多项式的内容
给定一个表示多项式整数系数的数组 arr[] ，任务是找到多项式的内容。
整系数多项式的内容定义为其整系数的最大公约数。 这是为了:
f(x)= amxm+am-1xm-1+……..+a 1 x + a 0 然后，多项式的内容= gcd(a m ，a m-1 ，a m-2 …。，一个 1 ，一个 0
示例:
输入: arr[] = {9，30，12} 输出: 3 解释: 给定多项式可以是:9x 2 + 30x + 12 因此，Content = gcd(9，30，12) = 3
输入: arr[] = {2，4，6 } T3】输出: 2
方法:思路是寻找数组所有元素的最大公约数，通过一次选择两个元素，反复寻找 GCD，就可以计算出来。那就是:
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 <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 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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
java 描述语言
<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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