Prime numbers after prime P with sum S
Given three numbers sum S, prime P and N, find all N prime numbers after prime P such that their sum is equal to S.
Examples :
Input : N = 2, P = 7, S = 28
Output : 11 17
Explanation : 11 and 17 are primes after
prime 7 and (11 + 17 = 28)
Input : N = 3, P = 2, S = 23
Output : 3 7 13
5 7 11
Explanation : 3, 5, 7, 11 and 13 are primes
after prime 2. And (3 + 7 + 13 = 5 + 7 + 11
= 23)
Input : N = 4, P = 3, S = 54
Output : 5 7 11 31
5 7 13 29
5 7 19 23
5 13 17 19
7 11 13 23
7 11 17 19
Explanation : All are prime numbers and
their sum is 54
Approach : The approach used is to produce all the primes less than S and greater than P. And then backtracking to find if such N primes exist whose sum equals S.
For example, S = 10, N = 2, P = 2
C++
// CPP Program to print all N primes after // prime P whose sum equals S #include <iostream> #include <vector> #include <cmath> using namespace std; // vector to store prime and N primes // whose sum equals given S vector<int> set; vector<int> prime; // function to check prime number bool isPrime(int x) { // square root of x int sqroot = sqrt(x); bool flag = true; // since 1 is not prime number if (x == 1) return false; // if any factor is found return false for (int i = 2; i <= sqroot; i++) if (x % i == 0) return false; // no factor found return true; } // function to display N primes whose sum equals S void display() { int length = set.size(); for (int i = 0; i < length; i++) cout << set[i] << " "; cout << "\n"; } // function to evaluate all possible N primes // whose sum equals S void primeSum(int total, int N, int S, int index) { // if total equals S And // total is reached using N primes if (total == S && set.size() == N) { // display the N primes display(); return; } // if total is greater than S // or if index has reached last element if (total > S || index == prime.size()) return; // add prime[index] to set vector set.push_back(prime[index]); // include the (index)th prime to total primeSum(total+prime[index], N, S, index+1); // remove element from set vector set.pop_back(); // exclude (index)th prime primeSum(total, N, S, index+1); } // function to generate all primes void allPrime(int N, int S, int P) { // all primes less than S itself for (int i = P+1; i <=S ; i++) { // if i is prime add it to prime vector if (isPrime(i)) prime.push_back(i); } // if primes are less than N if (prime.size() < N) return; primeSum(0, N, S, 0); } // Driver Code int main() { int S = 54, N = 2, P = 3; allPrime(N, S, P); return 0; } |
Java
// Java Program to print // all N primes after prime // P whose sum equals S import java.io.*; import java.util.*; class GFG { // vector to store prime // and N primes whose sum // equals given S static ArrayList<Integer> set = new ArrayList<Integer>(); static ArrayList<Integer> prime = new ArrayList<Integer>(); // function to check // prime number static boolean isPrime(int x) { // square root of x int sqroot = (int)Math.sqrt(x); // since 1 is not // prime number if (x == 1) return false; // if any factor is // found return false for (int i = 2; i <= sqroot; i++) if (x % i == 0) return false; // no factor found return true; } // function to display N // primes whose sum equals S static void display() { int length = set.size(); for (int i = 0; i < length; i++) System.out.print( set.get(i) + " "); System.out.println(); } // function to evaluate // all possible N primes // whose sum equals S static void primeSum(int total, int N, int S, int index) { // if total equals S // And total is reached // using N primes if (total == S && set.size() == N) { // display the N primes display(); return; } // if total is greater // than S or if index // has reached last // element // or if set size reached to maximum or greater than maximum if (total > S || index == prime.size() || set.size() >= N) return; // add prime.get(index) // to set vector set.add(prime.get(index)); // include the (index)th // prime to total primeSum(total + prime.get(index), N, S, index + 1); // remove element // from set vector set.remove(set.size() - 1); // exclude (index)th prime primeSum(total, N, S, index + 1); } // function to generate // all primes static void allPrime(int N, int S, int P) { // all primes less // than S itself for (int i = P + 1; i <= S ; i++) { // if i is prime add // it to prime vector if (isPrime(i)) prime.add(i); } // if primes are // less than N if (prime.size() < N) return; primeSum(0, N, S, 0); } // Driver Code public static void main(String args[]) { int S = 54, N = 2, P = 3; allPrime(N, S, P); } } // This code is contributed by // Manish Shaw(manishshaw1) |
Python3
