String相关算法

最近在研究一些字符串的算法，准备做一个diff的小工具
首先第一步是解决求两个字符串里面最大公共字串的问题，趁着周末看了一些资料

从T.T.tick那里拿到的一些资料：

http://www.rainsts.net/article.asp?id=767
http://www.cnblogs.com/TtTiCk/archive/2007/08/04/842819.html

自己实现以上资料算法（未经过完整的单元测试，但在几个试验中可以获取正确的的最大公共子串了）：

package test;
import java.lang.String;

public class LCSTest {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		String str1 = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa" +
				"dddddddddddddddddddddddddddddddddd" +
				"ddddddddddddddddddddddddddddddddddddddd" +
				"dddddddddddddddddddddddddddddddddddddddddd" +
				"ddddddddddddddddddddddddddddddddddddddddddd" +
				"ddddddddddddddddddddddddddddddddddddddddddddd" +
				"ddddddddddddddddddddddddddddddddddddddddddddadfeasdf" +
				"amydonTangoisagoodpersonoBon";
		String str2 = "jayamTangoisfffffffffffffffffffffeeeeeeeeeeeeee" +
				"adfffffffffffffffffffffffffffffffffffffffffffffff" +
				"ffffffffffffffffffffffffffffffffffffffffffffffffffff" +
				"ffffffffffffffffffffffffffffffffffffffffffffffffffffff" +
				"ddddddddddddddddddddddddddddddddddddddddddddddd" +
				"agoodipersondoo";
		System.out.println(LCS(str1,str2));
	}
	
	public static String LCS(String str1, String str2){
		int[][] LCSArray = new int[str1.length()][str2.length()];
		int maxValue = 0;
		int xMax = 0;
		int yMax = 0;
		for (int x = 0; x< str1.length(); x++){
			for (int y=0; y<str2.length(); y++){
				if (str1.charAt(x)==str2.charAt(y)){
					if (x>0 && y>0){
						LCSArray[x][y]=LCSArray[x-1][y-1] +1;
						if (LCSArray[x][y]> maxValue){
							maxValue = LCSArray[x][y];
							xMax = x;
							yMax = y;
						}
					}else{
						LCSArray[x][y]=1;
					}
				}else {
					LCSArray[x][y]=0;
				}
				System.out.print(LCSArray[x][y]);
				if (y == str2.length()-1){
					System.out.println();
				}
			}
		}
		if (maxValue != 0){
			System.out.println("xMax:" + xMax);
			System.out.println("maxValue:" + maxValue);
			return str1.substring(xMax-maxValue+1, xMax+1);
		} else {
			return null;
		}

	}

}

另外，还在某个开源组织拿到的一些diff算法的代码：

namespace my.utils {
  using System;
  using System.Collections;
  using System.Text;
  using System.Text.RegularExpressions;

