Integer Replacement in C++

Suppose we have a positive integer n and we can do these operations as follow −

• If n is even, replace n with n/2.

• If n is odd, you can replace n with either n + 1 or n - 1.

We have to find the minimum number of replacements needed for n to become 1?

So if the number is 7, then the answer will be 4, as 7 → 8 → 4 → 2 → 1 or 7 → 6 → 3 → 2 → 1

To solve this, we will follow these steps −

• ret := 0, n := x

• while n > 1

  • if n is even, then c := n / 2

  • otherwise when n is even

    • if n is 3 or n/2 is even, then decrease n by 1, otherwise increase n by 1

  • increase ret by 1

• return ret.

Example (C++)

Let us see the following implementation to get a better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
class Solution {
   public:
   int bitCount(int x){
      int ret = 0;
      while(x){
         ret++;
         x >>= 1;
      }
      return ret;
   }
   int integerReplacement(int x) {
      int ret = 0;
      lli n = x;
      while(n > 1){
         if(n % 2 == 0){
            n >>= 1;
         }
         else if(n & 1){
            if(n == 3 || (((n >> 1) & 1 )== 0)){
               n--;
            } else {
               n++;
            }
         }
         ret++;
      }
      return ret;
   }
};
main(){
   Solution ob;
   cout << (ob.integerReplacement(7));
}

Input

7

Output

4