Google Code Jam '08 Round 1A Problem A - Minimum Scalar Product

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Points: 5 (partial)
Time limit: 30.0s
Memory limit: 1G

Problem type

You are given two vectors v_1 = (x_1, x_2, \dots, x_n) and v_2 = (y_1, y_2, \dots, y_n). The scalar product of these vectors is a single number, calculated as x_1 y_1 + x_2 y_2 + \dots + x_n y_n.

Suppose you are allowed to permute the coordinates of each vector as you wish. Choose two permutations such that the scalar product of your two new vectors is the smallest possible, and output that minimum scalar product.

Input Specification

The first line of the input file contains integer number T - the number of test cases. For each test case, the first line contains integer number n.

The next two lines contain n integers each, giving the coordinates of v_1 and v_2 respectively.

Output Specification

For each test case, output a line Case #X: Y where X is the test case number, starting from 1, and Y is the minimum scalar product of all permutations of the two given vectors.


Time limit: 30 seconds per test set.

Memory limit: 1 GB.

Small Dataset
  • T = 1000
  • 1 \le n \le 8
  • -1000 \le x_i, y_i \le 1000
Large Dataset
  • T = 10
  • 100 \le n \le 800
  • -100\,000 \le x_i, y_i \le 100\,000

Sample Input

1 3 -5
-2 4 1
1 2 3 4 5
1 0 1 0 1

Sample Output

Case #1: -25
Case #2: 6


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