Many people preparing for coding tests struggle with the difficulty and complexity of algorithm problems. Today, through a problem titled “Finding Interesting Primes,” we will introduce various algorithms for finding primes (premium numbers) and see how to efficiently solve the problem using Java.<\/p>\n
Write a function to find all primes less than or equal to a given number N. Here, a prime is defined as a natural number that has no divisors other than 1 and itself.<\/p>\n
Input<\/strong>: A natural number N is given on the first line. (2 \u2264 N \u2264 1000)<\/p>\n Output<\/strong>: Print all primes less than or equal to N on one line, separated by spaces.<\/p>\n To solve the above problem, it is essential to understand the definition of a prime and basic methods for finding primes. A prime is a number that cannot be divided by natural numbers other than 1 and itself, so we can efficiently find primes using division operations.<\/p>\n However, simply checking all numbers from 1 to N is inefficient, with a time complexity of O(N^2). Therefore, a more efficient algorithm is needed. We can efficiently find primes using the Sieve of Eratosthenes algorithm.<\/p>\n This algorithm works as follows:<\/p>\n Now we will implement the above algorithm in Java.<\/p>\n The code above goes through the following steps:<\/p>\n The time complexity of this algorithm is O(N log(log(N))), which operates efficiently even for large N. This is significantly more efficient than simply dividing all numbers.<\/p>\n In this lesson, we implemented the Sieve of Eratosthenes algorithm in Java to find primes. Familiarity with such basic algorithms can help you score higher when solving various algorithm problems in coding tests. Furthermore, remember that in coding tests, both the readability and optimization of your code are also important scoring factors, so it is necessary to keep this in mind when coding.<\/p>\n Let's continue working on various algorithm problems together to improve our skills!<\/p>\n","protected":false},"excerpt":{"rendered":"Example<\/h2>\n
\nInput: \n10\n\nOutput: \n2 3 5 7\n<\/pre>\n
Understanding and Analyzing the Problem<\/h2>\n
Sieve of Eratosthenes<\/h2>\n
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Java Code Implementation<\/h2>\n
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\npublic class PrimeSieve {\n public static void main(String[] args) {\n int N = 10; \/\/ The number N to use\n boolean[] isPrime = new boolean[N + 1];\n \n \/\/ Initialization\n for (int i = 2; i <= N; i++) {\n isPrime[i] = true;\n }\n\n \/\/ Sieve of Eratosthenes\n for (int i = 2; i * i <= N; i++) {\n if (isPrime[i]) {\n for (int j = i * i; j <= N; j += i) {\n isPrime[j] = false;\n }\n }\n }\n\n \/\/ Output results\n for (int i = 2; i <= N; i++) {\n if (isPrime[i]) {\n System.out.print(i + \" \");\n }\n }\n }\n}\n<\/code>\n<\/pre>\nExplanation<\/h2>\n
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Time Complexity<\/h2>\n
Conclusion<\/h2>\n