Lucky Number (APCS 2021-09 Advanced)

2.0s 256M

Start with a sequence of distinct positive integers. While more than one value remains, remove the minimum and keep whichever side has the larger sum; keep the right side on a tie. An empty side has sum zero. Output the final value.

Input

Read \(n\), then the \(n\) values.

Constraints

\(1\le n\le300000\); distinct values satisfy \(1\le a_i\le10^7\).

Output

Print the surviving value.

Scoring

Each scored test independently awards 5 points, totaling 100. Samples award no points.

  • 1: 50% — The sequence is a permutation of \(1..n\).
  • 2: 50% — No additional restrictions.

Sample Input 1

5
4 2 3 1 5

Sample Output 1

4

Sample Input 2

8
3 9 4 5 1 6 2 8

Sample Output 2

9

Source

g277 · 2021-09 APCS.

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.