You are given an array of N integer values and M update operations. An update consists of choosing an element of the array and dividing it by a given value. It is guaranteed that the element is divisible by the chosen value. After each update, you should compute the greatest common divisor of all the elements of the array.
Examples:
Input : 3 3 36 24 72 1 3 3 12 2 4 Output :12 6 6 After each operation the array values will be: 1. 12, 24, 72 2. 12, 24, 6 3. 12, 6, 6 Input :5 6 100 150 200 600 300 4 6 2 3 4 4 1 4 2 5 5 25 Output : 50 50 25 25 5 1
Approach: First, you should compute the Greatest Common Divisor(gcd) of all the initial numbers. Because the queries consist of dividing a number by one of its divisors it means that after each query the new gcd is a divisor of the old gcd. So for each query, you should simply compute the gcd between the updated value and the previous gcd.
Implementation:
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
void print_gcd_online( int n, int m,
int query[][2], int arr[])
{ // stores the gcd of the initial array elements
int max_gcd = 0;
int i = 0;
// calculates the gcd
for (i = 0; i < n; i++)
max_gcd = __gcd(max_gcd, arr[i]);
// performing online queries
for (i = 0; i < m; i++)
{
// index is 1 based
query[i][0]--;
// divide the array element
arr[query[i][0]] /= query[i][1];
// calculates the current gcd
max_gcd = __gcd(arr[query[i][0]], max_gcd);
// print the gcd after each step
cout << max_gcd << endl;
}
} // Driver code int main()
{ int n = 3;
int m = 3;
int query[m][2];
int arr[] = {36, 24, 72};
query[0][0] = 1;
query[0][1] = 3;
query[1][0] = 3;
query[1][1] = 12;
query[2][0] = 2;
query[2][1] = 4;
print_gcd_online(n, m, query, arr);
return 0;
} // This code is contributed by // sanjeev2552 |
// Java implementation of the approach class GFG {
// returns the gcd after all updates
// in the array
static int gcd( int a, int b)
{
if (a == 0 )
return b;
return gcd(b % a, a);
}
static void print_gcd_online( int n, int m,
int [][] query, int [] arr)
{
// stores the gcd of the initial array elements
int max_gcd = 0 ;
int i = 0 ;
for (i = 0 ; i < n; i++) // calculates the gcd
max_gcd = gcd(max_gcd, arr[i]);
// performing online queries
for (i = 0 ; i < m; i++) {
query[i][ 0 ]--; // index is 1 based
// divide the array element
arr[query[i][ 0 ]] /= query[i][ 1 ];
// calculates the current gcd
max_gcd = gcd(arr[query[i][ 0 ]], max_gcd);
// print the gcd after each step
System.out.println(max_gcd);
}
}
// Driver code
public static void main(String[] args)
{
int n = 3 ;
int m = 3 ;
int [][] query = new int [m][ 2 ];
int [] arr = new int [] { 36 , 24 , 72 };
query[ 0 ][ 0 ] = 1 ;
query[ 0 ][ 1 ] = 3 ;
query[ 1 ][ 0 ] = 3 ;
query[ 1 ][ 1 ] = 12 ;
query[ 2 ][ 0 ] = 2 ;
query[ 2 ][ 1 ] = 4 ;
print_gcd_online(n, m, query, arr);
}
} |
# Python3 implementation of the # above approach # Returns the gcd after all # updates in the array def gcd(a, b):
if a = = 0 :
return b
return gcd(b % a, a)
def print_gcd_online(n, m, query, arr):
# Stores the gcd of the initial
# array elements
max_gcd = 0
for i in range ( 0 , n): # calculates the gcd
max_gcd = gcd(max_gcd, arr[i])
# performing online queries
for i in range ( 0 , m):
query[i][ 0 ] - = 1 # index is 1 based
# divide the array element
arr[query[i][ 0 ]] / / = query[i][ 1 ]
# calculates the current gcd
max_gcd = gcd(arr[query[i][ 0 ]], max_gcd)
