204. Count Primes

Count the number of prime numbers less than a non-negative number, n.

Example:

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

 

Approach #1: C++.

class Solution {
public:
    int countPrimes(int n) {
        vector<int> matrix(n+5, 1);
        helper(n, matrix);
        int ans = 0;
        if (n <= 1) return 0;
        for (int j = 2; j < n; ++j) 
            if (matrix[j] == 1)
                ans++;
        return ans;
    }
    
    void helper(int n, vector<int>& matrix) {
        for (int i = 2; i*i < n; ++i) {
            if (matrix[i] == 1)
                for (int j = i+i; j <= n; j += i) {
                    matrix[j] = 0;
                }
        }
    }
};

　　

Approach #2: Java.

class Solution {
    public int countPrimes(int n) {
        boolean[] notPrime = new boolean[n];
        int count = 0;
        for (int i = 2; i < n; ++i) {
            if (notPrime[i] == false) {
                count++;
                for (int j = 2; i*j < n; ++j) {
                    notPrime[i*j] = true;
                }
            }
        }
        return count;
    }
}

　　

Approach #3: Python.

class Solution:
    def countPrimes(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n < 3:
            return 0
        primes = [True] * n
        primes[0] = primes[1] = False
        for i in range(2, int(n**0.5)+1):
            if primes[i]:
                primes[i*i : n : i] = [False] * len(primes[i*i : n : i])
        return sum(primes)

　　

Time Submitted	Status	Runtime	Language
a few seconds ago	Accepted	240 ms	python3
3 minutes ago	Accepted	20 ms	java
7 minutes ago	Accepted	24 ms	cpp