Algorithm dossier

  • Category: DP
  • Worst-case complexity: O(n²)
  • Approach: DP
  • Data structure: Array
  • First formalised: 1960s

Why this snippet is Longest Increasing Subsequence

Why LIS (naive DP). f[i] = length of the longest increasing subsequence *ending at* i. Recurrence: scan all j < i and extend any subsequence where a[j] < a[i]. Take the max at the end. Faster variant. Patience-sort with binary insertion runs in O(n log n); the naive DP shown here is O(n²) but easier to motivate.

How to read a redacted algorithm

Algodle strips identifier names so the snippet has to be read for its shape: the control flow, the data structures it manipulates, the order in which it visits its input. Loops with two pointers crawling toward each other are usually search or partition. A recursion that splits its input in half and recurses on both halves is divide-and-conquer. A priority queue plus graph traversal is almost certainly Dijkstra, Prim, or A*. Six hint columns — category, complexity, approach, data structure, era — let you triangulate even when the snippet itself is opaque.