  /// <summary>
  /// This Class implements the Difference Algorithm published in
  /// "An O(ND) Difference Algorithm and its Variations" by Eugene Myers
  /// Algorithmica Vol. 1 No. 2, 1986, p 251.  
  /// 
  /// There are many C, Java, Lisp implementations public available but they all seem to come
  /// from the same source (diffutils) that is under the (unfree) GNU public License
  /// and cannot be reused as a sourcecode for a commercial application.
  /// There are very old C implementations that use other (worse) algorithms.
  /// Microsoft also published sourcecode of a diff-tool (windiff) that uses some tree data.
  /// Also, a direct transfer from a C source to C# is not easy because there is a lot of pointer
  /// arithmetic in the typical C solutions and i need a managed solution.
  /// These are the reasons why I implemented the original published algorithm from the scratch and
  /// make it avaliable without the GNU license limitations.
  /// I do not need a high performance diff tool because it is used only sometimes.
  /// I will do some performace tweaking when needed.
  /// 
  /// The algorithm itself is comparing 2 arrays of numbers so when comparing 2 text documents
  /// each line is converted into a (hash) number. See DiffText(). 
  /// 
  /// Some chages to the original algorithm:
  /// The original algorithm was described using a recursive approach and comparing zero indexed arrays.
  /// Extracting sub-arrays and rejoining them is very performance and memory intensive so the same
  /// (readonly) data arrays are passed arround together with their lower and upper bounds.
  /// This circumstance makes the LCS and SMS functions more complicate.
  /// I added some code to the LCS function to get a fast response on sub-arrays that are identical,
  /// completely deleted or inserted.
  /// 
  /// The result from a comparisation is stored in 2 arrays that flag for modified (deleted or inserted)
  /// lines in the 2 data arrays. These bits are then analysed to produce a array of Item objects.
  /// 
  /// Further possible optimizations:
  /// (first rule: don't do it; second: don't do it yet)
  /// The arrays DataA and DataB are passed as parameters, but are never changed after the creation
  /// so they can be members of the class to avoid the paramter overhead.
  /// In SMS is a lot of boundary arithmetic in the for-D and for-k loops that can be done by increment
  /// and decrement of local variables.
  /// The DownVector and UpVector arrays are alywas created and destroyed each time the SMS gets called.
  /// It is possible to reuse tehm when transfering them to members of the class.
  /// See TODO: hints.
  /// 
  /// diff.cs: A port of the algorythm to C#
  /// Created by Matthias Hertel, see http://www.mathertel.de
  /// This work is licensed under a Creative Commons Attribution 2.0 Germany License.
  /// see http://creativecommons.org/licenses/by/2.0/de/
  /// 
  /// Changes:
  /// 2002.09.20 There was a "hang" in some situations.
  /// Now I undestand a little bit more of the SMS algorithm. 
  /// There have been overlapping boxes; that where analyzed partial differently.
  /// One return-point is enough.
  /// A assertion was added in CreateDiffs when in debug-mode, that counts the number of equal (no modified) lines in both arrays.
  /// They must be identical.
  /// 
  /// 2003.02.07 Out of bounds error in the Up/Down vector arrays in some situations.
  /// The two vetors are now accessed using different offsets that are adjusted using the start k-Line. 
  /// A test case is added. 
  /// 
  /// 2006.03.05 Some documentation and a direct Diff entry point.
  /// 
  /// 2006.03.08 Refactored the API to static methods on the Diff class to make usage simpler.
  /// 2006.03.10 using the standard Debug class for self-test now.
  ///            compile with: csc /target:exe /out:diffTest.exe /d:DEBUG /d:TRACE /d:SELFTEST Diff.cs
  /// </summary>
	
  public class Diff {

    /// <summary>details of one difference.</summary>
    public struct Item {
      /// <summary>Start Line number in Data A.</summary>
      public int StartA;
      /// <summary>Start Line number in Data B.</summary>
      public int StartB;

      /// <summary>Number of changes in Data A.</summary>
      public int deletedA;
      /// <summary>Number of changes in Data A.</summary>
      public int insertedB;
    } // Item

    /// <summary>
    /// Shortest Middle Snake Return Data
    /// </summary>
    private struct SMSRD {
      internal int x, y; 
      // internal int u, v;  // 2002.09.20: no need for 2 points 
    } 


    #region self-Test

#if (SELFTEST)
    /// <summary>
    /// start a self- / box-test for some diff cases and report to the debug output.
    /// </summary>
    /// <param name="args">not used</param>
    /// <returns>always 0</returns>
    public static int Main(string[] args) {
      StringBuilder ret = new StringBuilder();
      string a, b;

      System.Diagnostics.ConsoleTraceListener ctl = new System.Diagnostics.ConsoleTraceListener(false);
      System.Diagnostics.Debug.Listeners.Add(ctl);

      System.Console.WriteLine("Diff Self Test...");
      
      // test all changes
      a = "a,b,c,d,e,f,g,h,i,j,k,l".Replace(',', '\n');
      b = "0,1,2,3,4,5,6,7,8,9".Replace(',', '\n');
      System.Diagnostics.Debug.Assert(TestHelper(Diff.DiffText(a, b, false, false, false))
        == "12.10.0.0*", 
        "all-changes test failed.");
      System.Diagnostics.Debug.WriteLine("all-changes test passed.");
      // test all same
      a = "a,b,c,d,e,f,g,h,i,j,k,l".Replace(',', '\n');
      b = a;
      System.Diagnostics.Debug.Assert(TestHelper(Diff.DiffText(a, b, false, false, false))
        == "",
        "all-same test failed.");
      System.Diagnostics.Debug.WriteLine("all-same test passed.");

