两个字符串的编辑距离

// project1.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include<string.h>

#define LENGTH 100

//两个字符串的编辑距离
//编辑距离就是将两个字符串变成相同字符串所需要的最小操作次数
//纯暴力搜索法，复杂度O(N*M)
int calEditDist(char strX[],int begX,int endX,char *strY,int begY,int endY){
if(endX==0){
if(endY==0)
return 0;
else return endY-begY+1;
}
if(endY==0){
if(endX==0)
return 0;
else return endX-begX+1;
}

if(strX[endX]==strY[endY])
return calEditDist(strX,begX,endX-1,strY,begY,endY-1);
else{
int t1 = calEditDist(strX,begX,endX-1,strY,begY,endY);
int t2 = calEditDist(strX,begX,endX,strY,begY,endY-1);
int t3 = calEditDist(strX,begX,endX-1,strY,begY,endY-1);
t1 = t1 < t2 ? t1 : t2;
return (t1 < t3 ? t1 : t3) + 1;
}
}

//针对暴力方法的改进，利用空间换时间
//依然自顶向下
int dp[LENGTH][LENGTH];//备忘数组,注意要放在函数外
int calEditDist_opt(char strX[],int begX,int endX,char *strY,int begY,int endY){
if(endX == 0){
if(endY == 0)
return 0;
else
return endY - begY + 1;
}
if(endY == 0){
if(endX == 0)
return 0;
else
return endX - begX + 1;
}
if(strX[endX] == strY[endY]){
if(dp[endX-1][endY-1] == 0)
dp[endX-1][endY-1] = calEditDist_opt(strX,begX,endX-1,strY,begY,endY-1);
return dp[endX-1][endY-1];
}
else{
int t1, t2, t3;
if(dp[endX-1][endY] == 0)
dp[endX-1][endY] = calEditDist_opt(strX,begX,endX-1,strY,begY,endY);
t1 = dp[endX-1][endY];

if(dp[endX][endY-1] == 0)
dp[endX][endY-1] = calEditDist_opt(strX,begX,endX,strY,begY,endY-1);
t2 = dp[endX][endY-1];

if(dp[endX-1][endY-1] == 0)
dp[endX-1][endY-1] =calEditDist_opt(strX,begX,endX-1,strY,begY,endY-1);
t3 = dp[endX-1][endY-1];

t1 = t1 < t2 ? t1 : t2;
return (t1 < t3 ? t1 : t3) + 1;
}
}

//方法3，自底向上
int dp2[LENGTH][LENGTH];//表示strX[0..i]与strY[0..j]的编辑距离
int calEditDist_opt_two(char strX[],int begX,int endX,char *strY,int begY,int endY)
{
int i, j;
for(i = begX; i <= endX; ++i)
dp2[i][0] = i+1;
for(j = begY; j <= endY; ++j)
dp2[0][j] = j+1;
for(i = begX+1; i <= endX; ++i){
for(j = begY+1; j <= endY; ++j){
if(strX[i] == strY[j])
dp2[i][j] = dp2[i-1][j-1];
else{
int t1 = dp2[i-1][j];
t1 = t1 < dp2[i][j-1] ? t1 :dp2[i][j-1];
t1 = t1 < dp2[i-1][j-1] ? t1 : dp2[i-1][j-1];
dp2[i][j] = t1 + 1;
}
}
}
return dp2[endX][endY];
}

int _tmain(int argc, _TCHAR* argv[])
{
char str1[LENGTH]="abbaeaabccbaeeaee";
char str2[LENGTH]="aaaaaaaaa";
char str3[LENGTH]="abababababab";
printf("%d\n",calEditDist(str1,0,strlen(str1)-1,str3,0,strlen(str3)-1));
printf("%d\n",calEditDist_opt(str1,0,strlen(str1)-1,str3,0,strlen(str3)-1));
printf("%d\n",calEditDist_opt_two(str1,0,strlen(str1)-1,str3,0,strlen(str3)-1));
return 0;
}