字符串编辑距离

这篇文章是在新浪博客上写的，现搬过来，算是第一篇吧~

题目如下，最后给出实现代码，该代码仍在测试中，仅供学习交流！

编写一个程序计算两个字符串的编辑距离。编辑距离的定义和计算方法如下：

Given two strings A and B, edit A to B with the minimum number of edit operations:

a) .Replace a letter with another letter

b) .Insert a letter

c) .Delete a letter

E.g.

A = interestingly _i__nterestingly

B = bioinformatics bioinformatics__

1011011011001111

Edit distance = 11

Instead of minimizing the number of edge operations, we can associate a cost function to the
operations and minimize the total cost. Such cost is called edit distance. Instead of using string edit, in computational biology, people like to use string alignment.We use similarity function, instead of cost function, to evaluate the goodness
of the alignment.

E.g. of similarity function: match – 2, mismatch, insert, delete – -1.

Consider two strings ACAATCC and AGCATGC.

One of their alignment is



In the above alignment, space (‘_’) is introduced to both strings. There are 5 matches, 1
mismatch, 1 insert, and 1 delete.The alignment has similarity score 7.

A_CAATCC

AGCA_TGC

Note that the above alignment has the maximum score.Such alignment is called optimal
alignment.String alignment problem tries to find the alignment with the maximum similarity
score!String alignment problem is also called global alignment problem.

Needleman-Wunsch algorithm

Consider two strings S[1..n] and T[1..m].Define V(i, j) be the score of the optimal alignment
between S[1..i] and T[1..j].

Basis:

V(0, 0) = 0

V(0, j) = V(0, j-1) + d(_, T[j])：Insert j times

V(i, 0) = V(i-1, 0) + d(S[i], _)：Delete i times

that is:



Example (I):





实现代码如下：
头文件StrEditDistance.h

#pragma once
#include <string>

class CStrEditDistance
{
public:
	CStrEditDistance(std::string& vStrRow, std::string& vStrColumn);
	~CStrEditDistance(void);

	int  getScore()				{ return m_Score;   }
	int  getEditDis()			{ return m_EditDis; }
	void setEditDis(int vDis)	{ m_EditDis = vDis; }
	void setScore(int vScore)	{ m_Score = vScore; }
private:
	void process(const std::string& vStrRow, const std::string& vStrColumn);
	int getMaxValue(int a, int b, int c)
	{
		if (a < b){ if (b < c) return c; return b; }
		else { if (b > c) return a; return a < c ? c : a; }
	}
private:
	int			m_EditDis;
	int			m_Score;
};

源文件StrEditDistance.cpp

#include "StrEditDistance.h"
#include <iostream>
#include <iomanip>

#define MATCH		2
#define MISS_MATCH	-1
#define INSERT		-1
#define DELETE		-1

CStrEditDistance::CStrEditDistance(std::string& vStrRow, std::string& vStrColumn)
{
	process(vStrRow, vStrColumn);
}

CStrEditDistance::~CStrEditDistance(void)
{
}

/***********************************************************************/
//FUNCTION:
void CStrEditDistance::process(const std::string& vStrRow, const std::string& vStrColumn)
{
	int editDis = 0;					//编辑距离
	int row = vStrColumn.length();		
	int column = vStrRow.length();
	const int sizeR = row + 1;
	const int sizeC = column + 1;

	int **pScore = new int*[sizeR];		//二维指针
	for (int i = 0; i <= row; i++)
		pScore[i] = new int[sizeC];

	//初始化第一行和第一列
	for (int c = 0; c <= column; c++)
		pScore[0][c] = 0 - c;
	for (int r = 0; r <= row; r++)
		pScore[r][0] = 0 - r;

	//从v(1,1)开始每列计算
	for (int c = 1; c <= column; c++)
	{
		for (int r = 1; r <= row; r++)
		{
			//计算v(i,j), 其值等于A:v(i-1,j)+insert、B:v(i,j-1)+delet e、C:v(i-1,j-1)+@(i,j)中的最大的一个 
			int valueMatch;
			if (vStrColumn[r-1] == vStrRow[c-1])
 				valueMatch = MATCH;
			else
				valueMatch = MISS_MATCH;   
			int A = pScore[r-1][c] + INSERT;
			int B = pScore[r][c-1] + DELETE;
			int C = pScore[r-1][c-1] + valueMatch;
			pScore[r][c] = getMaxValue(A, B, C);
		}
	}

	//计算编辑距离
	int r = row, c = column;
	while(r > 0 && c > 0)
	{
		if (pScore[r][c]+1 == pScore[r-1][c])	    { editDis++; r--; continue; }
		else if (pScore[r][c]+1 == pScore[r][c-1])  { editDis++; c--; continue; }
		else if (pScore[r][c]+1 == pScore[r-1][c-1]){ editDis++; r--; c--; continue; }
		else { r--; c--; }
	}
	if (r > 0 && c == 0)		editDis += r;
	else if (c > 0 && r == 0)	editDis += c;

	std::cout << std::endl;
	//----------------DEBUG-------------------//
	//打印中间数据
 	for (int i = 0; i <= row; i++)
 	{
 		for (int j = 0; j <= column; j++)
			std::cout << std::setw(2) << pScore[i][j] << "  ";
	    std::cout << std::endl;
 	}
	std::cout << std::endl;

	//设置编辑距离和得分
	setEditDis(editDis);
	setScore(pScore[row][column]);

	for (int i = 0; i <= row; i++)			//释放内存
	{
		delete pScore[i];
		pScore[i] = NULL;
	}
	delete[] pScore;
}

main.cpp文件如下：

#include "StrEditDistance.h"
#include <iostream>

#define MAX_SIZE	100

int main(int, char **)
{
	char sRow[MAX_SIZE];
	char sColumn[MAX_SIZE];

	std::cout << "input row string : ";
	std::cin.getline(sRow, MAX_SIZE);
	std::cout << "input column str : ";
	std::cin.getline(sColumn, MAX_SIZE);
 
	std::string strRow(sRow), strColumn(sColumn);
  	CStrEditDistance *pStrEdit = new CStrEditDistance(strRow, strColumn);
	std::cout << "The score is : " << pStrEdit->getScore() << std::endl;
	std::cout << "The edit distance is : " << pStrEdit->getEditDis() << std::endl;
  	delete pStrEdit;

	system("pause");
	return 0;
}