Printing Factory (APCS 2025-11 Expert)

2.0s 256M

A printer must complete \(n\) nonoverlapping, nonpreemptive jobs. Job \(i\) starts no earlier than \(s_i\), takes \(t_i\) time units, and finishes by \(d_i\). Choose their order and starting times. Find the largest nonnegative integer \(g\) such that every gap between consecutive jobs is at least \(g\). Time before the first job and after the last does not count.

Input Format

Read \(n\), followed by \(n\) triples \(s_i,d_i,t_i\).

Output Format

Print the largest integer \(g\).

Constraints

\(2\le n\le8\); \(0\le s_i<d_i\le1000\); \(1\le t_i\le d_i-s_i\). A feasible schedule with \(g=0\) is guaranteed.

Scoring

  • 30 points: \(n\le3\).
  • 70 points: no additional restrictions.

Each scored test is worth 5 points.

Sample Input 1

3
1 9 3
3 20 4
4 15 2

Sample Output 1

5

Sample Input 2

3
1 4 2
0 6 3
2 8 1

Sample Output 2

0

Source

APCS 2025-11 High Level, based on the public reconstruction: ZeroJudge r627。

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