204. Count Primes

原文题目：

204. Count Primes

读题：

题目很简单，就是求小于n的质数的个数，注意是小于n，不等于n，也就是说n=2的时候，返回0，n=3时才是返回1

一下列出两种方法，一种方法超时，另一种方法逐步优化到46ms

//超时class Solution {public:int countPrimes(int n) {int count = 0;int i = 0;if (n < 2){return count;}for(i = 2;i<n;i++){if(isPrime(i)){count++;}}return count;}int isPrime(int m){int i = 0;if(m <2){return 0;}for(i = 2;i <= m/2;i++){if(m %i == 0){return 0;}}return 1;}};//129msclass Solution {public:int countPrimes(int n) {int count = 0;int i = 0;vector<bool> isprime;for (int i = 0; i < n; i++)isprime.push_back(true);for (int i = 2; i < n; i++){for (int j = i + i; j < n; j += i){isprime[j] = false;}}for (int i = 2; i < n; i++){if (i != 0 && i != 1 && isprime[i])count++;}return count;}};//73msclass Solution {public:int countPrimes(int n) {int count = 0;int i = 0;if(n <3){return 0;}if(n == 3){return 1;}if(n == 4){return 2;}vector<bool> isprime;for (int i = 0; i < n; i++)isprime.push_back(true);for (int i = 2; i*i < n; i++){for (int j = i + i; j < n; j += i){isprime[j] = false;}}for (int i = 2; i < n; i++){if (isprime[i])count++;}return count;}};//46msclass Solution {public:int countPrimes(int n) {int count = 0;int i = 0;if(n <3){return 0;}if(n == 3){return 1;}if(n == 4){return 2;}vector<bool> isprime;for (int i = 0; i < n; i++)isprime.push_back(true);for (int i = 2; i*i < n; i++){if(isprime[i]){for (int j = i + i; j < n; j += i){isprime[j] = false;}}}for (int i = 2; i < n; i++){if (isprime[i])count++;}return count;}};