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Leetcode 338. Counting Bits

时间:2016-07-30 10:18:14      阅读:237      评论:0      收藏:0      [点我收藏+]

338. Counting Bits

  • Total Accepted: 35688
  • Total Submissions: 61823
  • Difficulty: Medium

 

Given a non negative integer number num. For every numbers i in the range 0 ≤ i ≤ num calculate the number of 1‘s in their binary representation and return them as an array.

Example:
For num = 5 you should return [0,1,1,2,1,2].

Follow up:

  • It is very easy to come up with a solution with run time O(n*sizeof(integer)). But can you do it in linear time O(n) /possibly in a single pass?
  • Space complexity should be O(n).
  • Can you do it like a boss? Do it without using any builtin function like __builtin_popcount in c++ or in any other language.

 

Hint:

  1. You should make use of what you have produced already.
  2. Divide the numbers in ranges like [2-3], [4-7], [8-15] and so on. And try to generate new range from previous.
  3. Or does the odd/even status of the number help you in calculating the number of 1s?

 

 

思路:假设res[i]意味着数字i的二进制中1的个数。

i为偶数时,res[i]=res[i/2];i为奇数时,res[i]=res[i-1]+1。

 

其实也可以写成这样:res[i]=res[i/2] + i%2。

 

代码:

i为偶数时,res[i]=res[i/2];i为奇数时,res[i]=res[i-1]+1。

 1 class Solution {
 2 public:
 3     vector<int> countBits(int num) {
 4         vector<int> res(num+1,0);
 5         int i;
 6         for(i=1;i<=num;i++){
 7             if(i%2){//odd
 8                 res[i]=res[i-1]+1;
 9             }
10             else{
11                 res[i]=res[i>>1];
12             }
13         }
14         return res;
15     }
16 };

 

其实也可以写成这样:res[i]=res[i/2] + i%2。

 1 class Solution {
 2 public:
 3     vector<int> countBits(int num) {
 4         vector<int> res(num+1,0);
 5         int i;
 6         for(i=1;i<=num;i++){
 7             res[i]=res[i/2]+i%2;
 8         }
 9         return res;
10     }
11 };

 

Leetcode 338. Counting Bits

原文:http://www.cnblogs.com/Deribs4/p/5720307.html

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