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This is a medium difficulty Coding & Algorithms question, commonly asked during Onsite rounds at MathWorks.

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This question is commonly asked for Software Engineer candidates at MathWorks during technical interviews.

Minimize reduction cost and validate equal-sum pairs

Q: Minimize reduction cost and validate equal-sum pairs

This two-part question evaluates array manipulation and algorithmic problem-solving skills: the first task focuses on optimizing cumulative operation costs during iterative reductions while the second assesses combinatorial pairing under equal-sum constraints and computation of aggregate pairwise products.

You are given two independent coding tasks.

Task 1: Minimum total cost to reduce an array

You are given an integer array arr of length n.

You may repeatedly perform the following reduction operation until only one number remains:

Choose any two elements x and y currently in the array.
Remove both from the array.
Insert their sum x + y back into the array.
The cost of this operation is x + y .

Return the minimum possible total cost over all sequences of operations.

Input: arr (integers)

Output: minimum total cost (use 64-bit integer)

Notes/assumptions (make explicit in your solution):

n >= 1 .
Elements can be any integers; total cost should be computed using 64-bit arithmetic.

Task 2: Pair elements into equal-sum groups and sum products

You are given an integer array arr of even length 2m.

You must partition the array into m disjoint pairs such that:

Every element is used in exactly one pair.
The sum of the two numbers in each pair is the same constant S for all pairs.

If such a partition is possible, return:

The value $\sum_{i=1}^{m} (a_i \times b_i)$ , i.e., the sum of products of each pair.

If it is not possible to form such pairs, return -1.

Input: arr (even length)

Output: sum of pairwise products, or -1 (use 64-bit integer)

You are given two independent coding tasks.

Task 1: Minimum total cost to reduce an array

You are given an integer array arr of length n.

You may repeatedly perform the following reduction operation until only one number remains:

Choose any two elements x and y currently in the array.
Remove both from the array.
Insert their sum x + y back into the array.
The cost of this operation is x + y .

Return the minimum possible total cost over all sequences of operations.

Input: arr (integers)

Output: minimum total cost (use 64-bit integer)

Notes/assumptions (make explicit in your solution):

n >= 1 .
Elements can be any integers; total cost should be computed using 64-bit arithmetic.

Task 2: Pair elements into equal-sum groups and sum products

You are given an integer array arr of even length 2m.

You must partition the array into m disjoint pairs such that:

Every element is used in exactly one pair.
The sum of the two numbers in each pair is the same constant S for all pairs.

If such a partition is possible, return:

The value $\sum_{i=1}^{m} (a_i \times b_i)$ , i.e., the sum of products of each pair.

If it is not possible to form such pairs, return -1.

Input: arr (even length)

Output: sum of pairwise products, or -1 (use 64-bit integer)

Minimize reduction cost and validate equal-sum pairs

Quick Overview

Task 1: Minimum total cost to reduce an array

Task 2: Pair elements into equal-sum groups and sum products

Comments (0)

Minimize reduction cost and validate equal-sum pairs

Quick Overview

Task 1: Minimum total cost to reduce an array

Task 2: Pair elements into equal-sum groups and sum products

Comments (0)