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Content of a Polynomial

  • Difficulty Level : Basic
  • Last Updated : 22 Apr, 2021

Given an array arr[] which denotes the integer coefficients of the polynomial, the task is to find the content of the polynomial.
 

Content of polynomials with integer coefficients is defined as the greatest common divisor of its integer coefficients.
That is for:

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F(x) = amxm + am-1xm-1 + ……..+a1x + a0
Then, Content of Polynomial = gcd(am, am-1, am-2…., a1, a0)

Examples: 



Input: arr[]  = {9, 30, 12} 
Output: 3
Explanation:
Given Polynomial can be: 9x2 + 30x + 12
Therefore, Content = gcd(9, 30, 12) = 3

Input: arr[] = {2, 4, 6}
Output: 2

 

Approach: The idea is to find the Greatest common divisor of all the elements of the array which can be computed by finding the GCD repeatedly by choosing two elements at a time. That is:

gcd(a, b, c)
 = gcd(gcd(a, b), c)
 = gcd(a, gcd(b, c))
 = gcd(gcd(a, c), b)

Below is the implementation of the above approach:

C++




// C++ implementation to find the
// content of the polynomial
 
#include <bits/stdc++.h>
using namespace std;
 
#define newl "\n"
#define ll long long
#define pb push_back
 
// Function to find the content
// of the polynomial
int findContent(int arr[], int n)
{
    int content = arr[0];
 
    // Loop to iterate over the
    // elements of the array
    for (int i = 1; i < n; i++) {
 
        //__gcd(a, b) is a inbuilt
        // function for Greatest
        // Common Divisor
        content = __gcd(content, arr[i]);
    }
 
    return content;
}
 
// Driver Code
int main()
{
    int n = 3;
    int arr[] = { 9, 6, 12 };
 
    // Function call
    cout << findContent(arr, n);
    return 0;
}

Java




// Java implementation to find the
// content of the polynomial
class GFG{
 
// Function to find the content
// of the polynomial
static int findContent(int arr[], int n)
{
    int content = arr[0];
 
    // Loop to iterate over the
    // elements of the array
    for(int i = 1; i < n; i++)
    {
         
        //__gcd(a, b) is a inbuilt
        // function for Greatest
        // Common Divisor
        content = __gcd(content, arr[i]);
    }
    return content;
}
 
static int __gcd(int a, int b)
{
    return b == 0 ? a : __gcd(b, a % b);    
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 3;
    int arr[] = { 9, 6, 12 };
 
    // Function call
    System.out.print(findContent(arr, n));
}
}
 
// This code is contributed by sapnasingh4991

Python3




# Python3 implementation to find the
# content of the polynomial
from math import gcd
 
# Function to find the content
# of the polynomial
def findContent(arr, n):
     
    content = arr[0]
 
    # Loop to iterate over the
    # elements of the array
    for i in range(1, n):
 
        # __gcd(a, b) is a inbuilt
        # function for Greatest
        # Common Divisor
        content = gcd(content, arr[i])
 
    return content
 
# Driver Code
if __name__ == '__main__':
     
    n = 3
    arr = [ 9, 6, 12 ]
 
    # Function call
    print(findContent(arr, n))
 
# This code is contributed by mohit kumar 29

C#




// C# implementation to find the
// content of the polynomial
using System;
 
class GFG{
 
// Function to find the content
// of the polynomial
static int findContent(int []arr, int n)
{
    int content = arr[0];
 
    // Loop to iterate over the
    // elements of the array
    for(int i = 1; i < n; i++)
    {
         
        //__gcd(a, b) is a inbuilt
        // function for Greatest
        // Common Divisor
        content = __gcd(content, arr[i]);
    }
    return content;
}
 
static int __gcd(int a, int b)
{
    return b == 0 ? a : __gcd(b, a % b);    
}
 
// Driver Code
public static void Main(String[] args)
{
    int n = 3;
    int []arr = { 9, 6, 12 };
 
    // Function call
    Console.Write(findContent(arr, n));
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
 
// Javascript implementation to find the
// content of the polynomial
 
// Function to find the content
// of the polynomial
function findContent(arr, n)
{
    var content = arr[0];
 
    // Loop to iterate over the
    // elements of the array
    for(var i = 1; i < n; i++)
    {
         
        //__gcd(a, b) is a inbuilt
        // function for Greatest
        // Common Divisor
        content = __gcd(content, arr[i]);
    }
    return content;
}
 
function __gcd(a, b)
{
    return b == 0 ? a : __gcd(b, a % b);    
}
 
// Driver Code
var n = 3;
var arr = [ 9, 6, 12 ];
 
// Function call
document.write(findContent(arr, n));
 
// This code is contributed by kirti
 
</script>

 
 

Output: 
3

 

 




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