Maximal Square

Given a matrix filled with 0s and 1s, find the largest square whose cells are all 1, and return its area. This is LeetCode 221, a classic warm-up for two-dimensional dynamic programming: the answer for each cell turns out to depend on the answers already computed for a few of its neighbours. The squares must be axis-aligned (no rotated diamonds), and if the matrix is empty the area is 0.

Signature

maximalSquare(matrix)  // 2D array of 0/1 -> area of the largest all-1 square

matrix is a rectangular 2D array of numbers 0 and 1. Return a single number: the area (side length squared), not the side length.

Examples

maximalSquare([
  [1, 0, 1, 0, 0],
  [1, 0, 1, 1, 1],
  [1, 1, 1, 1, 1],
  [1, 0, 0, 1, 0],
]); // 4  — the biggest all-1 square is 2x2, so area = 2 * 2

maximalSquare([
  [1, 1, 1],
  [1, 1, 1],
  [1, 1, 1],
]); // 9  — the whole grid is one 3x3 square

maximalSquare([
  [1, 1, 1],
  [1, 0, 1],
  [1, 1, 1],
]); // 1  — the single 0 in the middle blocks any square bigger than 1x1

Notes

• Binary matrix — every cell is 0 or 1. Cells with a "0"/"1" string are coerced with Number(), so both forms work.
• Return the area — the answer is the side length squared. A 2x2 square returns 4, a 3x3 returns 9.
• Axis-aligned only — the square's sides run along the rows and columns. A diagonal run of 1s is not a square.
• Empty input — an empty matrix ([]) or a matrix with no columns ([[]]) has area 0.
• Do not mutate — leave the input matrix unchanged; build any bookkeeping in your own array.