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:

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 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;       // 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;       // 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       # 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;       // 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



Output:

3

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