How do you solve Minimum Sum of Squared Difference on LeetCode?

Minimum Sum of Squared Difference (LeetCode #2333) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Modifying the largest differences first is crucial for minimizing the squared differences.

What is the time complexity of Minimum Sum of Squared Difference?

The optimal solution for Minimum Sum of Squared Difference runs in O(n log n) time and uses O(n) space. The complexity arises from sorting the differences and maintaining the heap structure for modifications.

What is the brute force solution for Minimum Sum of Squared Difference?

The brute force approach for Minimum Sum of Squared Difference is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we calculate the sum of squared differences without any modifications to the arrays. This gives us a baseline to compare against when we start making modifications. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimum Sum of Squared Difference?

Minimum Sum of Squared Difference uses the following concepts: Array, Binary Search, Greedy, Sorting, Heap (Priority Queue). The recommended patterns to study are: Greedy, Heap (Priority Queue), Sorting.

What are the interview tips for Minimum Sum of Squared Difference?

Always clarify how many modifications you can make and how they can be applied. Discuss your thought process and reasoning behind choosing a particular approach. Be prepared to explain the trade-offs of your chosen solution in terms of time and space complexity.

What are common mistakes when solving Minimum Sum of Squared Difference?

Not considering the greedy approach of reducing the largest differences first. Failing to account for the fact that both k1 and k2 can be used interchangeably.

#2333

Minimum Sum of Squared Difference

Medium

ArrayBinary SearchGreedySortingHeap (Priority Queue)GreedyHeap (Priority Queue)Sorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n log n)Space O(n)

The optimal solution leverages a greedy approach, where we focus on reducing the largest differences first. By using the available modifications efficiently, we can minimize the sum of squared differences significantly.

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Algorithm

4 steps

1Step 1: Calculate the initial differences between nums1 and nums2.
2Step 2: Use a max-heap (or priority queue) to store the absolute differences.
3Step 3: While we have modifications left (k1 + k2), pop the largest difference from the heap, reduce it by 1, and push it back into the heap.
4Step 4: After all modifications, calculate the final sum of squared differences.

solution.py17 lines

1# Full working Python code
2import heapq
3
4def minSumSquaredDiff(nums1, nums2, k1, k2):
5    n = len(nums1)
6    diffs = []
7    for i in range(n):
8        diffs.append(abs(nums1[i] - nums2[i]))
9    heapq._heapify_max(diffs)
10    total_mods = k1 + k2
11    while total_mods > 0:
12        max_diff = heapq._heappop_max(diffs)
13        max_diff -= 1
14        heapq._heapify_max(diffs)
15        heapq.heappush(diffs, max_diff)
16        total_mods -= 1
17    return sum(d ** 2 for d in diffs)

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Complexity note: The complexity arises from sorting the differences and maintaining the heap structure for modifications.

1Modifying the largest differences first is crucial for minimizing the squared differences.
2The total number of modifications (k1 + k2) can be treated as a single resource to optimize the differences.

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