While there are many windows covered by inner loop, together, all windows for a given k exactly cover the input array, so inner loop is O(n). Combining inner and outer loops: O(n)*O(log n) = O(n log n).