Dynamic Programming

The fewest coins for an amount, defined by its own smaller copies. Plain recursion solves the same amounts again and again; a memo solves each once, and a table needs no recursion at all.

Two strings, one table of prefix pairs: each cell is the cheapest of a deletion, an insertion, or a change from its three neighbours, and a walk back from the corner reads the edits out.

Items with a weight and a value, a bag with a limit: each table cell asks whether taking one more item beats leaving it out, and the last row read backward names the items that won.

Shrink a picture by a column that is not a column: an energy map from the Sobel gradient, a table where each cell adds the cheapest of three above, and the lowest path removed.