# 397 Integer Replacement

### Problem:

Given a positive integer n and you can do 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. What is the minimum number of replacements needed for n to become 1?

Example 1:

``````Input:
8

Output:
3

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

Example 2:

``````Input:
7

Output:
4

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

### Solutions:

``````public class Solution {
public int integerReplacement(int n) {
HashMap<Long, Integer> result = new HashMap<Long, Integer>();
return process(n, result);
}
private int process(long n, HashMap<Long, Integer> result) {
if (result.containsKey(n)) {
return result.get(n);
}
int count = 0;
if (n == 1) {
return 0;
}
if (n % 2 == 0) {
count = process(n / 2, result) + 1;
}
else {
count = Math.min(process(n - 1, result), process(n + 1, result)) + 1;
}
result.put(n, count);
return count;
}
}
``````
``````public class Solution {
public int integerReplacement(int n) {
long t = n;
int cnt = 0;
while (t > 1) {
++cnt;
if ((t&1) == 1) {
if (((t&2) == 2) && (t != 3)) ++t;
else --t;
} else {
t >>= 1;
}
}
return cnt;
}
}
``````