# 397-integer-replacement

## Question

https://leetcode.com/problems/integer-replacement/description/

Given a positive integer n and you can do operations as follow:

1. If n is even, replace n with n/2.
2. If n is odd, you can replace n with either n + 1 or n - 1.

What is the minimum number of replacements needed for n to become 1?

Example:

``````Input:
8

Output:
3

Explanation:
8 -> 4 -> 2 -> 1
``````
``````Input:
7

Output:
4

Explanation:
7 -> 8 -> 4 -> 2 -> 1
or
7 -> 6 -> 3 -> 2 -> 1
``````

## Thought Process

1. Pattern Finding
1. Three cases
1. If n is even, we just follow the rule
2. If n is odd we need to look at the second last digit, if it is 1, adding 1 will be able to remove two 1s, otherwise we can just decrement it
3. One exception is 3, which we should decrement by 1
2. Time complexity O(log n)
3. Space complexity O(1)

## Solution

``````class Solution {
public int integerReplacement(int n) {
int count = 0;
while (n != 1) {
count++;
if (n % 2 == 0) n >>>= 1;
else if (n == 3 || ((n >>> 1) & 1) == 0) n -= 1;
else n += 1;
}
return count;
}
}
``````