397. Integer Replacement

Problem

Given a positive integer n, you can apply one of the following operations:

• If n is even, replace n with n / 2.

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

Return the minimum number of operations needed for n to become 1.

  Example 1:

Input: n = 8
Output: 3
Explanation: 8 -> 4 -> 2 -> 1

Example 2:

Input: n = 7
Output: 4
Explanation: 7 -> 8 -> 4 -> 2 -> 1
or 7 -> 6 -> 3 -> 2 -> 1

Example 3:

Input: n = 4
Output: 2

  Constraints:

• 1 <= n <= 2^31 - 1

Solution

class Solution {
    public int integerReplacement(int n) {
        Map<Integer, Integer> dp = new HashMap<>();
        return solve(n, dp);
    }

    private int solve(int n, Map<Integer, Integer> dp) {
        if (n == 1) {
            return 0;
        }
        if (dp.containsKey(n)) {
            return dp.get(n);
        }
        int ans;
        if (n % 2 == 0) {
            ans = 1 + solve(n >>> 1, dp);
        } else {
            ans = 1 + Math.min(solve(n + 1, dp), solve(n - 1, dp));
        }
        dp.put(n, ans);
        return ans;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).