Find the Integer Added to Array I

Problem Description

You are given two arrays of equal length, nums1 and nums2. Each element in nums1 has been increased (or decreased in the case of negative) by an integer, represented by the variable x. As a result, nums1 becomes equal to nums2. Two arrays are considered equal when they contain the same integers with the same frequencies. Return the integer x.

Key Insights

• The problem requires finding a single integer x that when added to every element of nums1 will make it equal to nums2.
• The difference between corresponding elements in nums2 and nums1 should be constant across all indices.
• By calculating the difference for any index, we can determine x.

Space and Time Complexity

Time Complexity: O(n) - where n is the length of the arrays, as we need to iterate through the arrays once to find the difference. Space Complexity: O(1) - no additional space is used that scales with input size.

Solution

To solve this problem, we can follow these steps:

1. Calculate the difference between the first elements of nums2 and nums1 to determine x.
2. Verify that adding x to each element of nums1 results in nums2 for every corresponding index.
3. If all elements match after the adjustment, return x.

We will use a simple loop to iterate through the elements of the arrays and verify the condition.

Code Solutions