Python BasicsHard

Finding Maximum scalar product of two vectors

Detailed guide and Python implementation for the 'Finding Maximum scalar product of two vectors' problem.

Problem Statement

Hard

Write a function max_scalar_product(v1, v2) that takes two lists of integers of equal length and returns the maximum possible scalar (dot) product. You can rearrange elements in both vectors in any order before computing the dot product. To maximize, sort both vectors in the same order and pair corresponding elements.

Constraints
  • 1 <= len(v1) == len(v2) <= 10^4
  • -10^5 <= v1[i], v2[i] <= 10^5

Examples

Example 1
Input
v1 = [1, 3, -5], v2 = [-2, 4, 1]
Output
23
Explanation

Sort both ascending: v1=[-5,1,3], v2=[-2,1,4]. Dot: (-5)*(-2)+1*1+3*4 = 10+1+12 = 23.

Example 2
Input
v1 = [1, 2, 3], v2 = [4, 5, 6]
Output
32
Explanation

Sort both ascending: [1,2,3] and [4,5,6]. Dot: 1*4+2*5+3*6 = 4+10+18 = 32.

Example 3
Input
v1 = [1, 1], v2 = [1, 1]
Output
2
Explanation

Any arrangement gives 1*1 + 1*1 = 2.

Need a Hint?
Consider using Arrays-specific data structures like sets or heaps.
Edge Cases to Watch
  • Empty input structures
  • Single element inputs
  • Large numerical bounds

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