# Integer Replacement in C++

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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
Updated on 02-May-2020 08:31:38