LeetCode——Integer Replacement

Question

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

Solution

这题比较有技巧。递归。偶数的时候直接除2，奇数的时候分两种情况，一种是(i+1) % 4 == 0的，表示(i+1)/2以后还是偶数，那么就可以一直除2除到为1为止，否则选择i - 1会更快。

Code

class Solution {
public:
    int integerReplacement(int n) {
        if (n == 1)
            return 0;
        if (n == 2)
            return 1;
        if (n == 3)
            return 2;
        if (n == INT_MAX)
            return 32;
        if (!(n & 1))
            return integerReplacement(n / 2) + 1;
        else {
            if ((n + 1) % 4 == 0)
                return integerReplacement(n + 1) + 1;
            else
                return integerReplacement(n - 1) + 1;
        }
    }
};