Sorting integers by sum of their digits - c

Question

I'm trying to write a program that will sort an array of 20 random numbers by the sums of their digits.
For example:
"5 > 11" because 5 > 1+1 (5 > 2).
I managed to sort the sums but is it possible to return to the original numbers or do it other way?
#include <stdio.h>
void sortujTab(int tab[], int size){
int sum,i;
for(int i=0;i<size;i++)
{
while(tab[i]>0){//sum as added digits of an integer
int p=tab[i]%10;
sum=sum+p;
tab[i]/=10;
}
tab[i]=sum;
sum=0;
}
for(int i=0;i<size;i++)//print of unsorted sums
{
printf("%d,",tab[i]);
}
printf("\n");
for(int i=0;i<size;i++)//sorting sums
for(int j=i+1;j<=size;j++)
{
if(tab[i]>tab[j]){
int temp=tab[j];
tab[j]=tab[i];
tab[i]=temp;
}
}
for(int i=0;i<20;i++)//print of sorted sums
{
printf("%d,",tab[i]);
}
}
int main()
{
int tab[20];
int size=sizeof(tab)/sizeof(*tab);
for(int i=0;i<=20;i++)
{
tab[i]=rand()%1000;// assamble the value
}
for(int i=0;i<20;i++)
{
printf("%d,",tab[i]);//print unsorted
}
printf("\n");
sortujTab(tab,size);
return 0;
}

Answer 1

There are two basic approach :
Create a function that return the sum for an integer, say sum(int a), then call it on comparison, so instead of tab[i] > tab [j] it becomes sum(tab[i]) > sum (tab[j])
Store the sum into a different array, compare with the new array, and on swapping, swap both the original and the new array
The first solution works well enough if the array is small and takes no extra memory, while the second solution didn't need to repeatedly calculate the sum. A caching approach is also possible with map but it's only worth it if there are enough identical numbers in the array.

Answer 2

Since your numbers are non-negative and less than 1000, you can encode the sum of the digits in the numbers itself. So, this formula will be true: encoded_number = original_number + 1000 * sum_of_the_digits. encoded_number/1000 will decode the sum of the digits, and encoded_number%1000 will decode the original number. Follow the modified code below. The numbers enclosed by parentheses in the output are original numbers. I've tried to modify minimally your code.
#include <stdio.h>
#include <stdlib.h>
void sortujTab(int tab[], int size)
{
for (int i = 0; i < size; i++) {
int sum = 0, n = tab[i];
while (n > 0) { //sum as added digits of an integer
int p = n % 10;
sum = sum + p;
n /= 10;
}
tab[i] += sum * 1000;
}
for (int i = 0; i < size; i++) { //print of unsorted sums
printf("%d%c", tab[i] / 1000, i < size - 1 ? ',' : '\n');
}
for (int i = 0; i < size; i++) { //sorting sums
for (int j = i + 1; j < size; j++) {
if (tab[i] / 1000 > tab[j] / 1000) {
int temp = tab[j];
tab[j] = tab[i];
tab[i] = temp;
}
}
}
for (int i = 0; i < size; i++) { //print of sorted sums
printf("%d(%d)%c", tab[i] / 1000, tab[i] % 1000, i < size - 1 ? ',' : '\n');
}
}
int main(void)
{
int tab[20];
int size = sizeof(tab) / sizeof(*tab);
for (int i = 0; i < size; i++) {
tab[i] = rand() % 1000; // assamble the value
}
for (int i = 0; i < size; i++) {
printf("%d%c", tab[i], i < size - 1 ? ',' : '\n'); //print unsorted
}
sortujTab(tab, size);
return 0;
}
If the range of numbers doesn't allow such an encoding, then you can declare a structure with two integer elements (one for the original number and one for the sum of its digits), allocate an array for size elements of this structure, and initialize and sort the array using the digit sums as the keys.

Answer 3

You can sort an array of indexes rather than the array with data.
#include <stdio.h>
//poor man's interpretation of sumofdigits() :-)
int sod(int n) {
switch (n) {
default: return 0;
case 5: return 5;
case 11: return 2;
case 1000: return 1;
case 9: return 9;
}
}
void sortbyindex(int *data, int *ndx, int size) {
//setup default indexes
for (int k = 0; k < size; k++) ndx[k] = k;
//sort the indexes
for (int lo = 0; lo < size; lo++) {
for (int hi = lo + 1; hi < size; hi++) {
if (sod(data[ndx[lo]]) > sod(data[ndx[hi]])) {
//swap indexes
int tmp = ndx[lo];
ndx[lo] = ndx[hi];
ndx[hi] = tmp;
}
}
}
}
int main(void) {
int data[4] = {5, 11, 1000, 9};
int ndx[sizeof data / sizeof *data];
sortbyindex(data, ndx, 4);
for (int k = 0; k < sizeof data / sizeof *data; k++) {
printf("%d\n", data[ndx[k]]);
}
return 0;
}