Insert minimum number in array so that sum of array becomes prime
Last Updated :
18 Jan, 2024
Given an array of n integers. Find minimum number to be inserted in array, so that sum of all elements of array becomes prime. If sum is already prime, then return 0.
Examples :
Input : arr[] = { 2, 4, 6, 8, 12 }
Output : 5
Input : arr[] = { 3, 5, 7 }
Output : 0
Naive approach: The simplest approach to solve this problem is to first find the sum of array elements. Then check if this sum is prime or not, if sum is prime return zero otherwise find prime number just greater than this sum. We can find prime number greater than sum by checking if a number is prime or not from (sum+1) until we find a prime number. Once a prime number just greater than sum is found, return difference of sum and this prime number.
Below is implementation of above idea:
C++
// C++ program to find minimum number to
// insert in array so their sum is prime
#include <bits/stdc++.h>
using namespace std;
// function to check if a
// number is prime or not
bool isPrime(int n)
{
// Corner case
if (n <= 1)
return false;
// Check from 2 to n - 1
for (int i = 2; i < n; i++)
if (n % i == 0)
return false;
return true;
}
// Find prime number
// greater than a number
int findPrime(int n)
{
int num = n + 1;
// find prime greater than n
while (num)
{
// check if num is prime
if (isPrime(num))
return num;
// increment num
num = num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
int minNumber(int arr[], int n)
{
int sum = 0;
// To find sum of array elements
for (int i = 0; i < n; i++)
sum += arr[i];
// if sum is already prime
// return 0
if (isPrime(sum))
return 0;
// To find prime number
// greater than sum
int num = findPrime(sum);
// Return difference of
// sum and num
return num - sum;
}
// Driver code
int main()
{
int arr[] = { 2, 4, 6, 8, 12 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << minNumber(arr, n);
return 0;
}
// Java program to find minimum number to
// insert in array so their sum is prime
class GFG
{
// function to check if a
// number is prime or not
static boolean isPrime(int n)
{
// Corner case
if (n <= 1)
return false;
// Check from 2 to n - 1
for (int i = 2; i < n; i++)
if (n % i == 0)
return false;
return true;
}
// Find prime number
// greater than a number
static int findPrime(int n)
{
int num = n + 1;
// find prime greater than n
while (num > 0)
{
// check if num is prime
if (isPrime(num))
return num;
// increment num
num = num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
static int minNumber(int arr[], int n)
{
int sum = 0;
// To find sum of array elements
for (int i = 0; i < n; i++)
sum += arr[i];
// if sum is already prime
// return 0
if (isPrime(sum))
return 0;
// To find prime number
// greater than sum
int num = findPrime(sum);
// Return difference of
// sum and num
return num - sum;
}
// Driver Code
public static void main(String[]args)
{
int arr[] = { 2, 4, 6, 8, 12 };
int n = arr.length;
System.out.println(minNumber(arr, n));
}
}
// This code is contributed by Azkia Anam.
# Python3 program to find minimum number to
# insert in array so their sum is prime
# function to check if a
# number is prime or not
def isPrime(n):
# Corner case
if n <= 1:
return False
# Check from 2 to n - 1
for i in range(2, n):
if n % i == 0:
return False
return True
# Find prime number
# greater than a number
def findPrime(n):
num = n + 1
# find prime greater than n
while (num):
# check if num is prime
if isPrime(num):
return num
# Increment num
num += 1
return 0
# To find number to be added
# so sum of array is prime
def minNumber(arr):
s = 0
# To find sum of array elements
for i in range(0, len(arr)):
s += arr[i]
# If sum is already prime
# return 0
if isPrime(s) :
return 0
# To find prime number
# greater than sum
num = findPrime(s)
# Return difference of sum and num
return num - s
# Driver code
arr = [ 2, 4, 6, 8, 12 ]
print (minNumber(arr))
# This code is contributed by Sachin Bisht
// C# program to find minimum number to
// insert in array so their sum is prime
using System;
class GFG
{
// function to check if a
// number is prime or not
static bool isPrime(int n)
{
// Corner case
if (n <= 1)
return false;
// Check from 2 to n - 1
for (int i = 2; i < n; i++)
if (n % i == 0)
return false;
return true;
}
// Find prime number
// greater than a number
static int findPrime(int n)
{
int num = n + 1;
// find prime greater than n
while (num > 0)
{
// check if num is prime
if (isPrime(num))
return num;
// increment num
num = num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
static int minNumber(int []arr, int n)
{
int sum = 0;
// To find sum of array elements
for (int i = 0; i < n; i++)
sum += arr[i];
// if sum is already prime
// return 0
if (isPrime(sum))
return 0;
// To find prime number
// greater than sum
int num = findPrime(sum);
// Return difference of sum and num
return num - sum;
}
// Driver Code
public static void Main()
{
