动态规划之最长子序列和最长子串

  本文大部分参考July博客的关于动态规划的分析，代码贴在此仅作记忆和分享。

  概念解释：

  1） 最长子序列，两个字符串中满足相同顺序的子字符序列，如 abefgs和acehfg的最长子序列为aefg

   2)   最长子串，两个字符串中相同的子串，即必须是连续相同

   以上两个问题的代码如下：

  

/**
 * 动态规划求解最长子串和最长子序列问题
 * @author mwd
 * @2013-9-17
 *
 */
public class DanymicProgramming {
	private final int kLeft = 1;
	private final int kUp = 2;
	private final int kLeftUp = 3;
	
    /**
     * 获取最长公共子串，即必须是连续的
     * @param str1
     * @param str2
     * @return
     */
	private int lss(String str1,String str2){
		int maxLength = 0;
		int xIndex = 0;
		int yIndex = 0;
		
		if(str1 == null || str2 == null)
			return 0;
		int len1 = str1.length();
		int len2 = str2.length();
		
		if(len1 == 0 || len2 == 0)
			return 0;
		
		int[][] lssLength = new int[len1][len2];
		
		for(int i=0;i<len1;i++){
			for(int j=0;j<len2;j++){
				if(i==0 || j==0){
					if(str1.charAt(i) == str2.charAt(j))
						lssLength[i][j] = 1;
					else
						lssLength[i][j] = 0;
				}
				else{
					if(str1.charAt(i) == str2.charAt(j)){
						lssLength[i][j] = lssLength[i-1][j-1]+1;
					}
					else
						lssLength[i][j] = 0;
				}
				
				if(lssLength[i][j] > maxLength){
					maxLength = lssLength[i][j];
					xIndex = i;
					yIndex = j;
				}
			}
		}
		
		for(int i = xIndex-maxLength+1;i<=xIndex;i++){
			System.out.print(str1.charAt(i)+" ");
		}
		return maxLength;
	}
	
	/**
	 * 求取最长公共子序列
	 * @param str1
	 * @param str2
	 * @return
	 */
	private int LCS(String str1,String str2){
		if(str1 == null || str2 == null)
			return 0;
		
		int len1 = str1.length();
		int len2 = str2.length();
		if(len1 == 0 || len2 == 0)
			return 0;
		
		//方位
		int[][] lcsDirection = new int[len1][len2];
		for(int i=0;i<len1;i++)
			for(int j=0;j<len2;j++)
				lcsDirection[i][j] = 0;
		
		//长度初始化
		int[][] lcsLength = new int[len1][len2];
		for(int i=0;i<len1;i++)
			for(int j=0;j<len2;j++)
				lcsLength[i][j] = 0;
		
		for(int i=0;i<len1;i++)
			for(int j=0;j<len2;j++){
				if(i==0 || j==0){
					if(str1.charAt(i) == str2.charAt(j)){
						lcsLength[i][j] = 1;
						lcsDirection[i][j] = kLeftUp;
					}
					else if(i>0){
						lcsLength[i][j] = lcsLength[i-1][j];
						lcsDirection[i][j] = kUp;
					}
					else{
						lcsLength[i][j] = lcsLength[i][j-1];
						lcsDirection[i][j] = kLeft;
					}
				}
				
				else if(str1.charAt(i) == str2.charAt(j)){
					lcsLength[i][j] = lcsLength[i-1][j-1]+1;
					lcsDirection[i][j] = kLeftUp;
				}
				
				else if(lcsLength[i-1][j] > lcsLength[i][j-1]){
					lcsLength[i][j] = lcsLength[i-1][j];
					lcsDirection[i][j] = kUp;
				}
				
				else{
					lcsLength[i][j] = lcsLength[i][j-1];
					lcsDirection[i][j] = kLeft;
				}
			}
		
		for(int i=0;i<len1;i++){
			for(int j=0;j<len2;j++){
				System.out.print(lcsLength[i][j]+" ");
			}
			System.out.println();
		}
		lcsPrint(lcsDirection, str1, str2, len1-1, len2-1);  //打印公共子序列
		return lcsLength[len1-1][len2-1];   //返回公共子序列的长度
	}
	
	/**
	 * 利用递归，动态打印公共子序列
	 * @param lcsDirection
	 * @param str1
	 * @param str2
	 * @param row
	 * @param col
	 */
	private void lcsPrint(int[][] lcsDirection,String str1,String str2,int row,int col){
		if(str1 == null || str2 == null)
			return ;
		
		int len1 = str1.length();
		int len2 = str2.length();
		if(len1 == 0 || len2 == 0 || !(row < len1 && col < len2))
			return ;
		
		if(lcsDirection[row][col] == kLeftUp){
			if(row > 0 && col > 0)
				lcsPrint(lcsDirection, str1, str2, row-1, col-1);
			System.out.print(str1.charAt(row)+" ");
		}
		else if(lcsDirection[row][col] == kUp){
			if(row > 0 )
				lcsPrint(lcsDirection, str1, str2, row-1, col);
		}
		else{
			if(col > 0)
				lcsPrint(lcsDirection, str1, str2, row, col-1);
		}
		
	}
	public static void main(String[] args){
		String str1 = "acbefg";
		String str2 = "abecefg"; 
		
		DanymicProgramming danymic = new DanymicProgramming();
		System.out.println("公共子序列长度为："+danymic.lss(str1, str2));
		
	}
}