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

  1 #include <iostream>
  2 #include <queue>
  3 #include <climits>
  4 #include <algorithm>
  5 #include <memory.h>
  6 #include <stdio.h>
  7 using namespace std;
  8 
  9 
 10 int calSim_1(string s1,int b1,int e1,string s2,int b2,int e2)
 11 {
 12     if(b1 > e1)
 13     {
 14         if(b2 > e2)
 15         {
 16             return 0;
 17         }
 18         return e2 - b2 + 1;
 19     }
 20     if(b2 > e2)
 21     {
 22         if(b1 > e1)
 23         {
 24             return 0;
 25         }
 26         return e1 - b1 + 1;
 27     }
 28     if(s1[b1] == s2[b2])
 29     {
 30         return calSim_1(s1,b1+1,e1,s2,b2+1,e2);
 31     }
 32     else
 33     {
 34         int len1 = calSim_1(s1,b1,e1,s2,b2+1,e2);
 35         int len2 = calSim_1(s1,b1+1,e1,s2,b2,e2);
 36         int len3 = calSim_1(s1,b1+1,e1,s2,b2+1,e2);
 37 
 38         len1 = min(len1,len2);
 39         len1 = min(len1,len3);
 40         return len1+1;
 41     }
 42 }
 43 
 44 //递归+备忘录版本（DP）
 45 int opt[100][100];
 46 int calSim_2(string s1,int b1,int e1,string s2,int b2,int e2)
 47 {
 48     if(b1 > e1)
 49     {
 50         if(b2 > e2)
 51         {
 52             return 0;
 53         }
 54         return e2 - b2 + 1;
 55     }
 56     if(b2 > e2)
 57     {
 58         if(b1 > e1)
 59         {
 60             return 0;
 61         }
 62         return e1 - b1 + 1;
 63     }
 64     if(s1[b1] == s2[b2])
 65     {
 66         if(opt[b1+1][b2+1] == -1)
 67         {
 68             opt[b1+1][b2+1] = calSim_2(s1,b1+1,e1,s2,b2+1,e2);
 69         }
 70         return opt[b1+1][b2+1];
 71     }
 72     else
 73     {
 74         if(opt[b1][b2+1] == -1)
 75         {
 76             opt[b1][b2+1] = calSim_2(s1,b1,e1,s2,b2+1,e2);
 77         }
 78         int len1 = opt[b1][b2+1];
 79         if(opt[b1+1][b2] == -1)
 80         {
 81             opt[b1+1][b2] = calSim_2(s1,b1+1,e1,s2,b2,e2);
 82         }
 83         int len2 = opt[b1+1][b2];
 84         if(opt[b1+1][b2+1] == -1)
 85         {
 86             opt[b1+1][b2+1] = calSim_2(s1,b1+1,e1,s2,b2+1,e2);
 87         }
 88         int len3 = opt[b1+1][b2+1];
 89 
 90         len1 = min(len1,len2);
 91         len1 = min(len1,len3);
 92         return len1+1;
 93     }
 94 }
 95 
 96 //DP+非备忘录版本
 97 int dp[100][100];
 98 int calSim_3(string s1,string s2)
 99 {
100     int len1 = s1.length();
101     int len2 = s2.length();
102     int i,j;
103     for(i = 0 ; i <= s1.length() ; ++i)
104     {
105         dp[i][0] = i;
106     }
107     for(j = 0 ; j <= s2.length() ; ++j)
108     {
109         dp[0][j] = j;
110     }
111     for(i = 1 ; i <= s1.length() ; ++i)
112     {
113         for(j = 1 ; j <= s2.length() ; ++j)
114         {
115             if(s1[i-1] == s2[j-1])
116             {
117                 dp[i][j] = dp[i-1][j-1];
118             }
119             else
120             {
121                 dp[i][j] = dp[i-1][j] + 1;
122                 dp[i][j] = min(dp[i][j],dp[i][j-1]+1);
123                 dp[i][j] = min(dp[i][j],dp[i-1][j-1]+1);
124             }
125         }
126     }
127     return dp[s1.length()][s2.length()];
128 }
129 
130 int main()
131 {
132     memset(opt,-1,sizeof(opt));
133     string s1("abc");
134     string s2("ab");
135     cout<<calSim_3(s1,s2);
136     return 0;
137 }

 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~~