编程之美--3.3

题目描述：计算相似度，其实本质就是计算编辑距离

思路：一开始先递归，然后加备忘改DP，发现有很多重复子问题，再重新设计dp算法

#include <iostream>
#include <queue>
#include <climits>
#include <algorithm>
#include <memory.h>
#include <stdio.h>
using namespace std;


int calSim_1(string s1,int b1,int e1,string s2,int b2,int e2)
{
    if(b1 > e1)
    {
        if(b2 > e2)
        {
            return 0;
        }
        return e2 - b2 + 1;
    }
    if(b2 > e2)
    {
        if(b1 > e1)
        {
            return 0;
        }
        return e1 - b1 + 1;
    }
    if(s1[b1] == s2[b2])
    {
        return calSim_1(s1,b1+1,e1,s2,b2+1,e2);
    }
    else
    {
        int len1 = calSim_1(s1,b1,e1,s2,b2+1,e2);
        int len2 = calSim_1(s1,b1+1,e1,s2,b2,e2);
        int len3 = calSim_1(s1,b1+1,e1,s2,b2+1,e2);

        len1 = min(len1,len2);
        len1 = min(len1,len3);
        return len1+1;
    }
}

//递归+备忘录版本（DP）
int opt[100][100];
int calSim_2(string s1,int b1,int e1,string s2,int b2,int e2)
{
    if(b1 > e1)
    {
        if(b2 > e2)
        {
            return 0;
        }
        return e2 - b2 + 1;
    }
    if(b2 > e2)
    {
        if(b1 > e1)
        {
            return 0;
        }
        return e1 - b1 + 1;
    }
    if(s1[b1] == s2[b2])
    {
        if(opt[b1+1][b2+1] == -1)
        {
            opt[b1+1][b2+1] = calSim_2(s1,b1+1,e1,s2,b2+1,e2);
        }
        return opt[b1+1][b2+1];
    }
    else
    {
        if(opt[b1][b2+1] == -1)
        {
            opt[b1][b2+1] = calSim_2(s1,b1,e1,s2,b2+1,e2);
        }
        int len1 = opt[b1][b2+1];
        if(opt[b1+1][b2] == -1)
        {
            opt[b1+1][b2] = calSim_2(s1,b1+1,e1,s2,b2,e2);
        }
        int len2 = opt[b1+1][b2];
        if(opt[b1+1][b2+1] == -1)
        {
            opt[b1+1][b2+1] = calSim_2(s1,b1+1,e1,s2,b2+1,e2);
        }
        int len3 = opt[b1+1][b2+1];

        len1 = min(len1,len2);
        len1 = min(len1,len3);
        return len1+1;
    }
}

//DP+非备忘录版本
int dp[100][100];
int calSim_3(string s1,string s2)
{
    int len1 = s1.length();
    int len2 = s2.length();
    int i,j;
    for(i = 0 ; i <= s1.length() ; ++i)
    {
        dp[i][0] = i;
    }
    for(j = 0 ; j <= s2.length() ; ++j)
    {
        dp[0][j] = j;
    }
    for(i = 1 ; i <= s1.length() ; ++i)
    {
        for(j = 1 ; j <= s2.length() ; ++j)
        {
            if(s1[i-1] == s2[j-1])
            {
                dp[i][j] = dp[i-1][j-1];
            }
            else
            {
                dp[i][j] = dp[i-1][j] + 1;
                dp[i][j] = min(dp[i][j],dp[i][j-1]+1);
                dp[i][j] = min(dp[i][j],dp[i-1][j-1]+1);
            }
        }
    }
    return dp[s1.length()][s2.length()];
}

int main()
{
    memset(opt,-1,sizeof(opt));
    string s1("abc");
    string s2("ab");
    cout<<calSim_3(s1,s2);
    return 0;
}

 我的代码里没有加边界情况检查，这一点很重要，不要向我学习，O(∩_∩)O~~