Finding Maximum scalar product of two vectors
Detailed guide and Python implementation for the 'Finding Maximum scalar product of two vectors' problem.
Problem Statement
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.
- •1 <= len(v1) == len(v2) <= 10^4
- •-10^5 <= v1[i], v2[i] <= 10^5
Examples
v1 = [1, 3, -5], v2 = [-2, 4, 1]
23
Sort both ascending: v1=[-5,1,3], v2=[-2,1,4]. Dot: (-5)*(-2)+1*1+3*4 = 10+1+12 = 23.
v1 = [1, 2, 3], v2 = [4, 5, 6]
32
Sort both ascending: [1,2,3] and [4,5,6]. Dot: 1*4+2*5+3*6 = 4+10+18 = 32.
v1 = [1, 1], v2 = [1, 1]
2
Any arrangement gives 1*1 + 1*1 = 2.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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