Find the Integer Added to Array I

Find the Integer Added to Array I

1. What is this problem about?

The Find the Integer Added to Array I coding problem is an introductory-level array challenge. You are given two arrays of the same length, nums1 and nums2. nums2 was created by taking every element in nums1 and adding a specific integer $x$ to it. Your task is to find the value of $x$. This is a test of basic arithmetic logic and array traversal.

2. Why is this asked in interviews?

Companies like Bloomberg use this Array interview question as a "warm-up" or "ice-breaker." It tests if a candidate can quickly identify the most efficient way to solve a simple problem. While you could sort both arrays and compare, the interviewer is looking for the $O(N)$ solution that demonstrates an understanding of mathematical properties (like the sum of a series or minimum/maximum values).

3. Algorithmic pattern used

The simplest pattern is to find the difference between minimums. Since every element in nums1 was shifted by the same amount $x$ to create nums2, the relationship min(nums2) = min(nums1) + x must hold true. Therefore, $x = min(nums2) - min(nums1)$. Alternatively, you can use the difference of the sums of the arrays, but min/max is usually more robust against overflow.

4. Example explanation

Input: nums1 = [4, 1, 8] nums2 = [11, 8, 15]

1. Find the minimum of nums1: 1.
2. Find the minimum of nums2: 8.
3. Calculate the difference: 8 - 1 = 7. So, the integer added was 7. (Checking other elements: 4+7=11, 8+7=15. Correct!)

5. Common mistakes candidates make

• Over-engineering: Sorting both arrays ($O(N \log N)$) when a simple linear scan ($O(N)$) is sufficient.
• Inefficient Logic: Trying to find the difference between every possible pair of elements from both arrays.
• Sign Errors: Subtracting the minimum of nums2 from nums1 instead of the other way around, leading to the wrong sign for $x$.

6. Interview preparation tip

Even for easy problems, always mention the time and space complexity. For this problem, stating that you can find the answer in $O(N)$ time with $O(1)$ extra space shows that you value efficiency even in simple tasks. It's a great way to build confidence at the start of an interview.