How do you solve Find the Integer Added to Array II on LeetCode?

Find the Integer Added to Array II (LeetCode #3132) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding the relationship between the sums of the arrays and the minimum values is crucial for deriving the optimal solution.

What is the brute force solution for Find the Integer Added to Array II?

The brute force approach for Find the Integer Added to Array II is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying every possible pair of elements to remove from nums1 and calculating the required integer x for each case. This ensures we explore all possibilities, but it's inefficient due to the number of combinations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Integer Added to Array II?

Find the Integer Added to Array II uses the following concepts: Array, Two Pointers, Sorting, Enumeration. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find the Integer Added to Array II?

Always start with a brute force approach to ensure you understand the problem deeply. Look for patterns and relationships in the data that can simplify your calculations. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Find the Integer Added to Array II?

Failing to consider all combinations of elements to remove in the brute force approach. Not recognizing the relationship between the sums and the minimum values in the optimal solution.

#3132

Find the Integer Added to Array II

Medium

ArrayTwo PointersSortingEnumerationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution leverages the properties of the problem by calculating the required x directly based on the differences between the minimum values of the two arrays. This avoids unnecessary computations and reduces the time complexity significantly.

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Algorithm

4 steps

1Step 1: Calculate the total sum of nums1 and nums2.
2Step 2: Calculate the minimum of nums2.
3Step 3: Use the relationship between the sums and the minimum values to derive the value of x.
4Step 4: Return the calculated x.

solution.py6 lines

1def min_x(nums1, nums2):
2    total_sum_nums1 = sum(nums1)
3    total_sum_nums2 = sum(nums2)
4    min_nums2 = min(nums2)
5    return min_nums2 - (total_sum_nums1 - total_sum_nums2) // 3
6

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Complexity note: This complexity is achieved because we only need to traverse the arrays a few times to compute sums and minimums, rather than checking every combination.

1Understanding the relationship between the sums of the arrays and the minimum values is crucial for deriving the optimal solution.
2Brute force can be useful for small inputs but is inefficient for larger datasets.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.