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.
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:
- 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
- Minimum cost to make array size 1 by removing larger of pairs
- Count smaller elements on right side using Set in C++ STL
- Count smaller elements on right side
- Find the element before which all the elements are smaller than it, and after which all are greater
- Find maximum difference between nearest left and right smaller elements
- Permutation of an array that has smaller values from another array
- Find next Smaller of next Greater in an array
- Find closest smaller value for every element in array
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