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);
}

 1 #include <iostream>
 2 #include <string>
 3    using namespace std;
 4    int main(int argc, char **argv)
 5    {
 6        string str1 = "ABCBDAB";
 7        string str2 = "BDCABA";
 8 
 9        int x_len = str1.length();
10       int y_len = str2.length();
11 
12       int arr[50][50] = {{0,0}};
13 
14       int i = 0;
15       int j = 0;
16 
17       for(i = 1; i <= x_len; i++)
18       {
19           for(j = 1; j <= y_len; j++)
20           {
21               if(str1[i - 1] == str2[j - 1])
22               {
23                  arr[i][j] = arr[i - 1][j - 1] + 1;
24               }
25               else
26              {
27 
28                   if(arr[i][j - 1] >= arr[i - 1][j])
29                   {
30                       arr[i][j] = arr[i][j - 1];
31                   }
32                   else
33                   {
34                       arr[i][j] = arr[i -1][j];
35                   }
36               }
37 
38           }
39       }
40      for(i = 0 ; i <= x_len; i++)
41      {
42          for( j = 0; j <= y_len; j++)
43          {
44              cout << arr[i][j] << "  ";
45          }
46          cout << endl;
47      }
48      for(i = x_len, j = y_len; i >= 1 && j >= 1;)
49      {
50              if(str1[i - 1] == str2[j - 1])
51              {
52                  cout << str1[i - 1] << " ";//倒序打印的
53                  i--;
54                  j--;
55              }
56              else
57              {
58              //  if(arr[i][j -1] >= arr[i - 1][j])//打印：B A D B
59                  if(arr[i][j -1] > arr[i - 1][j]) //打印:A B C B
60                  {
61                      j--;
62                  }
63                  else
64                  {
65                      i--;
66                  }
67              }
68      }
69      cout << endl;
70      return 0;
71  }

C++

动态规划之LCS(最大公共子序列)

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