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 1
s present when written in binary. For example, 21
written in binary is 10101
which has 3 set bits. Also, 1 is not a prime.)
给定两个整数L和R,找到[L,R](含)范围内的数字的计数,其二进制表示中具有设置位的素数。一个素数的设定为其二进制中所存在的‘1’的个数是否为素数。
注意python中int型总共32位,所以只需要枚举出<32的素数的集合,即:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31。
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:
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L, R
will be integersL <= R
in the range[1, 10^6]
.
R - L
will be at most 10000.
def countPrimeSetBits(self, L, R):
"""
:type L: int
:type R: int
:rtype: int
"""
ans = 0
prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
for each in range(L, R + 1):
num = bin(each)
cnt = num.count('1')
if cnt in prime:
ans += 1
return ans