LeetCode Integer Replacement

原题链接在这里：https://leetcode.com/problems/integer-replacement/

题目：

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

题解：

n是偶数时除以2是确定的，问题是n是奇数时+1 还是 -1. 尽可能的消除1 bit, +1 或 -1后哪个1 bit少就选哪个.

若+1或-1后1 bit相同，那么除了3特殊情况下其他都选+1.

Time Complexity: O(1), int最多32位，最多64次操作.

Space: O(1).

AC Java:

 1 public class Solution {
 2     public int integerReplacement(int n) {
 3         int count = 0;
 4         while(n != 1){
 5             if((n & 1) == 0){
 6                 n >>>= 1;
 7             }else if(n == 3 || Integer.bitCount(n+1) > Integer.bitCount(n-1)){
 8                 n--;
 9             }else{
10                 n++;
11             }
12             count++;
13         }
14         return count;
15     }
16 }

除了3特例之外，看n的倒数第二位，若是1, n++, 若是0, n--.

Time Complexity: O(1). Space: O(1).

AC Java:

 1 public class Solution {
 2     public int integerReplacement(int n) {
 3         int count = 0;
 4         while(n != 1){
 5             if((n & 1) == 0){
 6                 n >>>= 1;
 7             }else if(n == 3 || ((n >>> 1) & 1) == 0){
 8                 n--;
 9             }else{
10                 n++;
11             }
12             count++;
13         }
14         return count;
15     }
16 }