숫자 n이 주어지면 작업은 그 원시값을 계산하는 것입니다. 원시(P로 표시됨)N#)은 처음 n개의 소수의 곱입니다. 원시 숫자의 계승은 숫자의 계승과 유사합니다. 원시에서는 모든 자연수를 곱하는 것이 아니라 소수만 곱하여 숫자의 원시를 계산합니다. P#으로 표시됩니다.
예:
Input: n = 3 Output: 30 Primorial = 2 * 3 * 5 = 30 As a side note factorial is 2 * 3 * 4 * 5 Input: n = 5 Output: 2310 Primorial = 2 * 3 * 5 * 7 * 11
에이 순진한 접근 1부터 n까지의 모든 숫자를 하나씩 확인하여 소수인지 아닌지 확인하고, 그렇다면 곱셈을 결과에 저장합니다. 마찬가지로 n까지 소수의 곱셈 결과를 저장합니다.
안 효율적인 방법은 다음을 사용하여 n까지의 모든 소수를 찾는 것입니다. 순다람의 체 그런 다음 모두 곱하여 원시값을 계산하세요.
C++
// C++ program to find Primorial of given numbers #include using namespace std; const int MAX = 1000000; // vector to store all prime less than and equal to 10^6 vector <int> primes; // Function for sieve of sundaram. This function stores all // prime numbers less than MAX in primes void sieveSundaram() { // In general Sieve of Sundaram produces primes smaller // than (2*x + 2) for a number given number x. Since // we want primes smaller than MAX we reduce MAX to half // This array is used to separate numbers of the form // i+j+2ij from others where 1 <= i <= j bool marked[MAX/2 + 1] = {0}; // Main logic of Sundaram. Mark all numbers which // do not generate prime number by doing 2*i+1 for (int i = 1; i <= (sqrt(MAX)-1)/2 ; i++) for (int j = (i*(i+1))<<1 ; j <= MAX/2 ; j += 2*i +1) marked[j] = true; // Since 2 is a prime number primes.push_back(2); // Print other primes. Remaining primes are of the // form 2*i + 1 such that marked[i] is false. for (int i=1; i<=MAX/2; i++) if (marked[i] == false) primes.push_back(2*i + 1); } // Function to calculate primorial of n int calculatePrimorial(int n) { // Multiply first n primes int result = 1; for (int i=0; i<n; i++) result = result * primes[i]; return result; } // Driver code int main() { int n = 5; sieveSundaram(); for (int i = 1 ; i<= n; i++) cout << 'Primorial(P#) of ' << i << ' is ' << calculatePrimorial(i) <<endl; return 0; }
Java // Java program to find Primorial of given numbers import java.util.*; class GFG{ public static int MAX = 1000000; // vector to store all prime less than and equal to 10^6 static ArrayList<Integer> primes = new ArrayList<Integer>(); // Function for sieve of sundaram. This function stores all // prime numbers less than MAX in primes static void sieveSundaram() { // In general Sieve of Sundaram produces primes smaller // than (2*x + 2) for a number given number x. Since // we want primes smaller than MAX we reduce MAX to half // This array is used to separate numbers of the form // i+j+2ij from others where 1 <= i <= j boolean[] marked = new boolean[MAX]; // Main logic of Sundaram. Mark all numbers which // do not generate prime number by doing 2*i+1 for (int i = 1; i <= (Math.sqrt(MAX) - 1) / 2 ; i++) { for (int j = (i * (i + 1)) << 1 ; j <= MAX / 2 ; j += 2 * i + 1) { marked[j] = true; } } // Since 2 is a prime number primes.add(2); // Print other primes. Remaining primes are of the // form 2*i + 1 such that marked[i] is false. for (int i = 1; i <= MAX / 2; i++) { if (marked[i] == false) { primes.add(2 * i + 1); } } } // Function to calculate primorial of n static int calculatePrimorial(int n) { // Multiply first n primes int result = 1; for (int i = 0; i < n; i++) { result = result * primes.get(i); } return result; } // Driver code public static void main(String[] args) { int n = 5; sieveSundaram(); for (int i = 1 ; i <= n; i++) { System.out.println('Primorial(P#) of '+i+' is '+calculatePrimorial(i)); } } } // This Code is contributed by mits
Python3 # Python3 program to find Primorial of given numbers import math MAX = 1000000; # vector to store all prime less than and equal to 10^6 primes=[]; # Function for sieve of sundaram. This function stores all # prime numbers less than MAX in primes def sieveSundaram(): # In general Sieve of Sundaram produces primes smaller # than (2*x + 2) for a number given number x. Since # we want primes smaller than MAX we reduce MAX to half # This array is used to separate numbers of the form # i+j+2ij from others where 1 <= i <= j marked=[False]*(int(MAX/2)+1); # Main logic of Sundaram. Mark all numbers which # do not generate prime number by doing 2*i+1 for i in range(1int((math.sqrt(MAX)-1)/2)+1): for j in range(((i*(i+1))<<1)(int(MAX/2)+1)(2*i+1)): marked[j] = True; # Since 2 is a prime number primes.append(2); # Print other primes. Remaining primes are of the # form 2*i + 1 such that marked[i] is false. for i in range(1int(MAX/2)): if (marked[i] == False): primes.append(2*i + 1); # Function to calculate primorial of n def calculatePrimorial(n): # Multiply first n primes result = 1; for i in range(n): result = result * primes[i]; return result; # Driver code n = 5; sieveSundaram(); for i in range(1n+1): print('Primorial(P#) of'i'is'calculatePrimorial(i)); # This code is contributed by mits