# Print the gcd after each step
print (max_gcd)
# Driver code if __name__ = = "__main__" :
n, m = 3 , 3
query = [[ 1 , 3 ], [ 3 , 12 ], [ 2 , 4 ]]
arr = [ 36 , 24 , 72 ]
print_gcd_online(n, m, query, arr)
# This code is contributed by Rituraj Jain |
// C# implementation of the approach using System;
class GFG
{ // returns the gcd after all // updates in the array static int gcd( int a, int b)
{ if (a == 0)
return b;
return gcd(b % a, a);
} static void print_gcd_online( int n, int m,
int [,] query,
int [] arr)
{ // stores the gcd of the
// initial array elements
int max_gcd = 0;
int i = 0;
for (i = 0; i < n; i++) // calculates the gcd
max_gcd = gcd(max_gcd, arr[i]);
// performing online queries
for (i = 0; i < m; i++)
{
query[i,0]--; // index is 1 based
// divide the array element
arr[query[i, 0]] /= query[i, 1];
// calculates the current gcd
max_gcd = gcd(arr[query[i, 0]], max_gcd);
// print the gcd after each step
Console.WriteLine(max_gcd);
}
} // Driver code public static void Main()
{ int n = 3;
int m = 3;
int [,] query = new int [m, 2];
int [] arr = new int [] { 36, 24, 72 };
query[0, 0] = 1;
query[0, 1] = 3;
query[1, 0] = 3;
query[1, 1] = 12;
query[2, 0] = 2;
query[2, 1] = 4;
print_gcd_online(n, m, query, arr);
} } // This code is contributed // by Subhadeep Gupta |
<?php // PHP implementation of the approach // returns the gcd after all updates // in the array function gcd( $a , $b )
{ if ( $a == 0)
return $b ;
return gcd( $b % $a , $a );
} function print_gcd_online( $n , $m ,
$query , $arr )
{ // stores the gcd of the
// initial array elements
$max_gcd = 0;
$i = 0;
// calculates the gcd
for ( $i = 0; $i < $n ; $i ++)
$max_gcd = gcd( $max_gcd ,
$arr [ $i ]);
// performing online queries
for ( $i = 0; $i < $m ; $i ++)
{
$query [ $i ][0]--; // index is 1 based
// divide the array element
$arr [ $query [ $i ][0]] /= $query [ $i ][1];
// calculates the current gcd
$max_gcd = gcd( $arr [ $query [ $i ][0]],
$max_gcd );
// print the gcd after each step
echo ( $max_gcd ), "\n" ;
}
} // Driver code $n = 3; $m = 3; $query ;
$arr = array ( 36, 24, 72 );
$query [0][0] = 1; $query [0][1] = 3;
$query [1][0] = 3; $query [1][1] = 12;
$query [2][0] = 2; $query [2][1] = 4;
print_gcd_online( $n , $m , $query , $arr );
// This code is contributed by Sach_Code ?> |
<script> // JavaScript implementation of the approach
// returns the gcd after all updates
// in the array
function gcd(a, b)
{
if (a == 0)
return b;
return gcd(b % a, a);
}
function print_gcd_online(n,m,query,arr)
{
// stores the gcd of the initial array elements
let max_gcd = 0;
let i = 0;
// calculates the gcd
for (i = 0; i < n; i++)
max_gcd = gcd(max_gcd, arr[i]);
// performing online queries
for (i = 0; i < m; i++)
{
// index is 1 based
query[i][0]--;
// divide the array element
arr[query[i][0]] /= query[i][1];
// calculates the current gcd
max_gcd = gcd(arr[query[i][0]], max_gcd);
// print the gcd after each step
document.write(max_gcd + "</br>" );
}
}
// Driver code
let n = 3;
let m = 3;
let query = new Array(m);
for (let i = 0; i < m; i++)
{
query[i] = new Array(2);
for (let j = 0; j < 2; j++)
{
query[i][j] = 0;
}
}
let arr = [36, 24, 72];
query[0][0] = 1;
query[0][1] = 3;
query[1][0] = 3;
query[1][1] = 12;
query[2][0] = 2;
query[2][1] = 4;
print_gcd_online(n, m, query, arr);
</script> |
12 6 6
Complexity Analysis:
- Time Complexity : O(m + n)
- Auxiliary Space: O(1)