MinRectArea.cs

void Main()
{
	var p1 = new List<(int x, int y)> {
		(1,1), (1,3), (3,1), (3,3), (2,2)
	};

	var p2 = new List<(int x, int y)> {
		(1,1), (1,3), (3,1), (3,3), (4,1), (4,3)
	};

	var p3 = new List<(int x, int y)> {
		(1,1), (1,4), (2,3), (3,1), (3,2), (3,3), (4,2), (4,3), (5,2)
	};

	var p4 = new List<(int x, int y)> {
		(1,3), (2,1), (2,0), (4,3), (0,4), (4,2), (1,0), (3,4), (2,4), (4,0)
	};

	var p5 = new List<(int x, int y)> {
		(1,1),(1,3),(3,1),(3,3),(4,1),(4,3)
	};

	var p6 = new List<(int x, int y)> {
	 	(0,1),(3,2),(0,0),(4,4),(2,0),(1,3),(0,4),(4,2),(1,0),(2,4)
	};

	var p = new Solution();
	(p.MinAreaRect(Solution.Points(p1)) == 4).Dump();
	(p.MinAreaRect(Solution.Points(p2)) == 2).Dump();
	(p.MinAreaRect(Solution.Points(p3)) == 1).Dump();
	(p.MinAreaRect(Solution.Points(p4)) == 9).Dump();
	(p.MinAreaRect(Solution.Points(p5)) == 2).Dump();
	(p.MinAreaRect(Solution.Points(p6)) == 8).Dump();

}

public class Solution
{
	public static int[][] Points(List<(int x, int y)> pts)
	{
		int n = 0;
		var p = new int[pts.Count][];
		foreach (var pt in pts)
		{
			if (p[n] is null)
				p[n] = new int[2];
			p[n][0] = pt.x;
			p[n][1] = pt.y;
			n++;
		}
		return p;
	}

	public int MinAreaRect(int[][] points)
	{
		const int X = 0;
		const int Y = 1;
		int minArea = int.MaxValue;
		var grid = new SparseGrid(points);

		for (int i = 0; i < points.Length - 1; i++)
		{
			for (int j = i + 1; j < points.Length; j++)
			{
				var p1x = points[i][X];
				var p1y = points[i][Y];
				var p2x = points[j][X];
				var p2y = points[j][Y];
				
				var provisionalArea = Math.Abs((p1x - p2x) * (p1y - p2y));
				if (provisionalArea == 0 || provisionalArea >= minArea)
					continue;
					
				if (grid.Exists(p1x, p2y) && grid.Exists(p2x, p1y))
					minArea = Math.Min(provisionalArea, minArea);
			}
		}

		return minArea == int.MaxValue ? 0 : minArea;
	}
}

public class SparseGrid
{
	Dictionary<int, Dictionary<int, int>> grid;

	public SparseGrid()
	{
		grid = new Dictionary<int, Dictionary<int, int>>();
	}

	public SparseGrid(int[][] points) : this()
	{
		foreach (var p in points)
		{
			Add(p[0], p[1]);
		}
	}

	public void Add(int x, int y)
	{
		if (!grid.ContainsKey(x))
			grid[x] = new Dictionary<int, int>();
		grid[x][y] = 1;
	}

	public bool Exists(int x, int y) => grid.ContainsKey(x) && grid[x].ContainsKey(y);
}