397. Integer Replacement¶

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397. Integer Replacement

Medium

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

1. If n is even, replace n with n / 2.
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 <= 231 - 1

Solution¶

class Solution {
    private HashMap<Long, Long> memo;
    public int integerReplacement(int n) {
        memo = new HashMap<>();
        long res = solve((long)(n));
        return (int)(res);
    }
    private long solve(long n) {
        if (n == 1) return 0;
        if (memo.containsKey((long)(n))) return memo.get(n);
        if (n % 2 == 0) return 1 + solve(n / 2);
        long op1 = 1 + solve(n + 1);
        long op2 = 1 + solve(n - 1);
        memo.put(n , (long)(Math.min(op1, op2)));
        return (long)(Math.min(op1, op2));
    }
}

Complexity Analysis¶

• Time Complexity: O(?)
• Space Complexity: O(?)

Approach¶

Detailed explanation of the approach will be added here