动态规划之LCS(最大公共子序列)

#include <stdio.h>
#include <string.h>

int b[50][50];
int c[50][50];
int length = 0;

void lcs(char *x, int m, char *y, int n)
{
    int i;
    int j;

    for(i = 1; i <= m; i++)
        c[i][0] = 0;

    for(i = 1; i <= n; i++)
        c[0][i] = 0;

    for(i = 1; i <= m; i++)
    {
        for(j = 1; j <= n; j++)
        {
            if(x[i-1] == y[j-1])
            {
                c[i][j] = c[i-1][j-1] + 1;
                b[i][j] = 1;
            }
            else if(c[i-1][j] > c[i][j-1])
            {
                c[i][j] = c[i-1][j];
                b[i][j] = 2;
            }
            else
            {
                c[i][j] = c[i][j-1];
                b[i][j] = 3;
            }
        }
    }
}

void show(int i, int j, char *x)
{
    if(i == 0 || j ==0)
        return;

    if(b[i][j] == 1)
    {
        show(i-1, j-1, x);
        length++;
        printf("%c", x[i-1]);
    }
    else if(b[i][j] == 2)
    {
        show(i-1, j, x);
    }
    else
    {
        show(i, j-1, x);
    }
}

int main()
{
    char *x = "xyzrfdt";
    char *y = "xzhrgfiut";   //xzrft

    int m = strlen(x);
    int n = strlen(y);
    lcs(x,m,y,n);

    printf("The string is: \n");
    show(m, n, x);
}

 #include <iostream>
 #include <string>
    using namespace std;
    int main(int argc, char **argv)
    {
        string str1 = "ABCBDAB";
        string str2 = "BDCABA";

        int x_len = str1.length();
       int y_len = str2.length();

       int arr[][] = {{,}};

       int i = ;
       int j = ;

       for(i = ; i <= x_len; i++)
       {
           for(j = ; j <= y_len; j++)
           {
               if(str1[i - ] == str2[j - ])
               {
                  arr[i][j] = arr[i - ][j - ] + ;
               }
               else
              {

                   if(arr[i][j - ] >= arr[i - ][j])
                   {
                       arr[i][j] = arr[i][j - ];
                   }
                   else
                   {
                       arr[i][j] = arr[i -][j];
                   }
               }

           }
       }
      for(i =  ; i <= x_len; i++)
      {
          for( j = ; j <= y_len; j++)
          {
              cout << arr[i][j] << "  ";
          }
          cout << endl;
      }
      for(i = x_len, j = y_len; i >=  && j >= ;)
      {
              if(str1[i - ] == str2[j - ])
              {
                  cout << str1[i - ] << " ";//倒序打印的
                  i--;
                  j--;
              }
              else
              {
              //  if(arr[i][j -1] >= arr[i - 1][j])//打印：B A D B
                  if(arr[i][j -] > arr[i - ][j]) //打印:A B C B
                  {
                      j--;
                  }
                  else
                  {
                      i--;
                  }
              }
      }
      cout << endl;
      return ;
  }

C++

运行结果：