猜测可能组合的方法

Question

For practice I want to write a program that will guess random positions of x and y. For example the first point would be

int x = 0;
int y = 0;

x += rand.Next(0, 4);
y += rand.Next(0, 4);

Then from that random point I will add the another random value to x and y to have a second point. However I want to go back to find those points randomly.

To make the points:

int x = 0;
int y = 0;
List<Point> points = new List<Point>();

for (int i = 0; i < numberOfPointsWanted; i++)
{
    x += rand.Next(0, 4);
    y += rand.Next(0, 4);
    points.Add(new Point(x, y));
}

Now I wish to guess those random points almost as if I did not have them stored in a list. Because each new point relies on its predecessor I assume some sort of recursion would be necessary. Almost like a brute force guessing application that will find those points. I am having trouble completing the method that would be able to guess every possible point given a number of desired points.

This is what I have thus far to find the rounds:

class Program
{
        static int nRounds = 2;
        static Point[] points = new Point[nRounds];
        static Point[] test = { new Point(1, 2), new Point(4, 1) };

        static bool CheckArray()
        {
            for (int i = 0; i < points.Length; i++)
                if (points[i] != test[i]) { return false; }

            return true;
        }

        static void PrintArray()
        {
            for (int i = 0; i < points.Length; i++)
                Console.Write("[" + tCount + "]\t" + points[i].X + " : " + points[i].Y + "\t");

            Console.Write("\n");
        }

        static int tCount = 0;
        static int rCount = 0;
        static void GetRounds(int inX, int inY)
        {
            for (int x = inX; x < 5; x++)
            {
                for (int y = inY; y < 5; y++)
                {
                    if (rCount < nRounds)
                    {
                        tCount++;
                        points[rCount] = new Point(x, y);
                        rCount++;
                        GetRounds(x, y);
                        if (CheckArray())
                        {
                            PrintArray();
                            return;
                        }
                        PrintArray();

                    }            
                }
            }
            rCount--;
        }

        static void Main(string[] args)
        {
            GetRounds(0, 0);
            Console.ReadKey();
        }
    }
}

I am trying to randomly generate points as shown above and then guess them based on a hashed value representing all of those points together.

This is what im expecting to see:

If only guessing two points

Point one :: Point two x and y respectively

x y :: x y
0 0 :: 0 1
0 0 :: 0 2
0 0 :: 0 3
0 0 :: 1 0
0 0 :: 1 1
0 0 :: 1 2
0 0 :: 1 3
0 0 :: 2 0
0 0 :: 2 1
0 0 :: 2 2
0 0 :: 2 3
0 0 :: 3 0
0 0 :: 3 1
0 0 :: 3 2
0 0 :: 3 3
0 1 :: 0 0
0 1 :: 0 1
0 1 :: 0 2

And so on until all possibilities of point one and point two are guessed

Answer 1

I'm not sure if this is exactly what you're looking for, but one way to get all those combinations is to use nested for loops:

for (int ax = 0; ax < 4; ax++)
{
    for (int ay = 0; ay < 4; ay++)
    {
        var pointA = new Point(ax, ay);

        for (int bx = 0; bx < 4; bx++)
        {
            for (int by = 0; by < 4; by++)
            {                    
                var pointB = new Point(bx, by);

                Console.WriteLine($"{pointA.X} {pointA.Y} :: {pointB.X} {pointB.Y}");
            }
        }
    }
}

Output

---

You were asking about a solution that would allow a variable number of points to be passed in. This is fairly simple to do - you just keep a List<List<Point>> of the results, and on each iteration you generate a list of possible point values (16 possible values when min is 0 and max is 3), and then generate a new list for every item in the existing results for each Point in the new set.

The problem is the size of the result set. Since a single point has 16 possible combinations of X and Y if we have a min value of 0 and a max value of 3, then for each additional point, we raise 16 to that power. So for 10 points, there are over a billion combinations.

private static List<List<Point>> GetAllCombinations(int min, int max, int count)
{
    var results = new List<List<Point>>();

    for (int i = 0; i < count; i++)
    {
        var thisSet = new List<Point>();

        for (int x = min; x <= max; x++)
        {
            for (int y = min; y <= max; y++)
            {
                thisSet.Add(new Point(x, y));
            }
        }

        // If this is our first time through, we just add each point
        // as a single-item list to our results
        if (results.Count == 0)
        {
            foreach (var item in thisSet)
            {
                results.Add(new List<Point> {item});
            }
        }
        // On subsequent iterations, for each list in our results, and
        // for each item in this set, we create a new list for each item,
        // adding to it a copy of the existing result list. We clear
        // the results in the beginning (after making a copy) and then
        // add each new list to it in the inner loop.
        else
        {
            // Make a copy of our existing results and clear the original list
            var tempResults = results.ToList();
            results.Clear();

            foreach (var existingItem in tempResults)
            {
                foreach (var newPoint in thisSet)
                {
                    // Now we populate our results again with a new set of 
                    // lists for each existingItem and each newPoint
                    var newItem = existingItem.ToList();
                    newItem.Add(newPoint);
                    results.Add(newItem);
                }
            }
        }
    }

    return results;
}

Example usage:

private static void Main()
{
    var results = GetAllCombinations(0, 3, 5);

    foreach (var result in results)
    {
        Console.WriteLine(string.Join(" :: ", result.Select(p => $"{p.X} {p.Y}")));
    }

    Console.WriteLine("With a min value of 0 and max value of 3, " +
                        $"5 points generated {results.Count} results.");

    GetKeyFromUser("Done! Press any key to exit...");
}

Output