---
tag: A7XZYGW44S
kind: concept
name: Longest increasing subsequence
aliases: [longest-increasing-subsequence-problem, longest-nondecreasing-subsequence, nondecreasing-subsequence]
sources:
  - wikipedia: en:4587078@r1355103452
    locator: Longest increasing subsequence
    note: adopted
    mention: wikipedia://en/4587078
    sections: [Summary]
same_as:
  wikidata: Q4183855
  wikipedia: Longest increasing subsequence
inventory: [PP295R2ZTP]
---

## Summary

In computer science, the **longest increasing subsequence** problem aims to find a [[subsequence|0F1PR74BRX]] of a given [[sequence|0G9EKM0E15]] in which the subsequence's elements are sorted in an ascending order and in which the subsequence is as long as possible. This subsequence is not necessarily contiguous or unique. The longest increasing subsequences are studied in the context of various disciplines related to mathematics, including algorithmics, random matrix theory, representation theory, and physics. The longest increasing subsequence problem is solvable in time $O(n \log n),$ where $n$ denotes the length of the input sequence.