这一路上,他一共遇到店5次,遇到花10次,已知最后一次遇到的是花,他正好把酒喝光了。
请你计算李白遇到店和花的次序,可以把遇店记为a,遇花记为b。则:babaabbabbabbbb 就是合理的次序。像这样的答案一共有多少呢?请你计算出所有可能方案的个数(包含题目给出的)。

PHP代码实现:

$count = 0;
    $a = array();

    function show($a, $num)
    {
        $i = 0;
        while ($i < $num) echo $a[$i++];
        echo '<br />';
    }

    function forward_recursion($i, $store, $flower, $wine)
    {
        if($store > 5 || $flower > 10){
            return;
        }
        else if($store == 5 && $flower == 10 && $i == 15){
            if ($GLOBALS['a'][14] == 'b' && $wine == 0){
                $GLOBALS['count']++;
                show($GLOBALS['a'], 15);
            }
            return;
        }

        $GLOBALS['a'][$i] = 'a';
        forward_recursion($i + 1, $store + 1, $flower, $wine * 2);    //逢店加一倍
        $GLOBALS['a'][$i] = 'b';
        forward_recursion($i + 1, $store, $flower + 1, $wine - 1);    //遇花喝一斗
    }

    forward_recursion(0,0,0,2);
    echo $count;

运行结果:

ababbbbbabababb
abbabbabbbababb
abbabbbaabbbabb
abbabbbabaabbbb
abbbaabbabbbabb
abbbaabbbaabbbb
abbbabaabbabbbb
baababbbbbababb
baabbabbabbbabb
baabbabbbaabbbb
baabbbaabbabbbb
babaababbbbbabb
babaabbabbabbbb
bababaababbbbbb
14
03-05 18:26