两个字符串的编辑距离

参考网上的实现

// 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
",calEditDist(str1,0,strlen(str1)-1,str3,0,strlen(str3)-1));
    printf("%d
",calEditDist_opt(str1,0,strlen(str1)-1,str3,0,strlen(str3)-1));
    printf("%d
",calEditDist_opt_two(str1,0,strlen(str1)-1,str3,0,strlen(str3)-1));
    return 0;
}