Find the Integer Added to Array I - Problem
Imagine you have two arrays of the same length: nums1 and nums2. Here's the twist - every element in nums1 has been modified by adding (or subtracting) the same integer value x to create nums2.
Your mission is to find that magical integer x that was used to transform nums1 into nums2.
Key Point: The arrays are considered equal when they contain the same integers with the same frequencies, but the order doesn't necessarily matter.
Example: If nums1 = [2, 6, 4] and nums2 = [9, 7, 5], then x = 3 because adding 3 to each element in nums1 gives us [5, 9, 7], which contains the same elements as nums2.
Input & Output
example_1.py — Basic Case
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Input:
nums1 = [2, 6, 4], nums2 = [9, 7, 5]
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Output:
3
💡 Note:
Adding 3 to each element in nums1: [2+3, 6+3, 4+3] = [5, 9, 7]. This contains the same elements as nums2 = [9, 7, 5], just in different order.
example_2.py — Negative Difference
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Input:
nums1 = [10, 6, 9], nums2 = [5, 1, 4]
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Output:
-5
💡 Note:
Subtracting 5 from each element in nums1: [10-5, 6-5, 9-5] = [5, 1, 4]. This exactly matches nums2.
example_3.py — Single Element
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Input:
nums1 = [1], nums2 = [7]
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Output:
6
💡 Note:
With single element arrays, x = 7 - 1 = 6. Adding 6 to nums1[0] gives us nums2[0].
Constraints
- 1 ≤ nums1.length == nums2.length ≤ 100
- -1000 ≤ nums1[i], nums2[i] ≤ 1000
- It is guaranteed that there exists an integer x such that nums1[i] + x == nums2[j] for some arrangement
Visualization
Tap to expand
Understanding the Visualization
1
Crime Scene Analysis
We have two sets of evidence - the original (nums1) and the tampered version (nums2)
2
Organize the Evidence
Sort both arrays to match corresponding pieces of evidence
3
Find the Pattern
Compare any pair to discover the systematic shift applied to all evidence
4
Crack the Case
The difference reveals the constant offset used in the transformation
Key Takeaway
🎯 Key Insight: Since every element undergoes the same transformation, sorting both arrays aligns corresponding elements perfectly. We only need to check one pair to discover the universal shift constant!
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Explanation
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