      // test snake
      a = "a,b,c,d,e,f".Replace(',', '\n');
      b = "b,c,d,e,f,x".Replace(',', '\n');
      System.Diagnostics.Debug.Assert(TestHelper(Diff.DiffText(a, b, false, false, false))
        == "1.0.0.0*0.1.6.5*",
        "snake test failed.");
      System.Diagnostics.Debug.WriteLine("snake test passed.");

      // 2002.09.20 - repro
      a = "c1,a,c2,b,c,d,e,g,h,i,j,c3,k,l".Replace(',', '\n');
      b = "C1,a,C2,b,c,d,e,I1,e,g,h,i,j,C3,k,I2,l".Replace(',', '\n');
      System.Diagnostics.Debug.Assert(TestHelper(Diff.DiffText(a, b, false, false, false))
        == "1.1.0.0*1.1.2.2*0.2.7.7*1.1.11.13*0.1.13.15*",
        "repro20020920 test failed.");
      System.Diagnostics.Debug.WriteLine("repro20020920 test passed.");
      
      // 2003.02.07 - repro
      a = "F".Replace(',', '\n');
      b = "0,F,1,2,3,4,5,6,7".Replace(',', '\n');
      System.Diagnostics.Debug.Assert(TestHelper(Diff.DiffText(a, b, false, false, false))
        == "0.1.0.0*0.7.1.2*", 
        "repro20030207 test failed.");
      System.Diagnostics.Debug.WriteLine("repro20030207 test passed.");
      
      // Muegel - repro
      a = "HELLO\nWORLD";
      b = "\n\nhello\n\n\n\nworld\n";
      System.Diagnostics.Debug.Assert(TestHelper(Diff.DiffText(a, b, false, false, false))
        == "2.8.0.0*", 
        "repro20030409 test failed.");
      System.Diagnostics.Debug.WriteLine("repro20030409 test passed.");

    // test some differences
      a = "a,b,-,c,d,e,f,f".Replace(',', '\n');
      b = "a,b,x,c,e,f".Replace(',', '\n');
      System.Diagnostics.Debug.Assert(TestHelper(Diff.DiffText(a, b, false, false, false))
        == "1.1.2.2*1.0.4.4*1.0.6.5*", 
        "some-changes test failed.");
      System.Diagnostics.Debug.WriteLine("some-changes test passed.");

      System.Diagnostics.Debug.WriteLine("End.");
      System.Diagnostics.Debug.Flush();

      return (0);
    }


    public static string TestHelper(Item []f) {
      StringBuilder ret = new StringBuilder();
      for (int n = 0; n < f.Length; n++) {
        ret.Append(f[n].deletedA.ToString() + "." + f[n].insertedB.ToString() + "." + f[n].StartA.ToString() + "." + f[n].StartB.ToString() + "*");
      }
      // Debug.Write(5, "TestHelper", ret.ToString());
      return (ret.ToString());
    }
#endif
    #endregion


    /// <summary>
    /// Find the difference in 2 texts, comparing by textlines.
    /// </summary>
    /// <param name="TextA">A-version of the text (usualy the old one)</param>
    /// <param name="TextB">B-version of the text (usualy the new one)</param>
    /// <returns>Returns a array of Items that describe the differences.</returns>
    public Item [] DiffText(string TextA, string TextB) {
      return(DiffText(TextA, TextB, false, false, false));
    } // DiffText

      
    /// <summary>
    /// Find the difference in 2 text documents, comparing by textlines.
    /// The algorithm itself is comparing 2 arrays of numbers so when comparing 2 text documents
    /// each line is converted into a (hash) number. This hash-value is computed by storing all
    /// textlines into a common hashtable so i can find dublicates in there, and generating a 
    /// new number each time a new textline is inserted.
    /// </summary>
    /// <param name="TextA">A-version of the text (usualy the old one)</param>
    /// <param name="TextB">B-version of the text (usualy the new one)</param>
    /// <param name="trimSpace">When set to true, all leading and trailing whitespace characters are stripped out before the comparation is done.</param>
    /// <param name="ignoreSpace">When set to true, all whitespace characters are converted to a single space character before the comparation is done.</param>
    /// <param name="ignoreCase">When set to true, all characters are converted to their lowercase equivivalence before the comparation is done.</param>
    /// <returns>Returns a array of Items that describe the differences.</returns>
    public static Item [] DiffText(string TextA, string TextB, bool trimSpace, bool ignoreSpace, bool ignoreCase) {
      // prepare the input-text and convert to comparable numbers.
      Hashtable h = new Hashtable(TextA.Length + TextB.Length);

