The snail's shell

Problem

A cone snail's shell grows at its edge, one line of pigment at a time: each new cell is painted according to its neighbors in the line before, and that is how the triangles on it appear. Leilani Kahale, a malacologist, wants to predict the edge after several generations.

Write a function that takes row, a string of # (painted cell) and . (unpainted) with at least one character, and k, a whole number from 0 up. In each generation every cell changes at the same time, looking at the previous row: a cell becomes # if exactly one of its two neighbors (the one on the left or the one on the right) was #, and . if both were or neither was; its own state does not matter. Beyond the edges everything counts as .. Return the row, with the same length, after k generations; when k is 0, return the row as it is.

With "...#..." and 3: the first generation gives "..#.#..", the second ".#...#." (the center had # on both sides) and the third "#.#.#.#", so it returns "#.#.#.#".

Examples

• The example

  "...#...", 3 → "#.#.#.#"

• Zero generations

  "..#..", 0 → "..#.."

• A single cell goes blank

  "#", 1 → "."

• The whole row painted

  "#####", 1 → "#...#"

• It starts at the edge

  "#....", 2 → "#.#.."

Besides these, the challenge has hidden tests that are revealed when you submit your solution.

You start with this

def paint_edge(row, k):
    pass

function paintEdge(row, k) {
}