Leetcode #2333: Minimum Sum of Squared Difference
In this guide, we solve Leetcode #2333 Minimum Sum of Squared Difference in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given two positive 0-indexed integer arrays nums1 and nums2, both of length n. The sum of squared difference of arrays nums1 and nums2 is defined as the sum of (nums1[i] - nums2[i])2 for each 0 <= i < n.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Binary Search, Sorting, Heap (Priority Queue)
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: nums1 = [1,2,3,4], nums2 = [2,10,20,19], k1 = 0, k2 = 0
Output: 579
Explanation: The elements in nums1 and nums2 cannot be modified because k1 = 0 and k2 = 0.
The sum of square difference will be: (1 - 2)2 + (2 - 10)2 + (3 - 20)2 + (4 - 19)2 = 579.
Python Solution
class Solution:
def minSumSquareDiff(
self, nums1: List[int], nums2: List[int], k1: int, k2: int
) -> int:
d = [abs(a - b) for a, b in zip(nums1, nums2)]
k = k1 + k2
if sum(d) <= k:
return 0
left, right = 0, max(d)
while left < right:
mid = (left + right) >> 1
if sum(max(v - mid, 0) for v in d) <= k:
right = mid
else:
left = mid + 1
for i, v in enumerate(d):
d[i] = min(left, v)
k -= max(0, v - left)
for i, v in enumerate(d):
if k == 0:
break
if v == left:
k -= 1
d[i] -= 1
return sum(v * v for v in d)
Complexity
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.