编辑距离算法

编辑距离算法底聪2010030020006编辑距离算法，即Levenshtein Distance （LD）算法。

这个算法其实是一个动态规划（DP）。

levenshtein() 返回两个字符串之间的Levenshtein 距离。

Levenshtein 距离，又称编辑距离，指的是两个字符串之间，由一个转换成另一个所需的最少编辑操作次数。

许可的编辑操作包括将一个字符替换成另一个字符，插入一个字符，删除一个字符。

例如把kitten 转换为sitting：sitten （k→s）sittin （e→i）sitting （→g）levenshtein() 函数给每个操作（替换、插入和删除）相同的权重。

不过，您可以通过设置可选的insert、replace、delete 参数，来定义每个操作的代价。

PHP String 函数，下面是C语言实现.代码Here is the definition of the class (distance.h):class Distance{public:int LD (char const *s, char const *t);private:int Minimum (int a, int b, int c);int *GetCellPointer (int *pOrigin, int col, int row, int nCols);int GetAt (int *pOrigin, int col, int row, int nCols);void PutAt (int *pOrigin, int col, int row, int nCols, int x);};Here is the implementation of the class (distance.cpp):#include "distance.h"#include <string.h>#include <malloc.h>//****************************// Get minimum of three values//****************************int Distance::Minimum (int a, int b, int c){int mi;mi = a;if (b < mi) {mi = b;}if (c < mi) {mi = c;}return mi;}//**************************************************// Get a pointer to the specified cell of the matrix//**************************************************int *Distance::GetCellPointer (int *pOrigin, int col, int row, int nCols) {return pOrigin + col + (row * (nCols + 1));}//*****************************************************// Get the contents of the specified cell in the matrix//*****************************************************int Distance::GetAt (int *pOrigin, int col, int row, int nCols){int *pCell;pCell = GetCellPointer (pOrigin, col, row, nCols);return *pCell;}//*******************************************************// Fill the specified cell in the matrix with the value x//*******************************************************void Distance::putAt (int *pOrigin, int col, int row, int nCols, int x) {int *pCell;pCell = GetCellPointer (pOrigin, col, row, nCols);*pCell = x;}//*****************************// Compute Levenshtein distance//*****************************int Distance::LD (char const *s, char const *t){int *d; // pointer to matrixint n; // length of sint m; // length of tint i; // iterates through sint j; // iterates through tchar s_i; // ith character of schar t_j; // jth character of tint cost; // costint result; // resultint cell; // contents of target cellint above; // contents of cell immediately aboveint left; // contents of cell immediately to leftint diag; // contents of cell immediately above and to leftint sz; // number of cells in matrix// Step 1n = strlen (s);m = strlen (t);if (n == 0) {return m;}if (m == 0) {return n;}sz = (n+1) * (m+1) * sizeof (int);d = (int *) malloc (sz);// Step 2for (i = 0; i <= n; i++) {PutAt (d, i, 0, n, i);}for (j = 0; j <= m; j++) {PutAt (d, 0, j, n, j);}// Step 3for (i = 1; i <= n; i++) {s_i = s[i-1];// Step 4for (j = 1; j <= m; j++) {t_j = t[j-1];// Step 5if (s_i == t_j) {cost = 0;}else {cost = 1;}// Step 6above = GetAt (d,i-1,j, n);left = GetAt (d,i, j-1, n);diag = GetAt (d, i-1,j-1, n);cell = Minimum (above + 1, left + 1, diag + cost);PutAt (d, i, j, n, cell);}}// Step 7result = GetAt (d, n, m, n);free (d);return result;}这个是自己尝试着写了下：#include "stdio.h"#include "malloc.h"#include "string.h"#define MAX(a,b) ((a)>(b)?(a):(b))void matrix_print(char *matrix, int row, int col){int i, j;for(i=0; i<row; i++){for(j=0; j<col; j++){printf("%4.2d", matrix[i*col+j]); } printf("\n");}}char matrix_value(char left, char top, char top_left, int cost) {char ret;ret = left<top?left:top;return ret<top_left?ret+1:top_left+(char)cost;}void main(){char *matrix;char str1[255], str2[255];int row, col;int i, j;int dis;double sim;printf("please input str1: ");scanf("%s", str1);printf("please input str2: ");scanf("%s", str2);//// 矩阵要比行列各多一来存储矩阵行列序号//row = strlen(str1) + 1;col = strlen(str2) + 1;//// 申请空间//matrix = (char*) malloc(col*row);//// 初始化首行、首列//for(i=0; i<row; i++) matrix[i*col] = i;for(j=0; j<col; j++) matrix[j] = j;//// 根据算法填充矩阵//// 当字符相同时cost=0, 否则cost=1. 也就是代码中的 !(str1[i-1]==str2[j-1])//// 取待填值(val)位置的3个邻居left,top,top-left的值来进行比较，取最小值(min)。

// 当 left或top 为最小值时, val=min+1.// 当 top-left 为最小值时, val=min+cost.//for(i=1; i<row; i++){for(j=1; j<col; j++) matrix[i*col+j] = matrix_value(matrix[i*col+j-1], matrix[(i-1)*col+j], matrix[(i-1)*col+j-1], !(str1[i-1]==str2[j-1]));}//// 打印矩阵//matrix_print(matrix, row, col);//// 矩阵最后的格子就是“编辑距离”//dis = matrix[(row*col - 1];printf("distance = %d\n", dis);//// 小应用。