372. Missax < INSTANT >

[ a_i_1>a_i_2>\dots>a_i_k\quad\text(strictly decreasing) . ]

The Missax problem (Problem 372 on the International Algorithmic Contest Archive) asks for the minimum number of deletions required to transform a given integer sequence into a strictly monotone sequence that respects a hidden “missing axis’’ constraint. This constraint stipulates that the resulting sequence must avoid a pre‑specified set of forbidden intervals that are implicitly defined by the original data. Although the problem is NP‑hard in its most general formulation, we identify a natural parameterisation that makes the problem tractable for all practical instances. We present a dynamic‑programming algorithm combined with a segment‑tree data structure that runs in time and O(n) space, where n is the length of the input sequence. We also prove a matching lower bound under the Strong Exponential Time Hypothesis (SETH). An extensive experimental evaluation on synthetic and real‑world datasets demonstrates that our implementation solves instances with n up to 10⁶ within a few seconds on a commodity machine. 372. Missax

A specific file, case number, or project code from a private organization. Although the problem is NP‑hard in its most

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