找到所有“字符相等”字符串的高效算法？

Question

我們如何編寫一個輸出輸入字符串的“同形字等價物 ”的高效函數？

例1 （偽代碼）：

homoglyphs_list = [
                     ["o", "0"], // "o" and "0" are homoglyphs
                     ["i", "l", "1"] // "i" and "l" and "1" are homoglyphs
                  ]

input_string    = "someinput"
output          = [
                   "someinput", "s0meinput", "somelnput",
                   "s0melnput", "some1nput", "s0me1nput"
                  ]

例2 ：

homoglyphs_list = [
                     ["rn", "m", "nn"],
                  ]

input_string    = "rnn"
output          = ["rnn", "rm", "mn", "rrn", "nnn", "nm", "nrn"]

例3 ：

homoglyphs_list = [
                     ["d", "ci", "a"], // "o" and "0" are homoglyphs
                     ["i", "l", "1"] // "i" and "l" and "1" are homoglyphs
                  ]
                  /*
                     notice that with the two rules above,
                     we can infer "d" = "ci" = "a" = "cl" = "c1"
                  */

input_string    = "pacerier"
output          = [
                   "pacerier",  "pacerler",  "pacer1er",  "pcicerier",
                   "pcicerler", "pcicer1er", "pclcerier", "pc1cerier",
                   "pclcerler", "pc1cerler", "pclcer1er", "pc1cer1er",
                   "pdcerier",  "pdcerler",  "pdcer1er"
                  ]

注意：輸出數組中成員的順序並不重要，我們可以假設給定的單純形映射被認為是正確的 （輸入不會給我們一個“無限循環”）。

我當前的算法有效，但它使用原始強制執行並且性能很糟糕。 例如，帶有同形字符["rn", "m", "nn"]的"mmmmm"輸入需要38秒才能運行：

// This is php code (non-pseudo just so we could test the running time), 
// but the question remains language-agnostic

public function Func($in, Array $mappings){
    $out_table = array();
    $out_table[$in] = null;
    while(true){
        $number_of_entries_so_far = count($out_table);
        foreach(array_keys($out_table) as $key){
            foreach($mappings as $mapping){
                foreach($mapping as $value){
                    for($a=0, $aa=strlen($key); $a<$aa; ++$a){
                        $pos = strpos($key, $value, $a);
                        if($pos === false){
                            continue;
                        }
                        foreach($mapping as $equal_value){
                            if($value === $equal_value){
                                continue;
                            }
                            $out_table[substr($key, 0, $pos) . $equal_value . substr($key, $pos + strlen($value))] = null;
                        }
                    }

                }
            }
        }
        if($number_of_entries_so_far === count($out_table)){
            // it means we have tried bruteforcing but added no additional entries,
            // so we can quit now
            break;
        }
    }
    return array_keys($out_table);
}

我們如何實現高效（快速）同形文字擴展算法？

Answer 1

你應該從遞歸實現中獲得一些性能，但我沒有考慮實際的性能。 這將避免多次循環輸出字符串並在每次迭代時計算輸出。 此外，我添加了一個“緩存”以防止計算兩次相同的同性字，為簡單起見它不會檢查映射，但你可以實現它，或者只是在每次調用映射改變之前清除緩存（但那是丑陋且容易引入錯誤）。

代碼如下：

cache = {}
def homoglyph(input_string, mappings):
    output = []
    character = input_string[0]
    if input_string in cache:
        return cache[input_string]
    elif not input_string:
        return []
    for charset in mappings:
        if character in charset:
            temp = input_string
            sub_homoglyphs = homoglyph(input_string[1:], mappings)
            for char in charset:
                temp[0] = char
                output.append(temp)
                #adding the homoglyph character to the rest of the string
                for subhomoglyph in sub_homoglyphs:
                    output.append(char+subhomoglyph)
    cache[input_string] = output
    return output

（這是用python編寫的，因為我不熟悉php語法，我實際上沒有運行這個，所以可能有錯誤，但邏輯的要點就在那里）