[leetcode]397. Integer Replacement

题目链接：https://leetcode.com/problems/integer-replacement/

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 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

方法一：

class Solution{
public:
    int integerReplacement(int n)
    {
        return getOne(n);
    }
    int getOne(int n)
    {
        if(n==INT32_MAX)
            return 32;
        else if(n==1)
            return 0;
        else if(n%2==0)
            return getOne(n/2)+1;
        else if(n%2!=0)
            return min(getOne(n+1),getOne(n-1))+1;
        return 0;
    }
};

方法二：

思路：

All you need is determine replace n with n + 1 or n - 1, when n is odd. since,

• if n is even, you get no choice, just replace it with n / 2.
• if n is odd, you can either add 1 or reduce 1.

If n + 1 % 4 == 0, replace n with n + 1 will short the path. Otherwise, replace n with n - 1 is always the right direction.

class Solution {
public:
    int integerReplacement(int n)
    {
        if (n == 1)
            return res;
        if (n == 3)
        {
            res += 2;
            return res;
        }
        if (n == INT32_MAX)
            return 32;

        res ++;
        if (n & 1)
            if ((n + 1) % 4 == 0)
                integerReplacement(n + 1);
            else
                integerReplacement(n - 1);
        else
            integerReplacement(n / 2);

        return res;
    }
private:
    int res = 0;
};