Description:

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:

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

Link:

https://leetcode.com/problems/integer-replacement/description/

解题方法：

DFS:
According to the question:
If n is even, replace n with n/2.
If n is odd, you can replace n with either n + 1 or n – 1.

DP doesn’t work for this question.

Tips:

There is special corner case: while n == INT_MAX. In this case, the best solution will be let n += 1, which is 2147483648.
Then divide by 2 for 31 times, which means the best solution will be 32. The tricky method is let n /= 2 while it equals to INT_MAX.

完整代码：

int integerReplacement(int n) {
    if(n == 1)
        return 0;
    if(n == 0 || n == 2)
        return 1;
    if(n == INT_MAX || n % 2 == 0)
        return integerReplacement(n / 2) + 1;
    else
        return min(integerReplacement(n + 1), integerReplacement(n - 1)) + 1;
}