C# // C# program to find Primorial of given numbers using System; using System.Collections; class GFG{ public static int MAX = 1000000; // vector to store all prime less than and equal to 10^6 static ArrayList primes = new ArrayList(); // Function for sieve of sundaram. This function stores all // prime numbers less than MAX in primes static void sieveSundaram() { // In general Sieve of Sundaram produces primes smaller // than (2*x + 2) for a number given number x. Since // we want primes smaller than MAX we reduce MAX to half // This array is used to separate numbers of the form // i+j+2ij from others where 1 <= i <= j bool[] marked = new bool[MAX]; // Main logic of Sundaram. Mark all numbers which // do not generate prime number by doing 2*i+1 for (int i = 1; i <= (Math.Sqrt(MAX) - 1) / 2 ; i++) { for (int j = (i * (i + 1)) << 1 ; j <= MAX / 2 ; j += 2 * i + 1) { marked[j] = true; } } // Since 2 is a prime number primes.Add(2); // Print other primes. Remaining primes are of the // form 2*i + 1 such that marked[i] is false. for (int i = 1; i <= MAX / 2; i++) { if (marked[i] == false) { primes.Add(2 * i + 1); } } } // Function to calculate primorial of n static int calculatePrimorial(int n) { // Multiply first n primes int result = 1; for (int i = 0; i < n; i++) { result = result * (int)primes[i]; } return result; } // Driver code public static void Main() { int n = 5; sieveSundaram(); for (int i = 1 ; i <= n; i++) { System.Console.WriteLine('Primorial(P#) of '+i+' is '+calculatePrimorial(i)); } } } // This Code is contributed by mits
PHP // PHP program to find Primorial // of given numbers $MAX = 100000; // vector to store all prime less // than and equal to 10^6 $primes = array(); // Function for sieve of sundaram. // This function stores all prime // numbers less than MAX in primes function sieveSundaram() { global $MAX $primes; // In general Sieve of Sundaram // produces primes smaller than // (2*x + 2) for a number given // number x. Since we want primes // smaller than MAX we reduce MAX // to half. This array is used to // separate numbers of the form // i+j+2ij from others where 1 <= i <= j $marked = array_fill(0 $MAX / 2 + 1 0); // Main logic of Sundaram. Mark all numbers which // do not generate prime number by doing 2*i+1 for ($i = 1; $i <= (sqrt($MAX) - 1) / 2 ; $i++) for ($j = ($i * ($i + 1)) << 1 ; $j <= $MAX / 2 ; $j += 2 * $i + 1) $marked[$j] = true; // Since 2 is a prime number array_push($primes 2); // Print other primes. Remaining primes // are of the form 2*i + 1 such that // marked[i] is false. for ($i = 1; $i <= $MAX / 2; $i++) if ($marked[$i] == false) array_push($primes (2 * $i + 1)); } // Function to calculate primorial of n function calculatePrimorial($n) { global $primes; // Multiply first n primes $result = 1; for ($i = 0; $i < $n; $i++) $result = $result * $primes[$i]; return $result; } // Driver code $n = 5; sieveSundaram(); for ($i = 1 ; $i<= $n; $i++) echo 'Primorial(P#) of ' . $i . ' is ' . calculatePrimorial($i) . 'n'; // This code is contributed by mits ?> JavaScript <script> // Javascript program to find Primorial // of given numbers let MAX = 100000; // vector to store all prime less // than and equal to 10^6 let primes = new Array(); // Function for sieve of sundaram. // This function stores all prime // numbers less than MAX in primes function sieveSundaram() { // In general Sieve of Sundaram // produces primes smaller than // (2*x + 2) for a number given // number x. Since we want primes // smaller than MAX we reduce MAX // to half. This array is used to // separate numbers of the form // i+j+2ij from others where 1 <= i <= j let marked = new Array(MAX / 2 + 1).fill(0); // Main logic of Sundaram. Mark all numbers which // do not generate prime number by doing 2*i+1 for (let i = 1; i <= (Math.sqrt(MAX) - 1) / 2 ; i++) for (let j = (i * (i + 1)) << 1 ; j <= MAX / 2 ; j += 2 * i + 1) marked[j] = true; // Since 2 is a prime number primes.push(2); // Print other primes. Remaining primes // are of the form 2*i + 1 such that // marked[i] is false. for (let i = 1; i <= MAX / 2; i++) if (marked[i] == false) primes.push(2 * i + 1); } // Function to calculate primorial of n function calculatePrimorial(n) { // Multiply first n primes let result = 1; for (let i = 0; i < n; i++) result = result * primes[i]; return result; } // Driver code let n = 5; sieveSundaram(); for (let i = 1 ; i<= n; i++) document.write('Primorial(P#) of ' + i + ' is ' + calculatePrimorial(i) + '
'); // This code is contributed by gfgking </script>
산출:
문자열을 char로 변환 java
Primorial(P#) of 1 is 2 Primorial(P#) of 2 is 6 Primorial(P#) of 3 is 30 Primorial(P#) of 4 is 210 Primorial(P#) of 5 is 2310
시간 복잡도 :- O(N)