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0204 - Count Primes

https://leetcode.com/problems/count-primes/

Problem Statement​

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

Example 1:

Input: n = 10
Output: 4
Explanation: There are 4 prime numbers less than 10, they are 2, 3, 5, 7.

Example 2:

Input: n = 0
Output: 0

Example 3:

Input: n = 1
Output: 0

Constraints:

  • 0 <= n <= 5 * 10^6

Approach 1: Sieve of Eratosthenes​

See Sieve of Eratosthenes.

Written by @wingkwong
class Solution {
public:
    vector<bool> seiveOfEratosthenes(const int n) {
      vector<bool> isPrime(n + 1, true);
      isPrime[0] = isPrime[1] = 0;
      for (int i = 2; i * i <= n; i++) {
        if (isPrime[i]) {
          for (int j = i * i; j <= n; j += i) {
            isPrime[j] = false;
          }
        }
      }
      return isPrime;
    }

    int countPrimes(int n) {
        if(n < 2) return 0;
        vector<bool> isPrime = seiveOfEratosthenes(n - 1);
        int cnt = 0;
        for(int i = 2; i < n; i++) cnt += isPrime[i] == true;
        return cnt;
    }
};