Online Queries for GCD of array after divide operations
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 to one of its divisors it means the 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.
C++
// 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 |
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Java
// 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); } } |
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Python3
# 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 |
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C#
// 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 |
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PHP
<?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 ?> |
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Output:
12 6 6
Time Complexity : O(m + n)
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