动态规划二：最长公共子序列（LCS）

 1 #include<string>
 2 #include<iostream>
 3 using namespace std;
 4 
 5 int arr[20][20] = {};
 6 void LCS(string str1, string str2){
 7     int len1 = str1.length();
 8     int len2 = str2.length();
 9     //边界
10     for (int i = 0; i <= len1; i++)
11         arr[i][0] = 0;
12     for (int j = 0; j <= len2; j++)
13         arr[0][j] = 0;
14     //检验
15     for (int i = 1; i <= len1; i++)
16     {
17         for (int j = 1; j <= len2; j++)
18         {
19             if (str1[i - 1] == str2[j - 1]) //记录
20             {
21                 arr[i][j] = arr[i - 1][j - 1] + 1;
22             }
23             else if (arr[i][j - 1] >= arr[i - 1][j])
24             {
25                 arr[i][j] = arr[i][j - 1];
26             }
27             else 
28             {
29                 arr[i][j] = arr[i - 1][j];
30             }
31         }
32     }
33 }
34 
35 void printLCS(string str1, string str2,int len1, int len2){
36     cout << "最长公共子序列长为：" << arr[len1][len2] << endl;
37     //倒序输出
38     while (len1&&len2){
39         if (str1[len1-1]==str2[len2-1])
40         {
41             cout << str1[len1 - 1];
42             len1--;
43             len2--;
44         }
45         else if (arr[len1][len2-1]>=arr[len1-1][len2])
46         {
47             len2--;
48         }
49         else{
50             len1--;
51         }
52     }
53     cout << endl;
54 }
55 
56 int main()
57 {
58     string str1 = "abcdsnnnn";
59     string str2 = "acbdanm";
60     LCS(str1, str2);
61     printLCS(str1, str2,str1.length(), str2.length());
62     return 0;
63 }