算法导论示例-LongestCommonSubsequence

/**
 * Introduction to Algorithms, Second Edition 
 * 15.4 Longest common subsequence
 * @author 土豆爸爸
 * 
 */
public class LongestCommonSubsequence {
    /**
     * 求两个字符串的最长公共子序列
     * @param x 字符串x
     * @param y 字符串y
     * @return 两个字符串的最长公共子序列
     */
    public static String lcs(String x, String y) {
        int m = x.length();
        int n = y.length();
        int[][] c = new int[m + 1][n + 1]; //构建计算矩阵
        for(int i = 1; i <= m; i++) {
            for(int j = 1; j <= n; j++) {
                if(x.charAt(i-1) == y.charAt(j-1)) { //如果相同右下
                    c[i][j] = c[i-1][j-1] + 1;
                } else if(c[i-1][j] >= c[i][j-1]) { //向大的方向移动
                    c[i][j] = c[i-1][j];
                } else {
                    c[i][j] = c[i][j-1];
                }
            }
        }
        return output(x, y, c, m, n).toString();
    }
    
    /**
     * 迭代输出.
     * @param x 字符串x
     * @param y 字符串y
     * @param c 计算矩阵
     * @param i 行索引
     * @param j 列索引
     * @return 输出最长公共子序列
     */
    private static StringBuilder output(String x, String y, int[][] c, int i, int j) {
        if(i == 0 || j == 0) {
            return new StringBuilder();
        } 
        if(x.charAt(i-1) == y.charAt(j-1)) {
            return output(x, y, c, i-1, j-1).append(x.charAt(i-1));
        } else if (c[i][j] == c[i-1][j]) {
            return output(x, y, c, i-1, j);
        } else {
            return output(x, y, c, i, j-1);
        }
    }
}

import junit.framework.TestCase;

public class LongestCommonSubsequenceTest extends TestCase {
    public void testLcm() {
        assertEquals("BCBA", LongestCommonSubsequence.lcs("ABCBDAB", "BDCABA"));
    }
}