最长公共子序列（LCS）

1  LCS(x,y,i,j)  
2      if x[i] = y[j]  
3          then C[i,j] ← LCS(x,y,i-1,j-1)+1  
4      else C[i,j] ← max{LCS(x,y,i-1,j),LCS(x,y,i,j-1)}  
5    return C[i,j]

 1 public class LCS {
 2     public static int[][] vals ;
 3 
 4     public static int getLCS(String str1,String str2){
 5         int len1 = str1.length();
 6         int len2 = str2.length();
 7 
 8         vals = new int[len1+1][len2+1];
 9 
10         for(int i=0;i<len1;i++){
11             // 二维数组从[1][1]开始进行有效存储
12             int fi = i+1;
13             for(int j=0;j<len2;j++){
14                 int fj = j+1;
15                 //字符相同
16                 if(str1.charAt(i) == str2.charAt(j)){
17                     // 满足第一种状况
18                     vals[fi][fj] = vals[fi-1][fj-1] + 1;
19                     //字符不相同
20                 }else if(str1.charAt(i) != str2.charAt(j)){
21                     //满足第二种状况
22                     vals[fi][fj] = Math.max(vals[fi-1][fj],vals[fi][fj-1]);
23                 }
24             }
25         }
26 
27         for(int i=0;i<len1;i++){
28             System.out.println(Arrays.toString(vals[i]));
29         }
30 
31         return vals[len1][len2];
32     }
34     public static void main(String[] args) {
36         String str1 = "ABCBDAB";
37         String str2 = "BDCABA";
38         System.out.println(getLCS(str1,str2));
41     }
42 }

[0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1]
[0, 1, 1, 1, 1, 2, 2]
[0, 1, 1, 2, 2, 2, 2]
[0, 1, 1, 2, 2, 3, 3]
[0, 1, 2, 2, 2, 3, 3]
[0, 1, 2, 2, 3, 3, 4]
4