Given an array arr[] of size N. The task is to reorder arr[] and find the maximum number of GCD pairs which follows the conditions given below.
- Choose any two elements of array Ai and Aj of array where 0 <= i < j < N.
- Calculate GCD after multiplying Aj with 2 like (Ai, 2 * Aj) which is greater than 1.
Examples
Input: arr[] = { 3, 6 . 5, 3}
Output: 4
Explanation: Reorder array like this : { 6, 5, 3, 3 } and below are the pairs formed from arr[].
P1 = GCD( 6, 5 * 2) => (6, 10) => 2 > 1
P2 = GCD( 6, 3 * 2) => (6, 6) => 6 > 1
P3 = GCD( 6, 3 * 2) => (6, 6) => 6 > 1
P4 = GCD( 3, 3 * 2) => (3, 6) => 3 > 1Input: arr[] = { 1, 7 }
Output: 0
Explanation: If array is order like { 7, 1 } no pair can be formed
GCD(7, 1 * 2) = > (7, 2 ), GCD(1, 7 * 2) => (1, 14) == 1
Approach: If we observe that if even elements are in starting position then the pairs of (GCD > 1) is maximum because there is a condition to multiply the arr[j] * 2, and the ordering of odd elements does not matter its number of pair always same. Follow the steps below to solve the given problem.
- Initialize the variable idx with value 0.
- Traverse the array.
- If arr[i] is even then swap with arr[idx] and increment idx by 1.
- After traversing all the elements.
- Initialize the variable ans with 0.
- Use two loops first with i and second with j = i + 1.
- Now if gcd(arr[i], 2 * arr[j] * 2) > 1 increment the ans by 1.
Below is the implementation of the above approach.
// C++ program for above approach #include <bits/stdc++.h> using namespace std;
// Function to find the maximum number of pairs int maximumpairs( int arr[], int n)
{ // Reorder array with even element first
int idx = 0;
for ( int i = 0; i < n; i++) {
if (arr[i] % 2 == 0) {
swap(arr[i], arr[idx]);
idx++;
}
}
// Now count the ans
int ans = 0;
for ( int i = 0; i < n; i++) {
for ( int j = i + 1; j < n; j++) {
if (__gcd(arr[i], 2 * arr[j]) > 1) {
ans++;
}
}
}
return ans;
} // Driver Code int main()
{ // Initializations
int arr[] = { 5, 3, 6, 3 };
int N = sizeof (arr) / sizeof ( int );
// Function Call
int ans = maximumpairs(arr, N);
cout << ans;
return 0;
} |
// Java program for the above approach import java.io.*;
import java.lang.*;
import java.util.*;
class GFG {
// find gcd
static int gcd( int a, int b)
{
if (b == 0 )
return a;
return gcd(b, a % b);
}
// Function to find the maximum number of pairs
static int maximumpairs( int arr[], int n)
{
// Reorder array with even element first
int idx = 0 ;
for ( int i = 0 ; i < n; i++) {
if (arr[i] % 2 == 0 ) {
//swap
int temp = arr[i];
arr[i] = arr[idx];
arr[idx] = temp;
idx++;
}
}
// Now count the ans
int ans = 0 ;
for ( int i = 0 ; i < n; i++) {
for ( int j = i + 1 ; j < n; j++) {
int a = arr[i];
int b = 2 * arr[j];
if (gcd(a, b) > 1 ) {
ans++;
}
}
}
return ans;
}
public static void main (String[] args)
{
// Initializations
int arr[] = { 5 , 3 , 6 , 3 };
int N = arr.length;
// Function Call
int ans = maximumpairs(arr, N);
System.out.println(ans);
}
} // This code is contributed by hrithikgarg03188 |
# Python program for above approach # Function to find GCD def gcd(a, b):
if (b = = 0 ):
return a
else :
return gcd(b, a % b)
# Function to find the maximum number of pairs def maximumpairs(arr,n):
# Reorder array with even element first
idx = 0
for i in range ( 0 , n):
if (arr[i] % 2 = = 0 ):
arr[i], arr[idx] = arr[idx], arr[i]
idx = idx + 1
# Now count the ans
ans = 0
for i in range ( 0 ,n):
for j in range (i + 1 ,n):
if (gcd(arr[i], 2 * arr[j]) > 1 ):
ans = ans + 1
return ans
# Driver Code # Initializations arr = [ 5 , 3 , 6 , 3 ]
N = len (arr)
# Function Call ans = maximumpairs(arr, N)
print (ans)
# This code is contributed by Taranpreet |
// C# program for the above approach using System;
class GFG {
// find gcd
static int gcd( int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
// Function to find the maximum number of pairs
static int maximumpairs( int []arr, int n)
{
// Reorder array with even element first
int idx = 0;
for ( int i = 0; i < n; i++) {
if (arr[i] % 2 == 0) {
//swap
int temp = arr[i];
arr[i] = arr[idx];
arr[idx] = temp;
idx++;
}
}
// Now count the ans
int ans = 0;
for ( int i = 0; i < n; i++) {
for ( int j = i + 1; j < n; j++) {
int a = arr[i];
int b = 2 * arr[j];
if (gcd(a, b) > 1) {
ans++;
}
}
}
return ans;
}
public static void Main ()
{
// Initializations
int []arr = { 5, 3, 6, 3 };
int N = arr.Length;
// Function Call
int ans = maximumpairs(arr, N);
Console.Write(ans);
}
} // This code is contributed by Samim Hossain Mondal. |
<script> // Javascript program for the above approach // find gcd function gcd(a, b)
{ if (b == 0)
return a;
return gcd(b, a % b);
} // Function to find the maximum number of pairs function maximumpairs(arr, n)
{ // Reorder array with even element first
let idx = 0;
for (let i = 0; i < n; i++) {
if (arr[i] % 2 == 0) {
//swap
let temp = arr[i];
arr[i] = arr[idx];
arr[idx] = temp;
idx++;
}
}
// Now count the ans
let ans = 0;
for (let i = 0; i < n; i++) {
for (let j = i + 1; j < n; j++) {
let a = arr[i];
let b = 2 * arr[j];
if (gcd(a, b) > 1) {
ans++;
}
}
}
return ans;
} // Initializations
let arr = [ 5, 3, 6, 3 ];
let N = arr.length;
// Function Call
let ans = maximumpairs(arr, N);
document.write(ans);
// This code is contributed by Samim Hossain Mondal.
</script>
|
4
Time Complexity: O(N * N * logN)
Auxiliary Space: O(1)