LeetCode //C - 204. Count Primes

204. Count Primes

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 ∗ 1 0 6 0 <= n <= 5 * 10^6 0<=n<=5∗106

From: LeetCode

Link: 204. Count Primes


Solution:

Ideas:

1. Edge Cases: If n is less than or equal to 2, there are no prime numbers less than n, so we return 0.

2. Initialization: We create an array isPrime of size n and initialize all elements to true. This array will helpus mark non-prime numbers.

3. Sieve of Eratosthenes:

  • For each number i starting from 2 up to the square root of n, if i is still marked as prime (isPrime[i] is true), we mark all its multiples as non-prime.
  • The inner loop starts at i * i because any smaller multiple of i would have already been marked by a smaller prime factor.

4. Counting Primes: After marking non-prime numbers, we iterate through the isPrime array and count how many numbers are still marked as prime.

5. Memory Management: Finally, we free the allocated memory for the isPrime array and return the count of prime numbers.

Code:
c 复制代码
int countPrimes(int n) {
    if (n <= 2) {
        return 0;
    }
    
    bool *isPrime = (bool *)malloc(n * sizeof(bool));
    for (int i = 2; i < n; ++i) {
        isPrime[i] = true;
    }
    
    for (int i = 2; i * i < n; ++i) {
        if (isPrime[i]) {
            for (int j = i * i; j < n; j += i) {
                isPrime[j] = false;
            }
        }
    }
    
    int count = 0;
    for (int i = 2; i < n; ++i) {
        if (isPrime[i]) {
            ++count;
        }
    }
    
    free(isPrime);
    return count;
}
相关推荐
闪电麦坤957 分钟前
数据结构:二维数组(2D Arrays)
数据结构·算法
凌肖战19 分钟前
力扣网C语言编程题:快慢指针来解决 “寻找重复数”
c语言·算法·leetcode
埃菲尔铁塔_CV算法40 分钟前
基于 TOF 图像高频信息恢复 RGB 图像的原理、应用与实现
人工智能·深度学习·数码相机·算法·目标检测·计算机视觉
NAGNIP2 小时前
一文搞懂FlashAttention怎么提升速度的?
人工智能·算法
Codebee2 小时前
OneCode图生代码技术深度解析:从可视化设计到注解驱动实现的全链路架构
css·人工智能·算法
刘大猫262 小时前
Datax安装及基本使用
java·人工智能·算法
猫猫的小茶馆3 小时前
【STM32】预分频因子(Prescaler)和重装载值(Reload Value)
c语言·stm32·单片机·嵌入式硬件·mcu·51单片机
JeffersonZU3 小时前
Linux/Unix文件IO(文件描述符、原子操作、文件数据结构、open、read、write、fcntl、dup)
linux·c语言·unix·gnu
Gyoku Mint5 小时前
深度学习×第4卷:Pytorch实战——她第一次用张量去拟合你的轨迹
人工智能·pytorch·python·深度学习·神经网络·算法·聚类