C++ program to find minimum how many operations needed to make number 0

Suppose we have a numeric string S with n digits. Consider S represents a digital clock and whole string shows an integer from 0 to 10^n - 1. If there are a smaller number of digits, it will show leading 0s. Follow the operations −

Decrease the number on clock by 1, or
Swap two digits

We want the clock will show 0 with minimum number of operations needed. We have to count the number of operations needed to do that.

So, if the input is like S = "1000", then the output will be 2, because we can swap first 1 with last 0, so the string will be "0001" now decrease it by 1 to get "0000".

Steps

To solve this, we will follow these steps −

n := size of S
x := digit at place S[n - 1]
for initialize i := 0, when i <= n - 2, update (increase i by 1), do:
   if S[i] is not equal to '0', then:
      x := x + (digit at place S[i]) + 1
return x

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;

int solve(string S) {
   int n = S.size();
   int x = S[n - 1] - '0';
   for (int i = 0; i <= n - 2; i++)
      if (S[i] != '0')
         x = x + S[i] + 1 - '0';
   return x;
}
int main() {
   string S = "1000";
   cout << solve(S) << endl;
}