通过节点获取最短路径

Question

我有这个数组：

Array
(
    [V] => Array
        (
            [0] => S
        )

    [L] => Array
        (
            [0] => M
            [1] => Z
            [2] => G
        )

    [S] => Array
        (
            [0] => T
            [1] => X
            [2] => K
        )

    [T] => Array
        (
            [0] => D
        )

    [B] => Array
        (
            [0] => E
            [1] => N
            [2] => Y
        )

    [W] => Array
        (
            [0] => J
            [1] => Y
        )

    [G] => Array
        (
            [0] => A
            [1] => K
        )

    [J] => Array
        (
            [0] => T
        )

    [X] => Array
        (
            [0] => H
        )

    [E] => Array
        (
            [0] => Z
        )

    [N] => Array
        (
            [0] => B
        )

    [Z] => Array
        (
            [0] => A
            [1] => M
        )

    [U] => Array
        (
            [0] => R
        )

    [F] => Array
        (
            [0] => C
            [1] => V
        )

    [I] => Array
        (
            [0] => F
        )

    [C] => Array
        (
            [0] => O
            [1] => P
            [2] => T
        )

    [Q] => Array
        (
            [0] => L
            [1] => V
        )

    [Y] => Array
        (
            [0] => C
        )

    [K] => Array
        (
            [0] => T
            [1] => P
            [2] => A
        )

    [A] => Array
        (
            [0] => J
        )

    [M] => Array
        (
            [0] => W
        )

    [R] => Array
        (
            [0] => I
        )

    [P] => Array
        (
            [0] => K
            [1] => N
        )

    [O] => Array
        (
            [0] => G
        )

    [H] => Array
        (
            [0] => Q
        )

    [D] => Array
        (
            [0] => U
        )

)

序列化：

a:26:{s:1:"V";a:1:{i:0;s:1:"S";}s:1:"L";a:3:{i:0;s:1:"M";i:1;s:1:"Z";i:2;s:1:"G";}s:1:"S";a:3:{i:0;s:1:"T";i:1;s:1:"X";i:2;s:1:"K";}s:1:"T";a:1:{i:0;s:1:"D";}s:1:"B";a:3:{i:0;s:1:"E";i:1;s:1:"N";i:2;s:1:"Y";}s:1:"W";a:2:{i:0;s:1:"J";i:1;s:1:"Y";}s:1:"G";a:2:{i:0;s:1:"A";i:1;s:1:"K";}s:1:"J";a:1:{i:0;s:1:"T";}s:1:"X";a:1:{i:0;s:1:"H";}s:1:"E";a:1:{i:0;s:1:"Z";}s:1:"N";a:1:{i:0;s:1:"B";}s:1:"Z";a:2:{i:0;s:1:"A";i:1;s:1:"M";}s:1:"U";a:1:{i:0;s:1:"R";}s:1:"F";a:2:{i:0;s:1:"C";i:1;s:1:"V";}s:1:"I";a:1:{i:0;s:1:"F";}s:1:"C";a:3:{i:0;s:1:"O";i:1;s:1:"P";i:2;s:1:"T";}s:1:"Q";a:2:{i:0;s:1:"L";i:1;s:1:"V";}s:1:"Y";a:1:{i:0;s:1:"C";}s:1:"K";a:3:{i:0;s:1:"T";i:1;s:1:"P";i:2;s:1:"A";}s:1:"A";a:1:{i:0;s:1:"J";}s:1:"M";a:1:{i:0;s:1:"W";}s:1:"R";a:1:{i:0;s:1:"I";}s:1:"P";a:2:{i:0;s:1:"K";i:1;s:1:"N";}s:1:"O";a:1:{i:0;s:1:"G";}s:1:"H";a:1:{i:0;s:1:"Q";}s:1:"D";a:1:{i:0;s:1:"U";}}

这意味着......

• V可以转到S
• L可以转到M，Z和G
• S可以转到T，X和K
• ...

我需要一种算法来查找从A到Z的最短路径。这种方式应保存为节点列表，如AJTDURIFCPNBEZ。

我只是尝试了这个递归：

function getWays($key = "A") {
    global $roads;

    echo $key;
    if($key == "Z"){
        echo "<br />";
        return;
    }

    foreach($roads[$key] as $next)
        if($next != "A")
            getWays($next);
}

这不起作用，它要复杂得多。你必须防止循环并提高性能（如果你已经找到较短的一个，请尽早忽略长路径。）

有人可以提供帮助吗？