recursion - data structure course - print all possible series - c

Question

I need to print all possible series that their sum is equal to N;
for example is n == 4 the output should be:
[1, 1, 1, 1]
[1, 1, 2]
[1, 2, 1]
[1, 3]
[2, 1, 1]
[2, 2]
[3, 1]
[4]
My way of thinking to solve this problem was:
print the series that the number i is not in the series
print the series that the number i is in the series, now need to find the sum of N-i.
my code:
#include <stdio.h>
#include <stdlib.h>
void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++)
{
printf(" %d ", arr[i]);
}
printf("\n");
}
void printAllHelper(int* a,int size, int sum, int used,int index) {
if (sum == 0) {
a -= used;
printArr(a, used);
}
else if (sum < 0 || index == size)
{
return;
}
else {
for(int i = 1 ; i <= size ; i ++)
{
printAllHelper(a, size, sum, used, index + 1);
if (i <= sum)
{
*a = i;
}
printAllHelper(a+1, size, sum -i, used +1, index + 1);
}
}
}
void printAll(int num) {
int* myArray = (int*)malloc(num * sizeof(int));
printAllHelper(myArray,num,num,0,0);
}
void main() {
printAll(4);
}
my output:
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
3 1
4
1 3
4
2 2
4
3 1
4
4
1 3
1 1 2
1 3
1 2 1
1 3
1 3
1 3
4
1 3
4
2 2
4
3 1
4
4
2 2
2 1 1
2 2
2 2
2 2
2 2
4
1 3
4
2 2
4
3 1
4
4
3 1
3 1
3 1
3 1
3 1
4
1 3
4
2 2
4
3 1
4
4
4
4
Please try to explain to me your way of thinking, and how you approach this kind of problem, I want to be the very best like no one ever was :(.....

Answer 1

Your reasoning is not quite correct, but your code is almost right. The loop in your else part should be
for(int i = 1 ; i <= sum ; i ++) {
*a = i;
printAllHelper(a+1, size, sum-i, used+1, index+1);
}
With this, I get the output
1 1 1 1
1 1 2
1 2 1
1 3
2 1 1
2 2
3 1
4
The idea is basically: "The numbers sum to sum if the first number i is any number from 1 to sum and the rest of the numbers sum to sum - i."
Also, note that your code shows some room for improvement, e.g. the used and index variables seem a bit redundant. And with not adding numbers larger than sum or smaller than 1, the check whether sum < 0 || index == size is not necessary, either. Thus you also do not need the size parameter. Your printAllHelper could be simplified to something like this:
void printAllHelper(int* a, int sum, int index) {
if (sum == 0) {
printArr(a, index);
} else {
for(int i = 1 ; i <= sum ; i++) {
a[index] = i;
printAllHelper(a, sum-i, index+1);
}
}
}
(Note: C is not my native language, if you see more things to improve, please comment.)