Find the Array Concatenation Value

Find the Array Concatenation Value

What is this problem about?

The Find the Array Concatenation Value interview question involves a unique reduction process. You pick the first and last elements of an array, concatenate their digits into a new number, and add that value to a running total. You repeat this for the new first and last elements until the array is empty. if only one element remains, you add its value directly. The goal is to return the final total sum.

Why is this asked in interviews?

IBM and other companies use the Find the Array Concatenation Value coding problem to test a candidate's ability to implement simulations accurately. It evaluates your skills in string manipulation (for concatenation) or mathematical digit shifting, as well as your mastery of the Two Pointers interview pattern.

Algorithmic pattern used

This problem follows the Two Pointers and Simulation patterns.

1. Pointers: Initialize left = 0 and right = n - 1.
2. Iteration: Use a while loop that runs as long as left < right.
3. Concatenation: Join nums[left] and nums[right]. This can be done by:

• Converting both to strings, joining them, and parsing back to an integer.
• Mathematically: val = nums[left] * 10^(digits in nums[right]) + nums[right].

1. Update: Add the value to total, then increment left and decrement right.
2. Middle Case: If left == right, add the single remaining element to the total.

Example explanation

Array: [7, 52, 2, 4]

1. First pair: 7 and 4. Concatenation: "7" + "4" = 74. total = 74.
2. Second pair: 52 and 2. Concatenation: "52" + "2" = 522. total = 74 + 522 = 596. Result: 596.

Common mistakes candidates make

• Integer Overflow: Concatenating two 5-digit numbers can exceed the 32-bit integer limit in some languages. Use long.
• Wrong Middle Handling: Adding the middle element twice or not at all.
• Inefficient Concatenation: Repeatedly using heavy string formatting in a loop when simple math or a string builder would be faster.

Interview preparation tip

Be comfortable with two-pointer traversals. They are the standard way to process an array from "both ends inward." Also, practice finding the number of digits in an integer without strings ($log10$ or division).