Convert nested loop to recursion - c

Question

I have used 3 nested loop. Now i want to convert these loops to recursive.
Also is there a general way to convert a loop into recursive?
#include <stdio.h>
#define f(x, y, z) ((x + y) * (y + z))
int main()
{
int test_case, p, q, r, i, j, k, a[100001], b[100001], c[100001], sum;
scanf("%d", &test_case);
while (test_case--) {
scanf("%d%d%d", &p, &q, &r);
sum = 0;
for (i = 0; i < p; i++) {
scanf("%d", &a[i]);
}
for (i = 0; i < q; i++) {
scanf("%d", &b[i]);
}
for (i = 0; i < p; i++) {
scanf("%d", &c[i]);
}
for (i = 0; i < q; i++) { // I have convert this to recursion.
for (j = 0; j < p; j++) {
for (k = 0; k < r; k++) {
if (b[i] >= a[j] && b[i] >= c[k]) {
sum += f(a[j], b[i], c[k]);
}
}
}
}
printf("%d\n", sum % 1000000007);
}
return 0;
}

Answer 1

A loop like:
for (int i=0; i<n; i++) {
func(i);
}
can be translated to recursion as:
void rec_fun(int i,int n) {
if (!(i<n)) return;
func(i);
rec_fun(i+1,n);
}
...
rec_fun(0,n);
So:
for (i = 0; i < q; i++) { // I have convert this to recursion.
for (j = 0; j < p; j++) {
for (k = 0; k < r; k++) {
if (b[i] >= a[j] && b[i] >= c[k]) {
sum += f(a[j], b[i], c[k]);
}
}
}
}
can be translated as:
void rec_k(int k,int r,int i,int j) { // k-loop
if (!(k<r)) return;
if (b[i] >= a[j] && b[i] >= c[k]) {
sum += f(a[j], b[i], c[k]);
}
rec_k(k+1,r,i,j); // recurse
}
void rec_j(int j,int p,int i,int r) { // j-loop
if (!(j<p)) return;
rec_k(0,r,i,j); // inner loop
rec_j(j+1,p,i,r); // recurse
}
void rec_i(int i,int q,int p,int r) { // i-loop
if (!(i<q)) return;
rec_j(0,p,i,r); // inner loop
rec_i(i+1,q,p,r); // recurse
}
...
rec_i(0,q,p,r);
I'm not sure this is either more readable or useful, but it meets your initial needs.

Answer 2

Let us assume that the intention of this code is to only calculate the sum.
You can make a function as
int recurse_sum(int i, int j, int k) {
int res = .... // Logic for calculating sum for these indices i, j, k.
k++;
if (k==r) {
k = 0;
j++;
}
if(j==p){
j=0;
i++;
}
if(i==q){
return res;
}
return res + recurse_sum(i,j,k);
}
Now you can just call with recurse_sum(0,0,0);
The rest of the parameters can either be made global or just passed along with i,j,k.
I hope this helps.
Edit:
As mentioned by #dlasalle this code can be made open to tail call recursion optimization by placing the call at the end of the function.
In that case you can have the following version.
int recurse_sum(int i, int j, int k, int sum) {
int res = .... // Logic for calculating sum for these indices i, j, k.
k++;
if (k==r) {
k = 0;
j++;
}
if(j==p){
j=0;
i++;
}
if(i==q){
return res + sum;
}
return recurse_sum(i,j,k,res+sum);
}
Here the function ends with returning the value from the inner call and hence can be easily optimized.
Ofcourse in this case it will have to be called as recurse_sum(0,0,0,0);

Answer 3

Thanks to #Jean-Baptiste Yunès .
I made these changes to my code to convert it to recursive.
#include<stdio.h>
#define f(x, y, z) ((x + y)*(y + z))
int sum=0;
void rec_k(int k,int r,int i,int j,int a[],int b[],int c[]) { // k-loop
if (!(k<r)) return;
if (b[i] >= a[j] && b[i] >= c[k]) {
sum += f(a[j], b[i], c[k]);
}
rec_k(k+1,r,i,j,a,b,c);
}
void rec_j(int j,int p,int i,int r,int a[],int b[],int c[]) { // j-loop
if (!(j<p)) return;
rec_k(0,r,i,j,a,b,c);
rec_j(j+1,p,i,r,a,b,c);
}
void rec_i(int i,int q,int p,int r,int a[],int b[],int c[]) { // i-loop
if (!(i<q)) return;
rec_j(0,p,i,r,a,b,c);
rec_i(i+1,q,p,r,a,b,c);
}
int main() {
int test_case, p, q, r, i, j, k, a[100001], b[100001], c[100001];
scanf("%d", &test_case);
while(test_case--) {
scanf("%d%d%d", &p, &q, &r);
sum=0;
for(i=0;i<p;i++) {
scanf("%d", &a[i]);
}
for(i=0;i<q;i++) {
scanf("%d", &b[i]);
}
for(i=0;i<p;i++) {
scanf("%d", &c[i]);
}
rec_i(0,q,p,r,a,b,c);
printf("%d\n", sum%1000000007);
}
return 0;
}