Luogu · P10428

[Lanqiao Cup 2024 Provincial B] Mountain Climbing

[蓝桥杯 2024 省 B] 爬山

Stable ID
luogu-p10428
Question status
Reported leap
Topics
algorithms

The question

Can a valid algorithm be established for a problem the source marks as “Recognised as a flawed problem”?

Algorithmic frontier

Reference frontier
Recognised as a flawed problem
Latest reported AI result
O ⁣(n+h)\mathcal{O}\!\left(n + h\right)

This compares source-reported bounds; it is not a correctness or novelty finding.

Results

2026-09-12

Claimed result: O ⁣(n+h)\mathcal{O}\!\left(n + h\right)

AI / model: Not identified

Reported method

The article proves all square roots can precede all halvings, replaces the halving budget by a penalty w per halving, proves the square-root gain is non-increasing along each chain so a bucketed greedy plus an integer binary search on w suffices; its own version is O(n + H log(H+1)) and nmsy's refinement brings it to O(n + H), where H = max h_i.

Verification

Source
Source reviewed
Theory
Theory not checked
Implementation
Code available
Prior art
Prior art not reviewed

The result page was opened and compared with the collection claim. Legacy audit state: audited_public.

The table's AI cell O(n+h) agrees with the article's final O(n + H) bound (h = H = max h_i); the article's own first solution is O(n + H log(H+1)). The baseline cell 认定错题 ("recognised as a flawed problem") is not supported anywhere on the linked page and needs separate evidence from a later node.

Credits

Result authors
nmsy
Published by
chen_zhe

Independent reproduction: Not yet performed

Prior-art review: Not yet performed

Sources and history

Sources and history

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