Minimizing array sum by subtracting larger elements from smaller ones
Given an array of n elements perform, we need to minimize array sum. We are allowed to perform below operation any number of times.
- Choose any two elements from the array say A and B where A > B and then subtract B from A.
Examples:
Input : 1
arr[] = 1
Output : 1
There is no need to apply the above operation
because there is only a single number that is 1.
Hence, the minimum sum of the array is 1.
Input : 3
arr[] = 2 4 6
Output : 6
Perform the following operations:-
subtract 2 from 4 then the array becomes 2 2 6
subtract 2 (at 2nd position) from 6 the array
becomes 2 2 4
subtract 2 (at 2nd position) from 4 the array
becomes 2 2 2
Now the sum of the array will be 6.
Approach : After applying all the operations, all the values in the given array will be equal otherwise we can still choose two numbers A and B such that A > B and can reduce the sum further. Value of each element after applying all the operation will be equal to gcd of the array i.e. ans.
Therefore, minimum possible sum will be equal to n * ans.
Below is the implementation of above approach:
C++
// CPP program to find the minimum // sum of the array. #include <bits/stdc++.h> using namespace std; // returns gcd of two numbers int gcd(int a, int b) { if (b == 0) return a; return gcd(b, a % b); } // returns the gcd of the array. int gcdofArray(int arr[], int n) { int ans = arr[0]; for (int i = 1; i < n; i++) ans = gcd(ans, arr[i]); return ans; } // Driver Function int main() { int arr[] = { 2, 4, 6 }, n; n = sizeof(arr) / sizeof(arr[0]); cout << n * gcdofArray(arr, n) << endl; return 0; } |
chevron_right
filter_none
Java
// java program to find the minimum // sum of the array. import java.io.*; class GFG { // returns gcd of two numbers static int gcd(int a, int b) { if (b == 0) return a; return gcd(b, a % b); } // returns the gcd of the array. static int gcdofArray(int arr[], int n) { int ans = arr[0]; for (int i = 1; i < n; i++) ans = gcd(ans, arr[i]); return ans; } // Driver Function public static void main (String[] args) { int arr[] = { 2, 4, 6 }, n; n = arr.length; System.out.println( n * gcdofArray(arr, n)) ; } } // This code is contributed by vt_m |
chevron_right
filter_none
Python3
# Python3 code to find the minimum # sum of the array. # returns gcd of two numbers def gcd(a, b): if b == 0: return a return gcd(b, a % b) # returns the gcd of the array. def gcdofArray(arr, n): ans = arr[0] for i in range(n): ans = gcd(ans, arr[i]) return ans # Driver Code arr = [ 2, 4, 6 ] n = len(arr) print(n * gcdofArray(arr, n)) # This code is contributed by "Sharad_Bhardwaj". |
chevron_right
filter_none
C#
// C# program to find the minimum // sum of the array. using System; class GFG { // returns gcd of two numbers static int gcd(int a, int b) { if (b == 0) return a; return gcd(b, a % b); } // returns the gcd of the array. static int gcdofArray(int []arr, int n) { int ans = arr[0]; for (int i = 1; i < n; i++) ans = gcd(ans, arr[i]); return ans; } // Driver code public static void Main () { int []arr = {2, 4, 6}; int n; n = arr.Length; Console.WriteLine(n * gcdofArray(arr, n)) ; } } // This code is contributed by vt_m. |
chevron_right
filter_none
PHP
<?php // PHP program to find the minimum // sum of the array. // returns gcd of two numbers function gcd($a, $b) { if ($b == 0) return $a; return gcd($b, $a % $b); } // returns the gcd of the array. function gcdofArray($arr, $n) { $ans = $arr[0]; for ($i = 1; $i < $n; $i++) $ans = gcd($ans, $arr[$i]); return $ans; } // Driver Code $arr = array( 2, 4, 6 ); $n = count($arr); echo $n * gcdofArray($arr, $n), "\n"; // This code is contributed by Sach ?> |
chevron_right
filter_none
Output:
6
Recommended Posts:
- Minimum sum of the elements of an array after subtracting smaller elements from larger
- Maximum difference between two elements such that larger element appears after the smaller number
- Minimizing array sum by applying XOR operation on all elements of the array
- Delete array elements which are smaller than next or become smaller
- Find elements larger than half of the elements in an array
- Count of smaller or equal elements in sorted array
- Rearrange array such that even index elements are smaller and odd index elements are greater
- Count smaller elements on right side and greater elements on left side using Binary Index Tree
- Minimum cost to make array size 1 by removing larger of pairs
- Count smaller elements on right side
- Count smaller elements on right side using Set in C++ STL
- Find the element before which all the elements are smaller than it, and after which all are greater
- Count of strings in the first array which are smaller than every string in the second array
- Find maximum difference between nearest left and right smaller elements
- Permutation of an array that has smaller values from another array
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
- Sum of digits with even number of 1's in their binary representation
- Pair with largest sum which is less than K in the array
- Find the smallest positive number missing from an unsorted array | Set 3
- Reduce number to a single digit by subtracting adjacent digits repeatedly
- Sort an array of strings according to string lengths using Map
