\n Algorithms are one of the key concepts in computer science and are particularly important in solving programming problems.
\n In this course, we will discuss the problem of ‘finding prime numbers’ and explain the algorithm and C++ code to solve it in detail.
\n A prime number is a natural number that can only be divided by 1 and itself, and it is one of the fundamental concepts in mathematics.
\n However, there are various approaches to solving this problem, each with different time complexities.\n <\/p>\n
\n Given an integer \n The first line contains a natural number \n Print all prime numbers from \n There are several methods to find prime numbers, but here we will use the classical method known as the ‘Sieve of Eratosthenes’. \n The Sieve of Eratosthenes algorithm has a time complexity of about \n Below is the C++ code that implements the above algorithm. \n - \n In this course, we introduced an algorithm to solve the problem of finding prime numbers and implemented it in C++. The Sieve of Eratosthenes is an efficient method for finding primes, and it is a common question in coding tests. <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"N<\/code>, write a program to find all prime numbers from 1<\/code> to N<\/code>.
\n A prime number is a number greater than 1 that has no divisors other than 1 and itself.\n <\/p>\nInput<\/h3>\n
N (1 \u2264 N \u2264 10^6)<\/code>.\n <\/p>\nOutput<\/h3>\n
1<\/code> to N<\/code>, one per line.\n <\/p>\nExample<\/h2>\n
Input:\n 10\n\n Output:\n 2\n 3\n 5\n 7\n <\/code><\/pre>\nAlgorithm Approach<\/h2>\n
\n This method can efficiently and relatively simply find prime numbers.
\n The Sieve of Eratosthenes works through the following procedure.\n <\/p>\n\n
1<\/code> to N<\/code>.<\/li>\nTime Complexity<\/h2>\n
O(N log log N)<\/code>.
\n It becomes more efficient as N<\/code> increases, ensuring fast performance even for N = 10^6<\/code>.\n <\/p>\nC++ Code<\/h2>\n
\n Comments will be added to each step to aid understanding.\n <\/p>\n#include Code Explanation<\/h2>\n
#include #include
\n Include C++ input, output, and vector libraries.
\n - int N;<\/code>: Declare an integer variable to hold user input.
\n - vector
\n Declare a vector to store the primality of numbers up to N<\/code>,
\n initializing all values to true<\/code>.
\n (0 and 1 are not primes, so set separately)
\n - for (int i = 2; i * i <= N; i++)<\/code>:
\n Start from 2 and iterate up to the square root of N<\/code> to find primes.
\n - The inner for (int j = i * i; j <= N; j += i)<\/code> loop removes multiples of i<\/code>.
\n - Finally, output all indices where isPrime[i]<\/code> is true<\/code>.\n <\/p>\nConclusion<\/h2>\n
\n Familiarize yourself with the algorithm and code to confidently tackle coding tests!\n <\/p>\n