动态规划之最长公共子序列的Java实现

这是算法导论动态规划一章讲的内容。

 

public class LCSProblem 
{
	public static void main(String[] args)
	{
		String[] x = {"", "A", "B", "C", "B", "D", "A", "B"};
		String[] y = {"", "B", "D", "C", "A", "B", "A"};
		
		int[][] b = getLength(x, y);
		
		Display(b, x, x.length-1, y.length-1);
	}
	
	public static int[][] getLength(String[] x, String[] y)
	{
		int[][] b = new int[x.length][y.length];
		int[][] c = new int[x.length][y.length];
		
		for(int i=1; i<x.length; i++)
		{
			for(int j=1; j<y.length; j++)
			{
				if( x[i] == y[j])
				{
					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] = 0;
				}
				else
				{
					c[i][j] = c[i][j-1];
					b[i][j] = -1;
				}
			}
		}	
		
		return b;
	}
	
	public static void Display(int[][] b, String[] x, int i, int j)
	{
		if(i == 0 || j == 0)
			return;
		
		if(b[i][j] == 1)
		{
			Display(b, x, i-1, j-1);
			System.out.print(x[i] + " ");
		}
		else if(b[i][j] == 0)
		{
			Display(b, x, i-1, j);
		}
		else if(b[i][j] == -1)
		{
			Display(b, x, i, j-1);
		}
	}
}