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;
	}
}