leetcode 762二进制表示中质数个位计算

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最新推荐文章于 2024-08-05 13:46:59 发布

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给定[L, R]区间，计算二进制表示中质数个位数的数字个数。例如，6到10之间有4个这样的数字（6, 7, 9, 10），因为它们的二进制表示中质数个位数分别为2, 3, 2, 2。解决方案是利用665772二进制表示的质数位特性进行计算。" 118897813,7522678,Python利用sys获取日志调用位置,"['Python', 'sys模块', '日志记录']

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题目：
Given two integers L and R, find the count of numbers in the range [L, R] (inclusive) having a prime number of set bits in their binary representation.

(Recall that the number of set bits an integer has is the number of 1s present when written in binary. For example, 21 written in binary is 10101 which has 3 set bits. Also, 1 is not a prime.)

Example 1:

Input: L = 6, R = 10
Output: 4
Explanation:
6 -> 110 (2 set bits, 2 is prime)
7 -> 111 (3 set bits, 3 is prime)
9 -> 1001 (2 set bits , 2 is prime)
10->1010 (2 set bits , 2 is prime)
Example 2:

Input: L = 10, R = 15
Output: 5
Explanation:
10 -> 1010 (2 set bits, 2 is prime)
11 -> 1011 (3 set bits, 3 is prime)
12 -> 1100 (2 set bits, 2 is prime)
13 -> 1101 (3 set bits, 3 is prime)
14 -> 1110 (3 set bits, 3 is prime)
15 -> 1111 (4 set bits, 4 is not prime)
Note:

L, R will be integers L <= R in the range [1, 10^6].
R - L will be at most 10000.
题解：
return sum(665772>>bin(i).count(‘1’)&1 for i in range(L,R+1))
解析：665772的二进制表示为：0b10100010100010101100，它的第2，3，5，7，11，13，17，19位都为1，而这些数是22以内的素数，题目已经说明R的范围是10^6，而106的二进制有22位