      // The A-Version of the data (original data) to be compared.
      DiffData DataA = new DiffData(DiffCodes(TextA, h, trimSpace, ignoreSpace, ignoreCase));

      // The B-Version of the data (modified data) to be compared.
      DiffData DataB = new DiffData(DiffCodes(TextB, h, trimSpace, ignoreSpace, ignoreCase));

      h = null; // free up hashtable memory (maybe)

      LCS(DataA, 0, DataA.Length, DataB, 0, DataB.Length);
      return CreateDiffs(DataA, DataB);
    } // DiffText
		

    /// <summary>
    /// Find the difference in 2 arrays of integers.
    /// </summary>
    /// <param name="ArrayA">A-version of the numbers (usualy the old one)</param>
    /// <param name="ArrayB">B-version of the numbers (usualy the new one)</param>
    /// <returns>Returns a array of Items that describe the differences.</returns>
    public static Item [] DiffInt(int[] ArrayA, int[] ArrayB) {
      // The A-Version of the data (original data) to be compared.
      DiffData DataA = new DiffData(ArrayA);

      // The B-Version of the data (modified data) to be compared.
      DiffData DataB = new DiffData(ArrayB);

      LCS(DataA, 0, DataA.Length, DataB, 0, DataB.Length);
      return CreateDiffs(DataA, DataB);
    } // Diff


    /// <summary>
    /// This function converts all textlines of the text into unique numbers for every unique textline
    /// so further work can work only with simple numbers.
    /// </summary>
    /// <param name="aText">the input text</param>
    /// <param name="h">This extern initialized hashtable is used for storing all ever used textlines.</param>
    /// <param name="trimSpace">ignore leading and trailing space characters</param>
    /// <returns>a array of integers.</returns>
    private static int[] DiffCodes(string aText, Hashtable h, bool trimSpace, bool ignoreSpace, bool ignoreCase) {
      // get all codes of the text
      string []Lines;
      int []Codes;
      int lastUsedCode = h.Count;
      object aCode;
      string s;

      // strip off all cr, only use lf as textline separator.
      aText = aText.Replace("\r", "");
      Lines = aText.Split('\n');

      Codes = new int[Lines.Length];

      for (int i = 0; i < Lines.Length; ++i) {
        s = Lines[i];
        if (trimSpace)
          s = s.Trim();

        if (ignoreSpace) {
          s = Regex.Replace(s, "\\s+", " ");            // TODO: optimization: faster blank removal.
        }

        if (ignoreCase)
          s = s.ToLower();
        
        aCode = h[s];
        if (aCode == null) {
          lastUsedCode++;
          h[s] = lastUsedCode;
          Codes[i] = lastUsedCode;
        } else {
          Codes[i] = (int)aCode;
        } // if
      } // for
      return(Codes);
    } // DiffCodes


    /// <summary>
    /// This is the algorithm to find the Shortest Middle Snake (SMS).
    /// </summary>
    /// <param name="DataA">sequence A</param>
    /// <param name="LowerA">lower bound of the actual range in DataA</param>
    /// <param name="UpperA">upper bound of the actual range in DataA (exclusive)</param>
    /// <param name="DataB">sequence B</param>
    /// <param name="LowerB">lower bound of the actual range in DataB</param>
    /// <param name="UpperB">upper bound of the actual range in DataB (exclusive)</param>
    /// <returns>a MiddleSnakeData record containing x,y and u,v</returns>
    private static SMSRD SMS(DiffData DataA, int LowerA, int UpperA, DiffData DataB, int LowerB, int UpperB) {
      SMSRD ret;
      int MAX = DataA.Length + DataB.Length + 1;

      int DownK = LowerA - LowerB; // the k-line to start the forward search
      int UpK = UpperA - UpperB; // the k-line to start the reverse search

      int Delta = (UpperA - LowerA) - (UpperB - LowerB);
      bool oddDelta = (Delta & 1) != 0;

