Investment Game (APCS 2023-10 Expert)

2.0s 256M

Daily returns are \(a_1,\ldots,a_n\). Choose one contiguous investment period and ignore the returns of at most \(k\) days within it using medals. All other returns in that period count. Choosing no period earns zero. Maximize the return.

Input Format

Read \(n,k\), then all daily returns.

Output Format

Print the maximum return.

Constraints

\(1\le n\le150000\), \(0\le k\le20\); \(-10000\le a_i\le10000\).

Scoring

  • 20 points: \(k=0,n\le2000\).
  • 20 points: \(k=0\).
  • 60 points: \(1\le k\le20\).

Each scored test is worth 5 points.

Sample Input 1

9 0
3 1 -2 3 -2 3 -5 2 2

Sample Output 1

6

Sample Input 2

9 2
3 1 -2 3 -2 3 -5 2 2

Sample Output 2

12

Sample Input 3

9 4
3 1 -2 3 -2 3 -5 2 2

Sample Output 3

14

Sample Input 4

3 0
-1 -5 -3

Sample Output 4

0

Source

APCS 2023-10 public archive version: m373。

Problem page help

Keyboard shortcuts

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.