给定两个数组A []和B [] ,任务是找到可被数组A []的所有元素整除的整数,并除以数组B []的所有元素。
例子:
Input: A[] = {1, 2, 2, 4}, B[] = {16, 32, 64}
Output: 4 8 16
4, 8 and 16 are the only numbers that
are multiples of all the elements of array A[]
and divide all the elements of array B[]
Input: A[] = {2, 3, 6}, B[] = {42, 84}
Output: 6 42
方法:如果X是第一个数组的所有元素的倍数,则X必须是第一个数组的所有元素的LCM的倍数。
同样,如果X是第二个数组的所有元素的因数,那么它必须是第二个数组的所有元素的GCD的因数,并且只有当第二个数组的GCD可被LCM整除时,这种X才会存在。第一个数组。
如果它是可整除的,则X可以是[LCM,GCD]范围内的任何值,该范围是LCM的倍数并平均除以GCD。
下面是上述方法的实现:
C++
// C++ implementation of the approach
#include
using namespace std;
// Function to return the LCM of two numbers
int lcm(int x, int y)
{
int temp = (x * y) / __gcd(x, y);
return temp;
}
// Function to print the requried numbers
void findNumbers(int a[], int n, int b[], int m)
{
// To store the lcm of array a[] elements
// and the gcd of array b[] elements
int lcmA = 1, gcdB = 0;
// Finding LCM of first array
for (int i = 0; i < n; i++)
lcmA = lcm(lcmA, a[i]);
// Finding GCD of second array
for (int i = 0; i < m; i++)
gcdB = __gcd(gcdB, b[i]);
// No such element exists
if (gcdB % lcmA != 0) {
cout << "-1";
return;
}
// All the multiples of lcmA which are
// less than or equal to gcdB and evenly
// divide gcdB will satisfy the conditions
int num = lcmA;
while (num <= gcdB) {
if (gcdB % num == 0)
cout << num << " ";
num += lcmA;
}
}
// Driver code
int main()
{
int a[] = { 1, 2, 2, 4 };
int b[] = { 16, 32, 64 };
int n = sizeof(a) / sizeof(a[0]);
int m = sizeof(b) / sizeof(b[0]);
findNumbers(a, n, b, m);
return 0;
}
Java
// Java implementation of the approach
import java.util.*;
class GFG
{
static int __gcd(int a, int b)
{
if (b == 0)
return a;
return __gcd(b, a % b);
}
// Function to return the LCM of two numbers
static int lcm(int x, int y)
{
int temp = (x * y) / __gcd(x, y);
return temp;
}
// Function to print the requried numbers
static void findNumbers(int a[], int n,
int b[], int m)
{
// To store the lcm of array a[] elements
// and the gcd of array b[] elements
int lcmA = 1, gcdB = 0;
// Finding LCM of first array
for (int i = 0; i < n; i++)
lcmA = lcm(lcmA, a[i]);
// Finding GCD of second array
for (int i = 0; i < m; i++)
gcdB = __gcd(gcdB, b[i]);
// No such element exists
if (gcdB % lcmA != 0)
{
System.out.print("-1");
return;
}
// All the multiples of lcmA which are
// less than or equal to gcdB and evenly
// divide gcdB will satisfy the conditions
int num = lcmA;
while (num <= gcdB)
{
if (gcdB % num == 0)
System.out.print(num + " ");
num += lcmA;
}
}
// Driver code
public static void main(String[] args)
{
int a[] = { 1, 2, 2, 4 };
int b[] = { 16, 32, 64 };
int n = a.length;
int m = b.length;
findNumbers(a, n, b, m);
}
}
// This code is contributed by 29AjayKumar
Python3
# Python3 implementation of the approach
from math import gcd
# Function to return the LCM of two numbers
def lcm( x, y) :
temp = (x * y) // gcd(x, y);
return temp;
# Function to print the requried numbers
def findNumbers(a, n, b, m) :
# To store the lcm of array a[] elements
# and the gcd of array b[] elements
lcmA = 1; __gcdB = 0;
# Finding LCM of first array
for i in range(n) :
lcmA = lcm(lcmA, a[i]);
# Finding GCD of second array
for i in range(m) :
__gcdB = gcd(__gcdB, b[i]);
# No such element exists
if (__gcdB % lcmA != 0) :
print("-1");
return;
# All the multiples of lcmA which are
# less than or equal to gcdB and evenly
# divide gcdB will satisfy the conditions
num = lcmA;
while (num <= __gcdB) :
if (__gcdB % num == 0) :
print(num, end = " ");
num += lcmA;
# Driver code
if __name__ == "__main__" :
a = [ 1, 2, 2, 4 ];
b = [ 16, 32, 64 ];
n = len(a);
m = len(b);
findNumbers(a, n, b, m);
# This code is contributed by AnkitRai01
C#
// C# implementation of the approach
using System;
class GFG
{
static int __gcd(int a, int b)
{
if (b == 0)
return a;
return __gcd(b, a % b);
}
// Function to return the LCM of two numbers
static int lcm(int x, int y)
{
int temp = (x * y) / __gcd(x, y);
return temp;
}
// Function to print the requried numbers
static void findNumbers(int []a, int n,
int []b, int m)
{
// To store the lcm of array a[] elements
// and the gcd of array b[] elements
int lcmA = 1, gcdB = 0;
// Finding LCM of first array
for (int i = 0; i < n; i++)
lcmA = lcm(lcmA, a[i]);
// Finding GCD of second array
for (int i = 0; i < m; i++)
gcdB = __gcd(gcdB, b[i]);
// No such element exists
if (gcdB % lcmA != 0)
{
Console.Write("-1");
return;
}
// All the multiples of lcmA which are
// less than or equal to gcdB and evenly
// divide gcdB will satisfy the conditions
int num = lcmA;
while (num <= gcdB)
{
if (gcdB % num == 0)
Console.Write(num + " ");
num += lcmA;
}
}
// Driver code
public static void Main(String[] args)
{
int []a = { 1, 2, 2, 4 };
int []b = { 16, 32, 64 };
int n = a.Length;
int m = b.Length;
findNumbers(a, n, b, m);
}
}
// This code is contributed by 29AjayKumar
Javascript
输出:
4 8 16