Slide Maze


https://moonstonelin.wordpress.com/2016/05/27/maze/
  有个迷宫游戏,从网上找了一个类似的,大家可以玩一下:http://www.bigfishgames.com/online-games/4038/slide-maze/index.html。注意跟一般迷宫游戏不同的是,小人只有到墙或者boundary才停下来,我们无法控制小人走的步数。
  写一个function,输入是这个迷宫,小人的起始位置,和他的目的地。要求输出一个move的序列,使小人能从起点到终点。
以链接里那个游戏的level one为例,输出(’Down’,’Right’,’Down’,’Right’,’Down’,’Left’,’Down’,’Left’,’Up’,’Left’)。
public List<List<Direction>> Maze(int[,] matrix, int startRow, int startColumn, int endRow, int endColumn)
{
    Dictionary<Tuple<int, int>, Tuple<int, int>> Lefts = new Dictionary<Tuple<int, int>, Tuple<int, int>>();
    Dictionary<Tuple<int, int>, Tuple<int, int>> Rights = new Dictionary<Tuple<int, int>, Tuple<int, int>>();
    Dictionary<Tuple<int, int>, Tuple<int, int>> Ups = new Dictionary<Tuple<int, int>, Tuple<int, int>>();
    Dictionary<Tuple<int, int>, Tuple<int, int>> Downs = new Dictionary<Tuple<int, int>, Tuple<int, int>>();
 
    int R = matrix.GetLength(0);
    int C = matrix.GetLength(1);
 
    for (int r = 0; r < R; r++)
    {
        // <<--
        int stopColumn = 0;
        for (int c = 0; c < C; c++)
        {
            if (matrix[r, c] == 0)
            {
                if ((c - 1 >= 0) && (matrix[r, c - 1] == 1))
                {
                    stopColumn = c;
                }
 
                Lefts.Add(new Tuple<int, int>(r, c), new Tuple<int, int>(r, stopColumn));
            }                 
        }
 
        // -->>
        stopColumn = C - 1;
        for (int c = C-1; c >= 0; c--)
        {
            if (matrix[r, c] == 0)
            {
                if ((c + 1 < C) && (matrix[r, c + 1] == 1))
                {
                    stopColumn = c;
                }
 
                if ((r == endRow) && (c == endColumn))
                {
                    stopColumn = c;
                }
 
                Rights.Add(new Tuple<int, int>(r, c), new Tuple<int, int>(r, stopColumn));
            }
        }
    }
 
    for (int c = 0; c < C; c++)
    {
        // up
        int stopRow = 0;
        for (int r = 0; r < R; r++)
        {
            if (matrix[r, c] == 0)
            {
                if ((r - 1 >= 0) && (matrix[r - 1, c] == 1))
                {
                    stopRow = r;
                }
 
                if ((r == endRow) && (c == endColumn))
                {
                    stopRow = r;
                }
 
                Ups.Add(new Tuple<int, int>(r, c), new Tuple<int, int>(stopRow, c));
            }
        }
 
        // down
        stopRow = R - 1;
        for (int r = R - 1; r >= 0; r--)
        {
            if (matrix[r, c] == 0)
            {
                if ((r + 1 < C) && (matrix[r + 1, c] == 1))
                {
                    stopRow = r;
                }
 
                if ((r == endRow) && (c == endColumn))
                {
                    stopRow = r;
                }
 
                Downs.Add(new Tuple<int, int>(r, c), new Tuple<int, int>(stopRow, c));
            }
        }
    }
 
    List<List<Direction>> result = new List<List<Direction>>();
    Stack<Direction> stack = new Stack<Direction>();
    HashSet<Tuple<int, int>> visited = new HashSet<Tuple<int, int>>();
 
    Helper(startRow, startColumn, endRow, endColumn, visited, Lefts, Rights, Ups, Downs, result, stack);
 
    return result;
}
 
private void Helper(int startRow, int startColumn, int endRow, int endColumn, HashSet<Tuple<int, int>> visited,
    Dictionary<Tuple<int, int>, Tuple<int, int>> Lefts,
    Dictionary<Tuple<int, int>, Tuple<int, int>> Rights,
    Dictionary<Tuple<int, int>, Tuple<int, int>> Ups,
    Dictionary<Tuple<int, int>, Tuple<int, int>> Downs,
    List<List<Direction>> result, Stack<Direction> stack)
{
    Tuple<int, int> t = new Tuple<int, int>(startRow, startColumn);
    if (visited.Contains(t))
    {
        return;
    }
 
    visited.Add(t);
 
    if ((startRow == endRow) && (startColumn == endColumn))
    {
        List<Direction> ds = new List<Direction>();
        ds.AddRange(stack);
        ds.Reverse();
        result.Add(ds);
        return;
    }
 
    Tuple<int, int> key = new Tuple<int, int>(startRow, startColumn);
 
    if (Lefts.ContainsKey(key))
    {
        stack.Push(Direction.Left);
        Helper(Lefts[key].Item1, Lefts[key].Item2, endRow, endColumn, visited, Lefts, Rights, Ups, Downs, result, stack);
        stack.Pop();
    }
 
    if (Rights.ContainsKey(key))
    {
        stack.Push(Direction.Right);
        Helper(Rights[key].Item1, Rights[key].Item2, endRow, endColumn, visited, Lefts, Rights, Ups, Downs, result, stack);
        stack.Pop();
    }
 
    if (Ups.ContainsKey(key))
    {
        stack.Push(Direction.Up);
        Helper(Ups[key].Item1, Ups[key].Item2, endRow, endColumn, visited, Lefts, Rights, Ups, Downs, result, stack);
        stack.Pop();
    }
 
    if (Downs.ContainsKey(key))
    {
        stack.Push(Direction.Down);
        Helper(Downs[key].Item1, Downs[key].Item2, endRow, endColumn, visited, Lefts, Rights, Ups, Downs, result, stack);
        stack.Pop();
    }
}





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