搜索字符串中未知模式的最有效方法是什么？

Question

I am trying to find patterns that:

• occur more than once
• are more than 1 character long
• are not substrings of any other known pattern

without knowing any of the patterns that might occur.

For example:

• The string "the boy fell by the bell" would return 'ell', 'the b', 'y ' .
• The string "the boy fell by the bell, the boy fell by the bell" would return 'the boy fell by the bell' .

Using double for-loops, it can be brute forced very inefficiently:

ArrayList<String> patternsList = new ArrayList<>();
int length = string.length();
for (int i = 0; i < length; i++) {
    int limit = (length - i) / 2;
    for (int j = limit; j >= 1; j--) {
        int candidateEndIndex = i + j;
        String candidate = string.substring(i, candidateEndIndex);

        if(candidate.length() <= 1) {
            continue;
        }

        if (string.substring(candidateEndIndex).contains(candidate)) {
            boolean notASubpattern = true;
            for (String pattern : patternsList) {
                if (pattern.contains(candidate)) {
                    notASubpattern = false;
                    break;
                }
            }

            if (notASubpattern) {
                patternsList.add(candidate);
            }
        }
    }
}

However, this is incredibly slow when searching large strings with tons of patterns.

Answer 1

You can build a suffix tree for your string in linear time: https://en.wikipedia.org/wiki/Suffix_tree

The patterns you are looking for are the strings corresponding to internal nodes that have only leaf children.

Answer 2

You could use n-grams to find patterns in a string. It would take O(n) time to scan the string for n-grams. When you find a substring by using a n-gram, put it into a hash table with a count of how many times that substring was found in the string. When you're done searching for n-grams in the string, search the hash table for counts greater than 1 to find recurring patterns in the string.

For example, in the string "the boy fell by the bell, the boy fell by the bell" using a 6-gram will find the substring "the boy fell by the bell". A hash table entry with that substring will have a count of 2 because it occurred twice in the string. Varying the number of words in the n-gram will help you discover different patterns in the string.

Dictionary<string, int>dict = new Dictionary<string, int>();
int count = 0;
int ngramcount = 6;
string substring = "";

// Add entries to the hash table
while (count < str.length) {
    // copy the words into the substring
    int i = 0;
    substring = "";
    while (ngramcount > 0 && count < str.length) {
        substring[i] = str[count];
        if (str[i] == ' ')
            ngramcount--;
        i++;
        count++;
    }
    ngramcount = 6;
    substring.Trim();  // get rid of the last blank in the substring
    // Update the dictionary (hash table) with the substring
    if (dict.Contains(substring)) {  // substring is already in hash table so increment the count
        int hashCount = dict[substring];
        hashCount++;
        dict[substring] = hashCount;
    }
    else
        dict[substring] = 1;
}

// Find the most commonly occurrring pattern in the string
// by searching the hash table for the greatest count.
int maxCount = 0;
string mostCommonPattern = "";
foreach (KeyValuePair<string, int> pair in dict) {
    if (pair.Value > maxCount) {
        maxCount = pair.Value;
        mostCommonPattern = pair.Key;
    }
}

Answer 3

I've written this just for fun. I hope I have understood the problem correctly, this is valid and fast enough; if not, please be easy on me :) I might optimize it a little more I guess, if someone finds it useful.

private static IEnumerable<string> getPatterns(string txt)
{
    char[] arr = txt.ToArray();
    BitArray ba = new BitArray(arr.Length);
    for (int shingle = getMaxShingleSize(arr); shingle >= 2; shingle--)
    {
        char[] arr1 = new char[shingle];
        int[] indexes = new int[shingle];
        HashSet<int> hs = new HashSet<int>();
        Dictionary<int, int[]> dic = new Dictionary<int, int[]>();
        for (int i = 0, count = arr.Length - shingle; i <= count; i++)
        {
            for (int j = 0; j < shingle; j++)
            {
                int index = i + j;
                arr1[j] = arr[index];
                indexes[j] = index;
            }
            int h = getHashCode(arr1);
            if (hs.Add(h))
            {
                int[] indexes1 = new int[indexes.Length];
                Buffer.BlockCopy(indexes, 0, indexes1, 0, indexes.Length * sizeof(int));
                dic.Add(h, indexes1);
            }
            else
            {
                bool exists = false;
                foreach (int index in indexes)
                    if (ba.Get(index))
                    {
                        exists = true;
                        break;
                    }
                if (!exists)
                {
                    int[] indexes1 = dic[h];
                    if (indexes1 != null)
                        foreach (int index in indexes1)
                            if (ba.Get(index))
                            {
                                exists = true;
                                break;
                            }
                }
                if (!exists)
                {
                    foreach (int index in indexes)
                        ba.Set(index, true);
                    int[] indexes1 = dic[h];
                    if (indexes1 != null)
                        foreach (int index in indexes1)
                            ba.Set(index, true);
                    dic[h] = null;
                    yield return new string(arr1);
                }
            }
        }
    }
}
private static int getMaxShingleSize(char[] arr)
{            
    for (int shingle = 2; shingle <= arr.Length / 2 + 1; shingle++)
    {
        char[] arr1 = new char[shingle];
        HashSet<int> hs = new HashSet<int>();
        bool noPattern = true;
        for (int i = 0, count = arr.Length - shingle; i <= count; i++)
        {
            for (int j = 0; j < shingle; j++)
                arr1[j] = arr[i + j];
            int h = getHashCode(arr1);
            if (!hs.Add(h))
            {
                noPattern = false;
                break;
            }
        }
        if (noPattern)
            return shingle - 1;
    }
    return -1;
}
private static int getHashCode(char[] arr)
{
    unchecked
    {
        int hash = (int)2166136261;
        foreach (char c in arr)
            hash = (hash * 16777619) ^ c.GetHashCode();
        return hash;
    }
}

