LCS最长公共子序列

  1#include <iostream>                                                                                                               
  2 using namespace std;
  3 
  4 void ProduceLcs(int m, int n, string **b, const string &str1)
  5 {
  6     if(m == 0 || n == 0)
  7         return;
  8     if(b[m][n] == "lefttop")
  9     {
 10         ProduceLcs(m - 1, n - 1, b, str1);
 11         cout << str1[m - 1];//注意打印的是str的第二位，所以要减1，因为m对应的是矩阵的行
 12     }else if(b[m][n] == "left")
 13     {
 14             ProduceLcs(m, n - 1, b, str1);
 15     }else
 16     {
 17             ProduceLcs(m - 1, n, b ,str1);
 18     }
 19     return;
 20 }
 21 
 22 
 23 int LcsLength(string str1, string str2)
 24 {
 25     int m = str1.size() + 1;
 26     int n = str2.size() + 1;
 27     int c[m][n];
 28     //方向数组
 29     string **b = new string *[m];
 30     for(int i = 0; i < m; ++i)
 31     {
 32         b[i] = new string[n];
 33     }
 34     for(int i = 0; i < m; ++i)
 35     {
 36         c[i][0] = 0;
 37     }
 38     for(int i = 0; i < n; ++i)
 39     {
 40         c[0][i] = 0;
 41     }
 42     for(int i = 1; i < m; ++i)
 43     {
 44         for(int j = 1; j < n; ++j)
 45         {
 46             if(str1[i - 1] == str2[j -1])
 47             {
 48                 c[i][j] = c[i - 1][j - 1] + 1;
 49                 b[i][j] = "lefttop"; //左上
 50             }else if(c[i - 1][j] >= c[i][j -1])
 51             {
 52                 c[i][j] = c[i - 1][j];
 53                 b[i][j] = "top"; //上
 54             }else
 55             {
 56                 c[i][j] = c[i][j - 1];
 57                 b[i][j] = "left"; //左
 58             }
 59         }
 60     }
 61     int len = 0;
 62     for(int i = 0; i < m; ++i)
 63     {
 64         for(int j = 0; j < n; ++j)
 65         {
 66             if(c[i][j] > len)
 67             {
 68                 len = c[i][j];
 69             }
 70         }
 71     }
 72     ProduceLcs(m-1, n-1, b, str1);
 73     cout << endl;
 74     return len;
 75 }
 76 
 77 int main(int argc, const char *argv[])
 78 {
 79     string str1 = "ABCBDAB";
 80     string str2 = "BDCABA";
 81     int max = LcsLength(str1, str2);
 82     cout << max << endl;
 83     return 0;
 84 }                                

代码如上，注意在回溯求路径时候，打印的是对应的string里的字符，注意下标要减1。