Grouping Game (APCS 2025-06 Expert)

2.0s 256M

Partition \(n\) people into exactly \(k\) nonempty groups. Pairwise distances are given. The quality is the smallest distance between people in different groups. Maximize this quality.

Input Format

Read \(n,k\) and an \(n\) by \(n\) distance matrix.

Output Format

Print the maximum quality.

Constraints

\(2\le k\le n\le500\). Distances are symmetric with zero diagonal and other entries in \([1,10^8]\).

Scoring

  • 20 points: \(n\le10\) and \(k=2\).
  • 80 points: No additional restrictions.

Each scored test is worth 5 points.

Sample Input 1

3 2
0 2 1
2 0 3
1 3 0

Sample Output 1

2

Sample Input 2

5 3
0 5 6 1 3
5 0 3 4 2
6 3 0 4 7
1 4 4 0 5
3 2 7 5 0

Sample Output 2

3

Source

APCS 2025-06 public archive version: q839。

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