Edit
My previous code has serious problems. This one is better:

private static IEnumerable<string> getPatterns(string txt)
{
    Dictionary<int, int> dicIndexSize = new Dictionary<int, int>();
    for (int shingle = 2, count0 = txt.Length / 2 + 1; shingle <= count0; shingle++)
    {   
        Dictionary<string, int> dic = new Dictionary<string, int>();
        bool patternExists = false;
        for (int i = 0, count = txt.Length - shingle; i <= count; i++)
        {
            string sub = txt.Substring(i, shingle);
            if (!dic.ContainsKey(sub))
                dic.Add(sub, i);
            else
            {   
                patternExists = true;
                int index0 = dic[sub];
                if (index0 >= 0)
                {
                    dicIndexSize[index0] = shingle;
                    dic[sub] = -1;
                }
            }
        }
        if (!patternExists)
            break;
    }
    List<int> lst = dicIndexSize.Keys.ToList();
    lst.Sort((a, b) => dicIndexSize[b].CompareTo(dicIndexSize[a]));
    BitArray ba = new BitArray(txt.Length);
    foreach (int i in lst)
    {
        bool ok = true;
        int len = dicIndexSize[i];
        for (int j = i, max = i + len; j < max; j++)
        {
            if (ok) ok = !ba.Get(j);
            ba.Set(j, true);
        }
        if (ok)
            yield return txt.Substring(i, len);
    }
}

Text in this book took 3.4sec in my computer.

Answer 4

Suffix arrays are the right idea, but there's a non-trivial piece missing, namely, identifying what are known in the literature as "supermaximal repeats". Here's a GitHub repo with working code: https://github.com/eisenstatdavid/commonsub . Suffix array construction uses the SAIS library, vendored in as a submodule. The supermaximal repeats are found using a corrected version of the pseudocode from findsmaxr in Efficient repeat finding via suffix arrays (Becher–Deymonnaz–Heiber) .

static void FindRepeatedStrings(void) {
  // findsmaxr from https://arxiv.org/pdf/1304.0528.pdf
  printf("[");
  bool needComma = false;
  int up = -1;
  for (int i = 1; i < Len; i++) {
    if (LongCommPre[i - 1] < LongCommPre[i]) {
      up = i;
      continue;
    }
    if (LongCommPre[i - 1] == LongCommPre[i] || up < 0) continue;
    for (int k = up - 1; k < i; k++) {
      if (SufArr[k] == 0) continue;
      unsigned char c = Buf[SufArr[k] - 1];
      if (Set[c] == i) goto skip;
      Set[c] = i;
    }
    if (needComma) {
      printf("\n,");
    }
    printf("\"");
    for (int j = 0; j < LongCommPre[up]; j++) {
      unsigned char c = Buf[SufArr[up] + j];
      if (iscntrl(c)) {
        printf("\\u%.4x", c);
      } else if (c == '\"' || c == '\\') {
        printf("\\%c", c);
      } else {
        printf("%c", c);
      }
    }
    printf("\"");
    needComma = true;
  skip:
    up = -1;
  }
  printf("\n]\n");
}

Here's a sample output on the text of the first paragraph:

Davids-MBP:commonsub eisen$ ./repsub input
["\u000a"
," S"
," as "
," co"
," ide"
," in "
," li"
," n"
," p"
," the "
," us"
," ve"
," w"
,"\""
,"–"
,"("
,")"
,". "
,"0"
,"He"
,"Suffix array"
,"`"
,"a su"
,"at "
,"code"
,"com"
,"ct"
,"do"
,"e f"
,"ec"
,"ed "
,"ei"
,"ent"
,"ere's a "
,"find"
,"her"
,"https://"
,"ib"
,"ie"
,"ing "
,"ion "
,"is"
,"ith"
,"iv"
,"k"
,"mon"
,"na"
,"no"
,"nst"
,"ons"
,"or"
,"pdf"
,"ri"
,"s are "
,"se"
,"sing"
,"sub"
,"supermaximal repeats"
,"te"
,"ti"
,"tr"
,"ub "
,"uffix arrays"
,"via"
,"y, "
]

Answer 5

I would use Knuth–Morris–Pratt algorithm (linear time complexity O(n) ) to find substrings. I would try to find the largest substring pattern, remove it from the input string and try to find the second largest and so on. I would do something like this:

string pattern = input.substring(0,lenght/2);
string toMatchString = input.substring(pattern.length, input.lenght - 1);

List<string> matches = new List<string>();

while(pattern.lenght > 0)
{
    int index = KMP(pattern, toMatchString);
    if(index > 0)
    {
        matches.Add(pattern);

        // remove the matched pattern occurences from the input string
        // I would do something like this:
        // 0 to pattern.lenght gets removed
        // check for all occurences of pattern in toMatchString and remove them
        // get the remaing shrinked input, reassign values for pattern & toMatchString
        // keep looking for the next largest substring
    }
    else
    {
        pattern = input.substring(0, pattern.lenght - 1);
        toMatchString = input.substring(pattern.length, input.lenght - 1);
    }
}

Where KMP implements Knuth–Morris–Pratt algorithm. You can find the Java implementations of it at Github or Princeton or write it yourself.

PS: I don't code in Java and it is quick try to my first bounty about to close soon. So please don't give me the stick if I missed something trivial or made a +/-1 error.