Debugging a Sums of Digit Factorials - c++

Question

I would to solve this problem illustrated in this image using C++
Define f(n) as the sum of the factorials of the digits of n. For example, f(342) = 3! + 4! + 2! = 32.
Define sf(n) as the sum of the digits of f(n). So sf(342) = 3 + 2 = 5.
Define g(i) to be the smallest positive integer n such that sf(n) = i. Though sf(342) is 5, sf(25) is also 5, and it can be verified that g(5) is 25.
Define sg(i) as the sum of the digits of g(i). So sg(5) = 2 + 5 = 7.
Further, it can be verified that g(20) is 267 and ∑ sg(i) for 1 ≤ i ≤ 20 is 156.
What is ∑ sg(i) for 1 ≤ i ≤ 150?
Image:
Here is my approach. My code takes long time running, and it works
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int factorial(int n);
std::vector<int> int_to_vector(int n);
int sum_vector(std::vector<int> v);
int get_smallest_number(std::vector<int> v, int sum, int n);
int sum_sg(int n )
int main() {
/* Enter your code here. Read input from STDIN. Print output to STDOUT */
int q;
int m,n;
int g;
int sum = 0;
std::vector<int> vec;
cin>>q;
if( 1<=q && q<=100000){
std::vector<int> s;
int fact = 0;
int sg = 0;
for ( int i = 0; i < q; i++){
cin>>n>>m;
fact = factorial(n);
s = int_to_vector(fact);
sum = sum_vector(s);
g = get_smallest_number(s, sum, n);
s = int_to_vector(g);
sum = sum_vector(s);
}
}
return 0;
}
int factorial(int n){
if (n==0) return 1;
return factorial(n-1)*n;
}
std::vector<int> int_to_vector(int n){
std::vector<int> numbers;
while(n>0)
{
numbers.push_back(n%10);
n/=10;
}
return numbers;
}
int sum_vector(std::vector<int> v){
int sum=0;
for(int i = 0; i < v.size(); i++){
sum+=v.at(i);
}
return sum;
}
int get_smallest_number(std::vector<int> v, int sum, int n){
int i = 0;
int factoriel = 1;
std::vector<int> vect;
int sum2 = 0;
while( i < n){
factoriel = factorial(i);
vect = int_to_vector(factoriel);
sum2 = sum_vector(vect);
if( sum2 == sum) return i;
i++ ;
}
return n;
}
I think on recursive solutions, but it seems somehow more complex to implement. Are there any solutions using modern C++ and STL?

Answer 1

Here is below a bad solution with less complexity, please any suggestion to have good and fast code rather than this below,
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
std::vector<int> factorial {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880};
std::vector<int> int_to_vector(int n);
int sum_vector(std::vector<int> v);
int find_g(int i);
int calculat_sum_fact(std::vector<int> v);
int main() {
/* Enter your code here. Read input from STDIN. Print output to STDOUT */
int m,n,q;
std::vector<int> vec;
std::vector<int> s;
std::vector<int> numbers;
cin>>q;
for (int i = 0; i < q; i++){
cin>>n>>m;
numbers.push_back(n);
// cout<< numbers.at(i);
}
for(int k = 0; k < numbers.size(); k++){
int sum = 0;
for (int i = 0; i < numbers.at(k)+1; i++){
s = int_to_vector(find_g(i));
sum += sum_vector(s);
}
cout << sum << "\n";
}
return 0;
}
std::vector<int> int_to_vector(int n){
std::vector<int> numbers;
while(n>0)
{
numbers.push_back(n%10);
n/=10;
}
return numbers;
}
int sum_vector(std::vector<int> v){
int sum=0;
for(int i = 0; i < v.size(); i++){
sum+=v.at(i);
}
return sum;
}
int find_g(int i){
std::vector<int> s ;
int sum = 0;
int j = 0;
//cout<<"sf 1= " << j << endl;
while(true){
s = int_to_vector(j);
sum = calculat_sum_fact(s);
s= int_to_vector(sum);
sum = sum_vector(s);
//cout<<"sf 2= " << j << endl;
if (sum == i) {
//cout<<"sf = " << j << endl;
return j;
//break;
}
//cout<<"sf = " << j << endl;
j++;
}
}
int calculat_sum_fact(std::vector<int> v){
int sum = 0;
for(int i = 0; i < v.size(); i++ ){
sum += factorial.at(v.at(i));
}
return sum;
}