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题目

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 1:

Input: 2
Output: [0,1,1]

Example 2:

Input: 5
Output: [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.

题目大意

给定一个非负整数num,对于范围0≤i≤num范围的每个数字i,计算其二进制数中的1的数目,并将它们作为数组返回。

解题思路

  • Bit Manipulation直觉想出利用位运算特性x&(x-1),求出每个数字二进制1的个数,写出解法1
  • 解法2只能wow(惊叹的意思)