      /// vector for the (0,0) to (x,y) search
      int[] DownVector = new int[2* MAX + 2];

      /// vector for the (u,v) to (N,M) search
      int[] UpVector = new int[2 * MAX + 2];
      
      // The vectors in the publication accepts negative indexes. the vectors implemented here are 0-based
      // and are access using a specific offset: UpOffset UpVector and DownOffset for DownVektor
      int DownOffset = MAX - DownK;
      int UpOffset = MAX - UpK;
	
      int  MaxD = ((UpperA - LowerA + UpperB - LowerB) / 2) + 1;
		
      // Debug.Write(2, "SMS", String.Format("Search the box: A[{0}-{1}] to B[{2}-{3}]", LowerA, UpperA, LowerB, UpperB));

      // init vectors
      DownVector[DownOffset + DownK + 1] = LowerA;
      UpVector[UpOffset + UpK - 1] = UpperA;
			
      for (int D = 0; D <= MaxD; D++) {

        // Extend the forward path.
        for (int k = DownK - D; k <= DownK + D; k += 2) {
          // Debug.Write(0, "SMS", "extend forward path " + k.ToString());

          // find the only or better starting point
          int x, y;
          if (k == DownK - D) {
            x = DownVector[DownOffset + k+1]; // down
          } else {
            x = DownVector[DownOffset + k-1] + 1; // a step to the right
            if ((k < DownK + D) && (DownVector[DownOffset + k+1] >= x))
              x = DownVector[DownOffset + k+1]; // down
          }
          y = x - k;

          // find the end of the furthest reaching forward D-path in diagonal k.
          while ((x < UpperA) && (y < UpperB) && (DataA.data[x] == DataB.data[y])) {
            x++; y++;
          }
          DownVector[DownOffset + k] = x;

          // overlap ?
          if (oddDelta && (UpK-D < k) && (k < UpK+D)) {
            if (UpVector[UpOffset + k] <= DownVector[DownOffset + k]) {
              ret.x = DownVector[DownOffset + k];
              ret.y = DownVector[DownOffset + k] - k;
              // ret.u = UpVector[UpOffset + k];      // 2002.09.20: no need for 2 points 
              // ret.v = UpVector[UpOffset + k] - k;
              return (ret);
            } // if
          } // if

        } // for k
				
        // Extend the reverse path.
        for (int k = UpK - D; k <= UpK + D; k += 2) {
          // Debug.Write(0, "SMS", "extend reverse path " + k.ToString());

          // find the only or better starting point
          int x, y;
          if (k == UpK + D) {
            x = UpVector[UpOffset + k-1]; // up
          } else {
            x = UpVector[UpOffset + k+1] - 1; // left
            if ((k > UpK - D) && (UpVector[UpOffset + k-1] < x))
              x = UpVector[UpOffset + k-1]; // up
          } // if
          y = x - k;

          while ((x > LowerA) && (y > LowerB) && (DataA.data[x-1] == DataB.data[y-1])) {
            x--; y--; // diagonal
          }
          UpVector[UpOffset + k] = x;

          // overlap ?
          if (! oddDelta && (DownK-D <= k) && (k <= DownK+D)) {
            if (UpVector[UpOffset + k] <= DownVector[DownOffset + k]) {
              ret.x = DownVector[DownOffset + k];
              ret.y = DownVector[DownOffset + k] - k;
              // ret.u = UpVector[UpOffset + k];     // 2002.09.20: no need for 2 points 
              // ret.v = UpVector[UpOffset + k] - k;
              return (ret);
            } // if
          } // if

        } // for k

      } // for D

      throw new ApplicationException("the algorithm should never come here.");
    } // SMS


    /// <summary>
    /// This is the divide-and-conquer implementation of the longes common-subsequence (LCS) 
    /// algorithm.
    /// The published algorithm passes recursively parts of the A and B sequences.
    /// To avoid copying these arrays the lower and upper bounds are passed while the sequences stay constant.
    /// </summary>
    /// <param name="DataA">sequence A</param>
    /// <param name="LowerA">lower bound of the actual range in DataA</param>
    /// <param name="UpperA">upper bound of the actual range in DataA (exclusive)</param>
    /// <param name="DataB">sequence B</param>
    /// <param name="LowerB">lower bound of the actual range in DataB</param>
    /// <param name="UpperB">upper bound of the actual range in DataB (exclusive)</param>
    private static void LCS(DiffData DataA, int LowerA, int UpperA, DiffData DataB, int LowerB, int UpperB) {
      // Debug.Write(2, "LCS", String.Format("Analyse the box: A[{0}-{1}] to B[{2}-{3}]", LowerA, UpperA, LowerB, UpperB));

