动态规划——最长公共子序列（LCS）

/**
* @brief longest common subsequence(LCS)
* @author An
* @data  2013.8.26
**/

#include <iostream>
#include <string>
using namespace std;

enum Direction { Zero, LeftUp, Up, Left };
static int m;    // length of the first sequence
static int n;     // length of the second sequence
static int **c;  // the length for every subsequence
static Direction **b;  // record the path

void LCS_Length( string x, string y );
void Print_LCS( string x, int i, int j );
void PrintTable();

int main()
{
string x = "ABCBDAB";
string y = "BDCABA";
LCS_Length( x, y );
Print_LCS( x, m, n );
cout << endl;
PrintTable();
}

void LCS_Length( string x, string y )
{
// initialize two tables
m = x.length();
n = y.length();
c = new int*[m + 1];
b = new Direction*[m + 1];
for ( int i = 0; i <= m; ++i )
{
c[i] = new int[n + 1];
b[i] = new Direction[n + 1];
}

// zero row and column
for ( int i = 0; i <= m; ++i )
{
c[i][0] = 0;
b[i][0] = Zero;
}
for ( int j = 1; j <= n; ++j )
{
c[0][j] = 0;
b[0][j] = Zero;
}

// calculate the two tables from bottom to top
for ( int i = 1; i <= m; ++i )
{
for ( int j = 1; j <= n; ++j )
{
if ( x[i - 1] == y[j - 1] )
{
c[i][j] = c[i - 1][j - 1] + 1;
b[i][j] = LeftUp;
}
else if ( c[i - 1][j] >= c[i][j - 1] )
{
c[i][j] = c[i - 1][j];
b[i][j] = Up;
}
else
{
c[i][j] = c[i][j - 1];
b[i][j] = Left;
}
} // end for
} //end for

} // end LCS_Length()

void Print_LCS( string x, int i, int j )
{
if ( i == 0 || j == 0 )
{
return;
}
if ( b[i][j] == LeftUp )
{
Print_LCS( x, i - 1, j - 1 );
cout << x[i - 1];
}
else if ( b[i][j] == Up )
{
Print_LCS( x, i - 1, j );
}
else
{
Print_LCS( x, i, j - 1 );
}
}

void PrintTable()
{
for ( int i = 0; i <= m; ++i )
{
for ( int j = 0; j <= n; ++j )
{
cout << c[i][j] << " ";
}
cout << endl;
}
cout << endl;
for ( int i = 0; i <= m; ++i )
{
for ( int j = 0; j <= n; ++j )
{
cout << b[i][j] << " ";
}
cout << endl;
}
}