int []arr = { 2, 4, 6, 8, 12 };
int n = arr.Length;
Console.Write(minNumber(arr, n));
}
}
// This code is contributed by nitin mittal
<?php
// PHP program to find minimum number to
// insert in array so their sum is prime
// function to check if a
// number is prime or not
function isPrime($n)
{
// Corner case
if ($n <= 1)
return false;
// Check from 2 to n - 1
for ($i = 2; $i < $n; $i++)
if ($n % $i == 0)
return false;
return true;
}
// Find prime number
// greater than a number
function findPrime($n)
{
$num = $n + 1;
// find prime greater than n
while ($num)
{
// check if num is prime
if (isPrime($num))
return $num;
// increment num
$num = $num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
function minNumber($arr, $n)
{
$sum = 0;
// To find sum of array elements
for ($i = 0; $i < $n; $i++)
$sum += $arr[$i];
// if sum is already prime
// return 0
if (isPrime($sum))
return 0;
// To find prime number
// greater than sum
$num = findPrime($sum);
// Return difference of
// sum and num
return $num - $sum;
}
// Driver Code
$arr = array(2, 4, 6, 8, 12);
$n = sizeof($arr);
echo minNumber($arr, $n);
// This code is contributed by nitin mittal
?>
<script>
// Javascript program to find minimum number to
// insert in array so their sum is prime
// function to check if a
// number is prime or not
function isPrime(n)
{
// Corner case
if (n <= 1)
return false;
// Check from 2 to n - 1
for (let i = 2; i < n; i++)
if (n % i == 0)
return false;
return true;
}
// Find prime number
// greater than a number
function findPrime(n)
{
let num = n + 1;
// find prime greater than n
while (num > 0)
{
// check if num is prime
if (isPrime(num))
return num;
// increment num
num = num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
function minNumber(arr,n)
{
let sum = 0;
// To find sum of array elements
for (let i = 0; i < n; i++)
sum += arr[i];
// if sum is already prime
// return 0
if (isPrime(sum))
return 0;
// To find prime number
// greater than sum
let num = findPrime(sum);
// Return difference of
// sum and num
return num - sum;
}
// Driver Code
let arr=[2, 4, 6, 8, 12 ];
let n = arr.length;
document.write(minNumber(arr, n));
//This code is contributed by avanitrachhadiya2155
</script>
Time Complexity: O( N2 )
Efficient Approach: We can optimize the above approach by efficiently pre calculating a large boolean array to check if a number is prime or not using sieve of eratosthenes. Once all prime number are generated, find prime number just greater than sum and return the difference between them.
Below is the implementation of this approach:
C++
// C++ program to find minimum number to
// insert in array so their sum is prime
#include <bits/stdc++.h>
using namespace std;
#define MAX 100005
// Array to store primes
bool isPrime[MAX];
// function to calculate primes
// using sieve of eratosthenes
void sieveOfEratostheneses()
{
memset(isPrime, true, sizeof(isPrime));
isPrime[1] = false;
for (int i = 2; i * i < MAX; i++)
{
if (isPrime[i])
{
for (int j = 2 * i; j < MAX; j += i)
isPrime[j] = false;
}
}
}
// Find prime number
// greater than a number
int findPrime(int n)
{
int num = n + 1;
// To return prime number
// greater than n
while (num)
{
// check if num is prime
if (isPrime[num])
return num;
// increment num
num = num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
int minNumber(int arr[], int n)
{
// call sieveOfEratostheneses
// to calculate primes
sieveOfEratostheneses();
int sum = 0;
// To find sum of array elements
for (int i = 0; i < n; i++)
sum += arr[i];
if (isPrime[sum])
return 0;
// To find prime number
// greater then sum
int num = findPrime(sum);
// Return difference of
// sum and num
return num - sum;
}
// Driver Code
int main()
{
int arr[] = { 2, 4, 6, 8, 12 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << minNumber(arr, n);
return 0;
}
// Java program to find minimum number to
// insert in array so their sum is prime
class GFG
{
static int MAX = 100005;
// Array to store primes
static boolean[] isPrime = new boolean[MAX];
// function to calculate primes
// using sieve of eratosthenes
static void sieveOfEratostheneses()
{
isPrime[1] = true;
for (int i = 2; i * i < MAX; i++)
{
if (!isPrime[i])
{
for (int j = 2 * i; j < MAX; j += i)
isPrime[j] = true;
}
}
}
// Find prime number greater
// than a number
static int findPrime(int n)
{
int num = n + 1;
// To return prime number
// greater than n
while (num > 0)
{
// check if num is prime
if (!isPrime[num])
return num;
// increment num
num = num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
static int minNumber(int arr[], int n)
{
// call sieveOfEratostheneses
// to calculate primes
sieveOfEratostheneses();
int sum = 0;
// To find sum of array elements
for (int i = 0; i < n; i++)
sum += arr[i];
if (!isPrime[sum])
return 0;
// To find prime number
// greater then sum
int num = findPrime(sum);
// Return difference of
// sum and num
return num - sum;
}
// Driver Code
