Leetcode #1874: Minimize Product Sum of Two Arrays
In this guide, we solve Leetcode #1874 Minimize Product Sum of Two Arrays 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
The product sum of two equal-length arrays a and b is equal to the sum of a[i] * b[i] for all 0 <= i < a.length (0-indexed). For example, if a = [1,2,3,4] and b = [5,2,3,1], the product sum would be 15 + 22 + 33 + 41 = 22.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Greedy, Array, Sorting
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: nums1 = [5,3,4,2], nums2 = [4,2,2,5]
Output: 40
Explanation: We can rearrange nums1 to become [3,5,4,2]. The product sum of [3,5,4,2] and [4,2,2,5] is 3*4 + 5*2 + 4*2 + 2*5 = 40.
Python Solution
class Solution:
def minProductSum(self, nums1: List[int], nums2: List[int]) -> int:
nums1.sort()
nums2.sort(reverse=True)
return sum(x * y for x, y in zip(nums1, nums2))
Complexity
The time complexity is , and the space complexity is . The space complexity is .
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.