A* / Dijkstra的算法简单实现（Pascal）

Question

我正在尝试使用这篇文章http://www.policyalmanac.org/games/aStarTutorial.htm 实现 A* 寻路算法（现在是 Dijkstra 的算法，即没有启发式算法）。但我无法弄清楚我的代码有什么问题（它找到了不正确的路径）。

而不是空的 begin ... end;应该是这一步：

如果它已经在打开列表中，请检查此路径是否为该路径 square 更好，使用 G 成本作为衡量标准。较低的 G 成本意味着 这是一条更好的道路。如果是这样，将正方形的父级更改为 当前方格，并重新计算该方格的 G 和 F 分数。

但我认为这并不重要，因为没有对角线运动。

uses
    crt;

const
    MAXX = 20;
    MAXY = 25;

type
    TArr = array [0..MAXY, 0..MAXX] of integer;

    TCell = record
        x: integer;
        y: integer;
    end;

    TListCell = record
        x: integer;
        y: integer;
        G: integer;
        parent: TCell;
    end;

    TListArr = array [1..10000] of TListCell;

    TList = record
        arr: TListArr;
        len: integer;
    end;

var
    i, j, minind, ind, c: integer;
    start, finish: TCell;
    current: TListCell;
    field: TArr;
    opened, closed: TList;

procedure ShowField;
var
    i, j: integer;
begin
    textcolor(15);
    for i := 0 to MAXX do
    begin
        for j := 0 to MAXY do
        begin
            case field[j, i] of
                99: textcolor(8);  // not walkable
                71: textcolor(14); // walkable
                11: textcolor(10); // start
                21: textcolor(12); // finish
                15: textcolor(2);  // path
                14: textcolor(5);
                16: textcolor(6);
            end;
            write(field[j, i], ' ');
        end;
        writeln;
    end;
    textcolor(15);
end; 


procedure AddClosed(a: TListCell);
begin
    closed.arr[closed.len + 1] := a;
    inc(closed.len);
end;


procedure AddOpened(x, y, G: integer);
begin
    opened.arr[opened.len + 1].x := x;
    opened.arr[opened.len + 1].y := y;
    opened.arr[opened.len + 1].G := G;
    inc(opened.len);
end;

procedure DelOpened(n: integer);
var
    i: integer;
begin
    AddClosed(opened.arr[n]);
    for i := n to opened.len - 1 do
        opened.arr[i] := opened.arr[i + 1];
    dec(opened.len);
end;


procedure SetParent(var a: TListCell; parx, pary: integer);
begin
    a.parent.x := parx;
    a.parent.y := pary;
end;


function GetMin(var a: TList): integer;
var
    i, min, mini: integer;
begin
    min := MaxInt;
    mini := 0;
    for i := 1 to a.len do
        if a.arr[i].G < min then
        begin
            min := a.arr[i].G;
            mini := i;
        end;

    GetMin := mini;
end;


function FindCell(a: TList; x, y: integer): integer;
var
    i: integer;
begin
    FindCell := 0;
    for i := 1 to a.len do
        if (a.arr[i].x = x) and (a.arr[i].y = y) then
        begin
            FindCell := i;
            break;
        end;
end;


procedure ProcessNeighbourCell(x, y: integer);
begin
    if (field[current.x + x, current.y + y] <> 99) then    // if walkable
        if (FindCell(closed, current.x + x, current.y + y) <= 0) then // and not visited before
            if (FindCell(opened, current.x + x, current.y + y) <= 0) then // and not added to list already
            begin
                AddOpened(current.x + x, current.y + y, current.G + 10);
                SetParent(opened.arr[opened.len], current.x, current.y);
                //  field[opened.arr[opened.len].x, opened.arr[opened.len].y]:=16;
            end
                else
            begin

            end;
end;


begin
    randomize;
    for i := 0 to MAXX do
        for j := 0 to MAXY do
            field[j, i] := 99;

    for i := 1 to MAXX - 1 do
        for j := 1 to MAXY - 1 do
            if random(5) mod 5 = 0 then
                field[j, i] := 99
            else field[j, i] := 71;

    // start and finish positions coordinates
    start.x := 5;
    start.y := 3;
    finish.x := 19;
    finish.y := 16;
    field[start.x, start.y] := 11;
    field[finish.x, finish.y] := 21;

    ShowField;

    writeln;

    opened.len := 0;
    closed.len := 0;
    AddOpened(start.x, start.y, 0);
    SetParent(opened.arr[opened.len], -1, -1);
    current.x := start.x;
    current.y := start.y;

    repeat
        minind := GetMin(opened);
        current.x := opened.arr[minind].x;
        current.y := opened.arr[minind].y;
        current.G := opened.arr[minind].G; 
        DelOpened(minind); 

        ProcessNeighbourCell(1, 0);  // look at the cell to the right
        ProcessNeighbourCell(-1, 0); // look at the cell to the left
        ProcessNeighbourCell(0, 1);  // look at the cell above
        ProcessNeighbourCell(0, -1); // look at the cell below

        if (FindCell(opened, finish.x, finish.y) > 0) then
            break;
    until opened.len = 0;

    // count and mark path
    c := 0;
    while ((current.x <> start.x) or (current.y <> start.y)) do
    begin
        field[current.x, current.y] := 15;
        ind := FindCell(closed, current.x, current.y);
        current.x := closed.arr[ind].parent.x;
        current.y := closed.arr[ind].parent.y;
        inc(c);
    end;


    ShowField;
    writeln(c);
    readln;
end.

编辑 2012 年 2 月 1 日：更新了代码，还修复了路径标记（应该有 or 代替 and），现在看起来可以工作了 :)

Answer 1

您发布了很多代码，您是否尝试过缩小失败的范围？

您是否将您的代码与维基百科上的pseudocode 进行了比较？

还请记住，dijkstra 只是启发式为 0 的 A*。

编辑：

您链接的文章（我现在意识到这与我用来学习 A* 的文章完全相同，很有趣）包含图解步骤。我建议您重新创建该地图/网格并在其上运行您的实现。然后逐步浏览图片：

1. 是否已将八个初始邻居添加到打开列表中？他们有正确的父母吗？
2. 是否根据启发式选择了正确的打开节点作为下一个要扫描的节点？
3. 封闭节点列表是否正确？
4. 等等……

Answer 2

您应该重写程序以使用循环而不是剪切和粘贴来访问每个邻居。如果这样做，您将避免以下错误：

if (field[current.x, current.y - 1] <> 99) then
    if (FindCell(closed, current.x, current.y - 1) <= 0) then
        if (FindCell(opened, current.x + 1, current.y) <= 0) then

（见最后一行不一致的current.x + 1, current.y。）

---

关于循环，我在想这样的事情（伪 Python）：

neighbor_offsets = [(0, 1), (0, -1), (1, 0), (-1, 0)]
for offset in neighbor_offsets:
    neighbor = current + offset
    if is_walkable(neighbor) and not is_visited(neighbor):
        # Open 'neighbor' with 'current' as parent:
        open(neighbor, current)

        # Perhaps check if the goal is reached:
        if neighbor == finish:
            goal_reached = True
            break

如果你不写循环而只是重构为

ProcessCell(x+1, y); 
ProcessCell(x-1, y); 
ProcessCell(x, y-1); 
ProcessCell(x, y-1);

那么这也是一个很大的进步。