public static void main(String[] args)
{
int arr[] = { 2, 4, 6, 8, 12 };
int n = arr.length;
System.out.println(minNumber(arr, n));
}
}
// This code is contributed by mits
# Python3 program to find minimum number to
# insert in array so their sum is prime
isPrime = [1] * 100005
# function to calculate prime
# using sieve of eratosthenes
def sieveOfEratostheneses():
isPrime[1] = False
i = 2
while i * i < 100005:
if(isPrime[i]):
j = 2 * i
while j < 100005:
isPrime[j] = False
j += i
i += 1
return
# Find prime number
# greater than a number
def findPrime(n):
num = n + 1
# find prime greater than n
while(num):
# check if num is prime
if isPrime[num]:
return num
# Increment num
num += 1
return 0
# To find number to be added
# so sum of array is prime
def minNumber(arr):
# call sieveOfEratostheneses to
# calculate primes
sieveOfEratostheneses()
s = 0
# To find sum of array elements
for i in range(0, len(arr)):
s += arr[i]
# If sum is already prime
# return 0
if isPrime[s] == True:
return 0
# To find prime number
# greater than sum
num = findPrime(s)
# Return difference of
# sum and num
return num - s
# Driver code
arr = [ 2, 4, 6, 8, 12 ]
print (minNumber(arr))
# This code is contributed by Sachin Bisht
// C# program to find minimum number to
// insert in array so their sum is prime
class GFG
{
static int MAX = 100005;
// Array to store primes
static bool[] isPrime = new bool[MAX];
// function to calculate primes
// using sieve of eratosthenes
static void sieveOfEratostheneses()
{
isPrime[1] = true;
for (int i = 2; i * i < MAX; i++)
{
if (!isPrime[i])
{
for (int j = 2 * i; j < MAX; j += i)
isPrime[j] = true;
}
}
}
// Find prime number greater
// than a number
static int findPrime(int n)
{
int num = n + 1;
// To return prime number
// greater than n
while (num > 0)
{
// check if num is prime
if (!isPrime[num])
return num;
// increment num
num = num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
static int minNumber(int[] arr, int n)
{
// call sieveOfEratostheneses
// to calculate primes
sieveOfEratostheneses();
int sum = 0;
// To find sum of array elements
for (int i = 0; i < n; i++)
sum += arr[i];
if (!isPrime[sum])
return 0;
// To find prime number
// greater then sum
int num = findPrime(sum);
// Return difference of
// sum and num
return num - sum;
}
// Driver Code
public static void Main()
{
int[] arr = { 2, 4, 6, 8, 12 };
int n = arr.Length;
System.Console.WriteLine(minNumber(arr, n));
}
}
// This code is contributed by mits
<?php
// PHP program to find minimum number to
// insert in array so their sum is prime
$MAX =100005;
// function to calculate primes
// using sieve of eratosthenes
function sieveOfEratostheneses()
{
$isPrime = array_fill(true,$MAX, NULL);
$isPrime[1] = false;
for ($i = 2; $i * $i < $MAX; $i++)
{
if ($isPrime[$i])
{
for ($j = 2 * $i; $j < $MAX; $j += $i)
$isPrime[$j] = false;
}
}
}
// Find prime number
// greater than a number
function findPrime($n)
{
$num = $n + 1;
// To return prime number
// greater than n
while ($num)
{
// check if num is prime
if ($isPrime[$num])
return $num;
// increment num
$num = $num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
function minNumber(&$arr, $n)
{
// call sieveOfEratostheneses
// to calculate primes
sieveOfEratostheneses();
$sum = 0;
// To find sum of array elements
for ($i = 0; $i < $n; $i++)
$sum += $arr[$i];
if ($isPrime[$sum])
return 0;
// To find prime number
// greater then sum
$num = findPrime($sum);
// Return difference of
// sum and num
return $num - $sum;
}
// Driver Code
$arr = array ( 2, 4, 6, 8, 12 );
$n = sizeof($arr) / sizeof($arr[0]);
echo minNumber($arr, $n);
return 0;
?>
<script>
// Javascript program to find minimum number to
// insert in array so their sum is prime
let MAX = 100005;
// Array to store primes
let isPrime = new Array(MAX).fill(0);
// function to calculate primes
// using sieve of eratosthenes
function sieveOfEratostheneses()
{
isPrime[1] = true;
for (let i = 2; i * i < MAX; i++)
{
if (!isPrime[i])
{
for (let j = 2 * i; j < MAX; j += i)
isPrime[j] = true;
}
}
}
// Find prime number greater
// than a number
function findPrime(n)
{
let num = n + 1;
// To return prime number
// greater than n
while (num > 0)
{
// check if num is prime
if (!isPrime[num])
return num;
// increment num
num = num + 1;
}
return 0;
}
// To find number to be added
// so sum of array is prime
function minNumber(arr, n)
{
// call sieveOfEratostheneses
// to calculate primes
sieveOfEratostheneses();
let sum = 0;
// To find sum of array elements
for (let i = 0; i < n; i++)
sum += arr[i];
if (!isPrime[sum])
return 0;
// To find prime number
// greater then sum
let num = findPrime(sum);
// Return difference of
// sum and num
return num - sum;
}
// driver program
let arr = [ 2, 4, 6, 8, 12 ];
let n = arr.length;
document.write(minNumber(arr, n));
// This code is contributed by code_hunt.
</script>
Time Complexity: O(N log(log N))
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