开赛算法

2024-05-09 16:35:04 14

Kasai的算法用于从后缀数组中获取最长公共前缀(LCP)数组。首先找到后缀数组。之后，Kasai的算法采用后缀数组列表来查找LCP。

对于LCP数组，它的取值为O（mlogn），其中m为模式长度，n为文本长度。Kasai算法使用O(n)来搜索主字符串中的模式。

输入输出

Input:
Main String: “banana”
Output:
Suffix Array :
5 3 1 0 4 2
Common Prefix Array :
1 3 0 0 2 0

算法

buildSuffixArray（文本）

输入：主字符串

输出：后缀数组，从正文开始构建

Begin
   n := size of text

   for i := 0 to n, do
      suffArray[i].index := i
      suffArray[i].rank[0] := text[i]
      if (i+1) < n, then
         suffArray[i].rank[1] := text[i+1]
      else
         suffArray[i].rank[1] := -1
   do

   sort the suffix array
   define index array to store indexes

   for k := 4 to (2*n)-1, increase k by k*2, do
      currRank := 0
      prevRank := suffArray[0].rank[0]
      suffArray[0].rank[0] := currRank
      index[suffArray[0].index] = 0

      for all character index i of text, do
         if suffArray[i].rank[0] = prevRank AND suffArray[i].rank[1] =
            suffArray[i-1].rank[1], then
            prevRank := suffArray[i].rank[0]
            suffArray[i].rank[0] := currRank
         else
            prevRank := suffArray[i].rank[0]
            suffArray[i].rank[0] := currRank + 1
            currRank := currRank + 1
            index[suffArray[i].index] := i
      done

      for all character index i of text, do
         nextIndex := suffArray[i].index + k/2
         if nextIndex< n, then
            suffArray[i].rank[1] := suffArray[index[nextIndex]].rank[0]
         else
            suffArray[i].rank[1] := -1
      done
      sort the suffArray
   done

   for all character index i of text, do
      insert suffArray[i].index into suffVector
   done
End

kasaiAlgorithm(text,suffVector)

输入- 主文本和后缀矢量作为后缀列表

输出：找到最长公共前缀的位置

Begin
   n := size of suffVector
   define longPrefix list of size n and fill all entries with 0
   define suffInverse list of size n and fill all entries with 0

   for all index values ‘i’ of suffVector, do
      suffInverse[suffVector[i]] = i
   done

   k := 0
      for i := 0 to n-1, do
         if suffInverse[i] = n-1 then
            k :=0
            ignore the bottom part and go for next iteration.
         j := suffVector[suffInverse[i]+1]

         while (i+k)<n AND (j+k) < n and text[i+k] = text[j+k], do
            increase k by 1
         done
         longPrefix[suffInverse[i]] := k
         if k > 0 then
            decrease k by 1
   done
   return longPrefix
End

示例

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;

struct suffix {
   int index;
   int rank[2];    // To store rank pair
};

bool compare(suffix s1, suffix s2) {    //compare suffixes for sort function
   if(s1.rank[0] == s2.rank[0]) {
      if(s1.rank[1] < s2.rank[1])
         return true;
      else
         return false;
   }else {
      if(s1.rank[0] < s2.rank[0])
         return true;
      else
         return false;
   }
}

vector<int> buildSuffixArray(string mainString) {
   int n = mainString.size();
   suffix suffixArray[n];

   for (int i = 0; i < n; i++) {
      suffixArray[i].index = i;
      suffixArray[i].rank[0] = mainString[i] - 'a';     //store old rank
      suffixArray[i].rank[1] = ((i+1)<n)?(mainString[i+1]-'a'):-1; //rank after alphabetical ordering
   }

   sort(suffixArray, suffixArray+n, compare);    //sort suffix array upto first 2 characters
   int index[n];  //index in suffixArray

   for (int k = 4; k < 2*n; k = k*2) {    //increase k as power of 2
      int currRank = 0;
      int prevRank = suffixArray[0].rank[0];
      suffixArray[0].rank[0] = currRank;
      index[suffixArray[0].index] = 0;

      for (int i = 1; i < n; i++) {    // Assigning rank to all suffix
         if (suffixArray[i].rank[0] == prevRank && suffixArray[i].rank[1] == suffixArray[i-1].rank[1]) {
            prevRank = suffixArray[i].rank[0];
            suffixArray[i].rank[0] = currRank;
         } else{    //increment rank and assign
            prevRank = suffixArray[i].rank[0];
            suffixArray[i].rank[0] = ++currRank;
         }
         index[suffixArray[i].index] = i;
      }

      for (int i = 0; i < n; i++) {    // Assign next rank to every suffix
         int nextIndex = suffixArray[i].index + k/2;
         suffixArray[i].rank[1] = (nextIndex < n)? suffixArray[index[nextIndex]].rank[0]: -1;
      }
      sort(suffixArray, suffixArray+n, compare); //sort upto first k characters
   }

   vector<int>suffixVector;
   for (int i = 0; i < n; i++)
      suffixVector.push_back(suffixArray[i].index);    //index of all suffix to suffix vector
      return  suffixVector;
}

vector<int> kasaiAlgorithm(string mainString, vector<int> suffixVector) {
   int n = suffixVector.size();
   vector<int> longPrefix(n, 0);    //size n and initialize with 0
   vector<int> suffixInverse(n, 0);

   for (int i=0; i < n; i++)
      suffixInverse[suffixVector[i]] = i;    //fill values of inverse Suffix list
   int k = 0;
   for (int i=0; i<n; i++) {     //for all suffix in main string
      if (suffixInverse[i] == n-1) {    //when suffix at position (n-1)
         k = 0;
         continue;
      }

      int j = suffixVector[suffixInverse[i]+1];    //nest string of suffix list
      while (i+k<n && j+k<n && mainString[i+k]==mainString[j+k]) //start from kth index
         k++;
      longPrefix[suffixInverse[i]] = k;    // prefix for the current suffix.
      if (k>0)
         k--;    //remofe first character of string
   }
   return longPrefix;
}

void showArray(vector<int> vec) {
   vector<int>::iterator it;

   for (it = vec.begin(); it < vec.end() ; it++)
      cout << *it << " ";
   cout << endl;
}

int main() {
   string mainString = "banana";
   vector<int>suffixArray = buildSuffixArray(mainString);
   int n = suffixArray.size();

   cout<< "Suffix Array : "<<endl;
   showArray(suffixArray);

   vector<int>commonPrefix = kasaiAlgorithm(mainString, suffixArray);

   cout<< "\nCommon Prefix Array : "<<endl;
   showArray(commonPrefix);
}

输出结果

Suffix Array :
5 3 1 0 4 2
Common Prefix Array :
1 3 0 0 2 0

开赛算法

输入输出

算法

示例

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