给定一个整数数组。找到一个整数X，它是给定数组中除一个元素外的所有元素的除数。
注意：所有元素的GCD都不是1。
例子：
Input : arr[] = {6, 18, 3, 12}
Output : 6
6 is the divisor of all except 3.
Input : arr[] = {40, 15, 30, 42}
Output : 3
3 is the divisor of all except 40.
方法：制作一个前缀数组P，使索引i包含从1到i的所有元素的GCD。类似地，制作一个后缀数组S，使索引i包含从i到n-1(最后一个索引)的所有元素的GCD。如果P [i-1]和S [i + 1]的GCD不是i处元素的除数，则它是必需的答案。
下面是上述方法的实现：
C++
// C++ program to find the divisor of all
// except for exactly one element in an array.
#include
using namespace std;
// Function that returns the divisor of all
// except for exactly one element in an array.
int getDivisor(int a[], int n)
{
// There's only one element in the array
if (n == 1)
return (a[0] + 1);
int P[n], S[n];
// Creating prefix array of GCD
P[0] = a[0];
for (int i = 1; i < n; i++)
P[i] = __gcd(a[i], P[i - 1]);
// Creating suffix array of GCD
S[n-1] = a[n-1];
for (int i = n - 2; i >= 0; i--)
S[i] = __gcd(S[i + 1], a[i]);
// Iterate through the array
for (int i = 0; i <= n; i++) {
// Variable to store the divisor
int cur;
// Getting the divisor
if (i == 0)
cur = S[i + 1];
else if (i == n - 1)
cur = P[i - 1];
else
cur = __gcd(P[i - 1], S[i + 1]);
// Check if it is not a divisor of a[i]
if (a[i] % cur != 0)
return cur;
}
return 0;
}
// Driver code
int main()
{
int a[] = { 12, 6, 18, 12, 16 };
int n = sizeof(a) / sizeof(a[0]);
cout << getDivisor(a, n);
return 0;
} Java
// Java program to find the divisor of all
// except for exactly one element in an array.
import java.io.*;
class GFG {
// Recursive function to return gcd of a and b
static int __gcd(int a, int b)
{
// Everything divides 0
if (a == 0)
return b;
if (b == 0)
return a;
// base case
if (a == b)
return a;
// a is greater
if (a > b)
return __gcd(a-b, b);
return __gcd(a, b-a);
}
// Function that returns the divisor of all
// except for exactly one element in an array.
static int getDivisor(int a[], int n)
{
// There's only one element in the array
if (n == 1)
return (a[0] + 1);
int P[] = new int[n];
int S[] = new int[n];
// Creating prefix array of GCD
P[0] = a[0];
for (int i = 1; i < n; i++)
P[i] = __gcd(a[i], P[i - 1]);
// Creating suffix array of GCD
S[n-1] = a[n-1];
for (int i = n - 2; i >= 0; i--)
S[i] = __gcd(S[i + 1], a[i]);
// Iterate through the array
for (int i = 0; i < n; i++) {
// Variable to store the divisor
int cur;
// Getting the divisor
if (i == 0)
cur = S[i + 1];
else if (i == n - 1)
cur = P[i - 1];
else
cur = __gcd(P[i - 1], S[i + 1]);
// Check if it is not a divisor of a[i]
if (a[i] % cur != 0)
return cur;
}
return 0;
}
// Driver code
public static void main (String[] args) {
int a[] = { 12, 6, 18, 12, 16 };
int n = a.length;
System.out.println(getDivisor(a, n));
}
}
// This code is contributed by anuj_67..Python 3
# Python 3 program to find the divisor of all
# except for exactly one element in an array.
from math import gcd
# Function to find the divisor of all
# except for exactly one element in an array.
def getDivisor(a, n):
# There's only one element in the array
if (n == 1):
return (a[0] + 1)
P = [0] * n
S = [0] * n
# Creating prefix array of GCD
P[0] = a[0]
for i in range(1, n):
P[i] = gcd(a[i], P[i - 1])
# Creating suffix array of GCD
S[n - 1] = a[n - 1]
for i in range(n - 2, -1, -1):
S[i] = gcd(S[i + 1], a[i])
# Iterate through the array
for i in range(0, n + 1):
# Variable to store the divisor
cur = 0
# Getting the divisor
if (i == 0):
cur = S[i + 1]
elif (i == n - 1):
cur = P[i - 1]
else:
cur = gcd(P[i - 1], S[i + 1])
# Check if it is not a divisor of a[i]
if (a[i] % cur != 0):
return cur
return 0;
# Driver Code
if __name__=='__main__':
a = [12, 6, 18, 12, 16]
n = len(a)
print(getDivisor(a, n))
# This code is contributed by Rupesh RaoC#
// C# program to find the divisor of all
// except for exactly one element in an array.
using System;
class GFG
{
// Recursive function to return gcd of a and b
static int __gcd(int a, int b)
{
// Everything divides 0
if (a == 0)
return b;
if (b == 0)
return a;
// base case
if (a == b)
return a;
// a is greater
if (a > b)
return __gcd(a - b, b);
return __gcd(a, b - a);
}
// Function that returns the divisor of all
// except for exactly one element in an array.
static int getDivisor(int[] a, int n)
{
// There's only one element in the array
if (n == 1)
return (a[0] + 1);
int[] P = new int[n];
int[] S = new int[n];
// Creating prefix array of GCD
P[0] = a[0];
for (int i = 1; i < n; i++)
P[i] = __gcd(a[i], P[i - 1]);
// Creating suffix array of GCD
S[n - 1] = a[n - 1];
for (int i = n - 2; i >= 0; i--)
S[i] = __gcd(S[i + 1], a[i]);
// Iterate through the array
for (int i = 0; i <= n; i++)
{
// Variable to store the divisor
int cur;
// Getting the divisor
if (i == 0)
cur = S[i + 1];
else if (i == n - 1)
cur = P[i - 1];
else
cur = __gcd(P[i - 1], S[i + 1]);
// Check if it is not a divisor of a[i]
if (a[i] % cur != 0)
return cur;
}
return 0;
}
// Driver code
public static void Main ()
{
int[] a = { 12, 6, 18, 12, 16 };
int n = a.Length;
Console.WriteLine(getDivisor(a, n));
}
}
// This code is contributed
// by Akanksha RaiPHP
$b)
return __gcd($a - $b, $b);
return __gcd($a, $b - $a);
}
// Function that returns the divisor of all
// except for exactly one element in an array.
function getDivisor($a, $n)
{
// There's only one element in the array
if ($n == 1)
return ($a[0] + 1);
$P = array() ;
$S = array() ;
// Creating prefix array of GCD
$P[0] = $a[0];
for ($i = 1; $i < $n; $i++)
$P[$i] = __gcd($a[$i], $P[$i - 1]);
// Creating suffix array of GCD
$S[$n - 1] = $a[$n - 1];
for ($i = $n - 2; $i >= 0; $i--)
$S[$i] = __gcd($S[$i + 1], $a[$i]);
// Iterate through the array
for ($i = 0; $i <= $n; $i++)
{
// Getting the divisor
if ($i == 0)
$cur = $S[$i + 1];
else if ($i == $n - 1)
$cur = $P[$i - 1];
else
$cur = __gcd($P[$i - 1], $S[$i + 1]);
// Check if it is not a divisor of a[i]
if ($a[$i] % $cur != 0)
return $cur;
}
return 0;
}
// Driver code
$a = array( 12, 6, 18, 12, 16 );
$n = sizeof($a);
echo getDivisor($a, $n);
// This code is contributed by Ryuga
?>输出：
6