An O(n^2) algorithm for determining the largest area of a rectangle that can be made from a given list of points

largestRectArea.ts

type Point = [number, number];

/** 
 * Determines the largest area of a rectangle that can be made from a given list of points.
 * Rectangles are assumed to be aligned with the axes (no rotations).
 * Runtime: O(n^2)
 */
function largestRectArea(points: Point[]): number {
	// Map from given x-coordinates to given y-coordinates
	const pointsMap: Map<number, Set<number>> = new Map();
	// initialize points map
	points.forEach((point) => {
		const ySet = pointsMap.get(point[0]);
		if (ySet) {
			ySet.add(point[1]);
		} else {
			pointsMap.set(point[0], new Set([point[1]]));
		}
	});

	let maxArea = 0;
	// Iterate through every pair of "diagonal" points
	for (let p1Index = 0; p1Index < points.length; p1Index++) {
		for (let p2Index = p1Index + 1; p2Index < points.length; p2Index++) {
			const point1 = points[p1Index],
				point2 = points[p2Index];
			const x1 = point1[0],
				y1 = point1[1],
				x2 = point2[0],
				y2 = point2[1];
			const area = Math.abs((x2 - x1) * (y2 - y1));
			// check if the other diagonal points were given
			const hasOtherCorners = pointsMap.get(x1)?.has(y2) && pointsMap.get(x2)?.has(y1);
			if (hasOtherCorners && area > maxArea) {
				maxArea = area;
			}
		}
	}

	return maxArea
}

// Example
const points: Point[] = [[0, 0], [2, 2], [0, 1], [4, 5], [1, 0], [-3, 5], [1, 1], [-3, -3], [0, 0], [0, 1], [2, 0], [0, 2], [4, -3]];
largestRectArea(points)