      // Fast walkthrough equal lines at the start
      while (LowerA < UpperA && LowerB < UpperB && DataA.data[LowerA] == DataB.data[LowerB]) {
        LowerA++; LowerB++;
      }

      // Fast walkthrough equal lines at the end
      while (LowerA < UpperA && LowerB < UpperB && DataA.data[UpperA-1] == DataB.data[UpperB-1]) {
        --UpperA; --UpperB;
      }
			
      if (LowerA == UpperA) {
        // mark as inserted lines.
        while (LowerB < UpperB)
          DataB.modified[LowerB++] = true;

      } else if (LowerB == UpperB) {
        // mark as deleted lines.
        while (LowerA < UpperA)
          DataA.modified[LowerA++] = true;

      } else {
        // Find the middle snakea and length of an optimal path for A and B
        SMSRD smsrd = SMS(DataA, LowerA, UpperA, DataB, LowerB, UpperB);
        // Debug.Write(2, "MiddleSnakeData", String.Format("{0},{1}", smsrd.x, smsrd.y));

        // The path is from LowerX to (x,y) and (x,y) ot UpperX
        LCS(DataA, LowerA, smsrd.x, DataB, LowerB, smsrd.y);
        LCS(DataA, smsrd.x, UpperA, DataB, smsrd.y, UpperB);  // 2002.09.20: no need for 2 points 
      }
    } // LCS()
		

    /// <summary>Scan the tables of which lines are inserted and deleted,
    /// producing an edit script in forward order.  
    /// </summary>
    /// dynamic array
    private static Item[] CreateDiffs(DiffData DataA, DiffData DataB) {
      ArrayList a = new ArrayList();
      Item aItem;
      Item []result;

      int StartA, StartB;
      int LineA, LineB;

      LineA = 0;
      LineB = 0;
      while (LineA < DataA.Length || LineB < DataB.Length) {
        if ((LineA < DataA.Length) && (! DataA.modified[LineA])
          && (LineB < DataB.Length) && (! DataB.modified[LineB])) {
          // equal lines
          LineA++; 
          LineB++;

        } else {
          // maybe deleted and/or inserted lines
          StartA = LineA;
          StartB = LineB;
  					
          while (LineA < DataA.Length && (LineB >= DataB.Length || DataA.modified[LineA]))
            // while (LineA < DataA.Length && DataA.modified[LineA])
            LineA++;

          while (LineB < DataB.Length && (LineA >= DataA.Length || DataB.modified[LineB]))
            // while (LineB < DataB.Length && DataB.modified[LineB])
            LineB++;

          if ((StartA < LineA) || (StartB < LineB)) {
            // store a new difference-item
            aItem = new Item();
            aItem.StartA = StartA;
            aItem.StartB = StartB;
            aItem.deletedA = LineA - StartA;
            aItem.insertedB = LineB - StartB;
            a.Add(aItem);
          } // if
        } // if
      } // while

      result = new Item[a.Count];
      a.CopyTo(result);

      return (result);
    }

  } // class Diff

  /// <summary>Data on one input file being compared.  
  /// </summary>
  internal class DiffData {

    /// <summary>Number of elements (lines).</summary>
    internal int Length;
			
    /// <summary>Buffer of numbers that will be compared.</summary>
    internal int[] data;

    /// <summary>
    /// Array of booleans that flag for modified data.
    /// This is the result of the diff.
    /// This means deletedA in the first Data or inserted in the second Data.
    /// </summary>
    internal bool[] modified;

    /// <summary>
    /// Initialize the Diff-Data buffer.
    /// </summary>
    /// <param name="data">reference to the buffer</param>
    internal DiffData(int[] initData) {
      data = initData;
      Length = initData.Length;
      modified = new bool[Length + 2];
    } // DiffData
		
  } // class DiffData

} // namespace

会继续再试，有新进展会贴上来 ^_^