# Python Program to print # all N primes after prime # P whose sum equals S import math # vector to store prime # and N primes whose # sum equals given S set = [] prime = [] # function to # check prime number def isPrime(x) : # square root of x sqroot = int(math.sqrt(x)) flag = True # since 1 is not # prime number if (x == 1) : return False # if any factor is # found return false for i in range(2, sqroot + 1) : if (x % i == 0) : return False # no factor found return True # function to display N # primes whose sum equals S def display() : global set, prime length = len(set) for i in range(0, length) : print (set[i], end = " ") print () # function to evaluate # all possible N primes # whose sum equals S def primeSum(total, N, S, index) : global set, prime # if total equals S # And total is reached # using N primes if (total == S and len(set) == N) : # display the N primes display() return # if total is greater # than S or if index # has reached last element if (total > S or index == len(prime)) : return # add prime[index] # to set vector set.append(prime[index]) # include the (index)th # prime to total primeSum(total + prime[index], N, S, index + 1) # remove element # from set vector set.pop() # exclude (index)th prime primeSum(total, N, S, index + 1) # function to generate # all primes def allPrime(N, S, P) : global set, prime # all primes less # than S itself for i in range(P + 1, S + 1) : # if i is prime add # it to prime vector if (isPrime(i)) : prime.append(i) # if primes are # less than N if (len(prime) < N) : return primeSum(0, N, S, 0) # Driver Code S = 54N = 2P = 3allPrime(N, S, P) # This code is contributed by # Manish Shaw(manishshaw1) |
C#
// C# Program to print all // N primes after prime P // whose sum equals S using System; using System.Collections.Generic; class GFG { // vector to store prime // and N primes whose sum // equals given S static List<int> set = new List<int>(); static List<int> prime = new List<int>(); // function to check prime number static bool isPrime(int x) { // square root of x int sqroot = (int)Math.Sqrt(x); // since 1 is not prime number if (x == 1) return false; // if any factor is // found return false for (int i = 2; i <= sqroot; i++) if (x % i == 0) return false; // no factor found return true; } // function to display N // primes whose sum equals S static void display() { int length = set.Count; for (int i = 0; i < length; i++) Console.Write(set[i] + " "); Console.WriteLine(); } // function to evaluate // all possible N primes // whose sum equals S static void primeSum(int total, int N, int S, int index) { // if total equals S And // total is reached using N primes if (total == S && set.Count == N) { // display the N primes display(); return; } // if total is greater than // S or if index has reached // last element if (total > S || index == prime.Count) return; // add prime[index] // to set vector set.Add(prime[index]); // include the (index)th // prime to total primeSum(total + prime[index], N, S, index + 1); // remove element // from set vector set.RemoveAt(set.Count - 1); // exclude (index)th prime primeSum(total, N, S, index + 1); } // function to generate // all primes static void allPrime(int N, int S, int P) { // all primes less than S itself for (int i = P + 1; i <=S ; i++) { // if i is prime add // it to prime vector if (isPrime(i)) prime.Add(i); } // if primes are // less than N if (prime.Count < N) return; primeSum(0, N, S, 0); } // Driver Code static void Main() { int S = 54, N = 2, P = 3; allPrime(N, S, P); } } // This code is contributed by // Manish Shaw(manishshaw1) |
PHP
<?php // PHP Program to print all // N primes after prime P // whose sum equals S // vector to store prime // and N primes whose // sum equals given S $set = array(); $prime = array(); // function to // check prime number function isPrime($x) { // square root of x $sqroot = sqrt($x); $flag = true; // since 1 is not // prime number if ($x == 1) return false; // if any factor is // found return false for ($i = 2; $i <= $sqroot; $i++) if ($x % $i == 0) return false; // no factor found return true; } // function to display N // primes whose sum equals S function display() { global $set, $prime; $length = count($set); for ($i = 0; $i < $length; $i++) echo ($set[$i] . " "); echo ("\n"); } // function to evaluate // all possible N primes // whose sum equals S function primeSum($total, $N, $S, $index) { global $set, $prime; // if total equals S // And total is reached // using N primes if ($total == $S && count($set) == $N) { // display the N primes display(); return; } // if total is greater // than S or if index // has reached last element if ($total > $S || $index == count($prime)) return; // add prime[index] // to set vector array_push($set, $prime[$index]); // include the (index)th // prime to total primeSum($total + $prime[$index], $N, $S, $index + 1); // remove element // from set vector array_pop($set); // exclude (index)th prime primeSum($total, $N, $S, $index + 1); } // function to generate // all primes function allPrime($N, $S, $P) { global $set, $prime; // all primes less // than S itself for ($i = $P + 1; $i <= $S ; $i++) { // if i is prime add // it to prime vector if (isPrime($i)) array_push($prime, $i); } // if primes are // less than N if (count($prime) < $N) return; primeSum(0, $N, $S, 0); } // Driver Code $S = 54; $N = 2; $P = 3; allPrime($N, $S, $P); // This code is contributed by // Manish Shaw(manishshaw1) ?> |
Output:
7 47 11 43 13 41 17 37 23 31
Optimizations :
The above solution can be optimized by pre-computing all required primes using Sieve of Eratosthenes
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