多项式的内容

给定一个数组arr [] ，它表示多项式的整数系数，任务是找到多项式的内容。

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

F(x) = a_mx^m + a_m-1x^m-1 + ……..+a₁x + a₀
Then, Content of Polynomial = gcd(a_m, a_m-1, a_m-2…., a₁, a₀)

例子：

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

方法：想法是找到阵列中所有元素的最大公约数，这可以通过一次选择两个元素来反复查找GCD来计算。那是：

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

下面是上述方法的实现：

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[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

输出：

3