338-比特位计数

LeetCode 338. Counting Bits

Given an integer n, return an array ans of length n + 1 such that for each i (0 <= i <= n), ans[i] is the number of 1's in the binary representation of i.

Example 1:

Input: n = 2
Output: [0,1,1]
Explanation:
0 --> 0
1 --> 1
2 --> 10

Example 2:

Input: n = 5
Output: [0,1,1,2,1,2]
Explanation:
0 --> 0
1 --> 1
2 --> 10
3 --> 11
4 --> 100
5 --> 101

method

• x & x-1可以去除x最低位的1

利用x & x-1的性质，可以利用res[x & x-1]再加上1求得res[x]，就不用每个数都算一遍

vector<int> countBits(int n) {
    vector<int> res(n + 1);
    for (int i = 1; i <= n; i++) {
        res[i] = res[i & (i - 1)] + 1;
    }
    return res;
}