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: 
");
    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[50][50] = {{0,0}};

      int i = 0;
      int j = 0;

      for(i = 1; i <= x_len; i++)
      {
          for(j = 1; j <= y_len; j++)
          {
              if(str1[i - 1] == str2[j - 1])
              {
                 arr[i][j] = arr[i - 1][j - 1] + 1;
              }
              else
             {

                  if(arr[i][j - 1] >= arr[i - 1][j])
                  {
                      arr[i][j] = arr[i][j - 1];
                  }
                  else
                  {
                      arr[i][j] = arr[i -1][j];
                  }
              }

          }
      }
     for(i = 0 ; i <= x_len; i++)
     {
         for( j = 0; j <= y_len; j++)
         {
             cout << arr[i][j] << "  ";
         }
         cout << endl;
     }
     for(i = x_len, j = y_len; i >= 1 && j >= 1;)
     {
             if(str1[i - 1] == str2[j - 1])
             {
                 cout << str1[i - 1] << " ";//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 -1] > arr[i - 1][j]) //打印:A B C B
                 {
                     j--;
                 }
                 else
                 {
                     i--;
                 }
             }
     }
     cout << endl;
     return 0;
 }

运行结果：