Count Primes — LeetCode 204 Python Solution

The problem

Given an integer n, return the number of prime numbers that are strictly less than n.

Example

Input

n = 10

Output

4

Explanation

There are 4 prime numbers less than 10, they are 2, 3, 5, 7.

Python solution

class Solution:
    def countPrimes(self, n: int) -> int:
        primes = [True] * n
        ans = 0
        for i in range(2, n):
            if primes[i]:
                ans += 1
                for j in range(i + i, n, i):
                    primes[j] = False
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 204. Count Primes is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Number Theory.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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