Hero Training (APCS 2020-10 Expert)

2.0s 256M

You are given a grid with \(m\) rows and \(n\) columns. Start in any cell of the top row. Each move goes one cell left, right, or down, without leaving the grid or visiting a cell twice. Finish in any cell of the bottom row. Your score is the sum of all visited cells, including the start and finish. Find the maximum score.

Input Format

The first line contains \(m,n\). The next \(m\) lines each contain the \(n\) values in one row, from left to right.

Output Format

Print the maximum score of a valid top-to-bottom path.

Constraints

\(1\le m\le50\), \(1\le n\le10000\). Every cell value lies between \(-100\) and \(100\).

Scoring

  • 20 points: \(m=1\), \(n\le100\).
  • 30 points: \(n\le100\).
  • 50 points: No additional restrictions.

Each scored test is worth 5 points.

Sample Input

1 5
2 1 4 -7 4

Sample Output

7

Source

APCS 2020-10 public archive version: f314。

Problem page help

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Main features

  • Sample tests — Runs the sample cases bundled with the problem and auto-compares against the expected output.
  • Custom test — Run your code with your own stdin. Optionally tick the "Compare with expected (diff)" box to verify against expected output line-by-line.
  • Template — Paste the default code template you set on your profile page.
  • Collab — Edit this problem together with classmates in real time.
  • Auto-draft — Editor contents auto-save to your browser every 1.5 seconds (per account / problem / language).
  • Submit — Send your code to the judge for grading; returns AC / WA / TLE etc.

Limits

  • Source code: at most 65,536 characters
  • Custom test stdin and expected output: at most 1 MB each (≈1 million characters)
  • Custom test and sample test share the sandbox; about 1 request per 3 s per user (sample test: 1 per 1 s)
  • Custom test and sample test both have a 15 second wall-clock cap (the official judge still uses the problem time limit)
  • Interactive problems do not offer custom test (cannot simulate interaction with the judge).
  • Submitting has no rate limit, but rapid repeated submissions on the same problem are treated as score farming.