这个问题很经典，典型的动态规划，动态规划就是填一个表，然后遍历一下就行了。

• 代码实现

/**
 * 源码名称：LCSequence.java 
 * 日期：2014-09-02 
 * 程序功能：LCS（不连续） 
 * 版权：CopyRight@A2BGeek 
 * 作者：A2BGeek
 */
public class LCSequence {
	private String mOne, mTwo;
	int[][] mMatrix;
	int[][] mB;
	String mResult;

	public LCSequence(String one, String two) {
		mOne = one;
		mTwo = two;
		int lengthOne = one.length();
		int lengthTwo = two.length();
		mMatrix = new int[lengthOne + 1][lengthTwo + 1];
		mB = new int[lengthOne + 1][lengthTwo + 1];
		mResult = "";
	}

	public void generateMatrix() {
		int lengthOne = mOne.length();
		int lengthTwo = mTwo.length();
		for (int i = 1; i <= lengthOne; i++) {
			mMatrix[i][0] = 0;
		}
		for (int j = 1; j <= lengthTwo; j++) {
			mMatrix[0][j] = 0;
		}
		mMatrix[0][0] = 0;
		// 1 stands for upleft, 2 stands for up, 3 stands for left
		for (int i = 1; i <= lengthOne; i++) {
			for (int j = 1; j <= lengthTwo; j++) {
				if (mOne.charAt(i - 1) == mTwo.charAt(j - 1)) {
					mMatrix[i][j] = mMatrix[i - 1][j - 1] + 1;
					mB[i][j] = 1;
				} else if (mMatrix[i - 1][j] >= mMatrix[i][j - 1]) {
					mMatrix[i][j] = mMatrix[i - 1][j];
					mB[i][j] = 2;
				} else if (mMatrix[i - 1][j] < mMatrix[i][j - 1]) {
					mMatrix[i][j] = mMatrix[i][j - 1];
					mB[i][j] = 3;
				}
			}
		}
	}

	public void getLCSequence(String str, int i, int j) {
		if (i == 0 || j == 0) {
			return;
		}
		if (mB[i][j] == 1) {
			getLCSequence(str, i - 1, j - 1);
			mResult += str.charAt(i - 1);
		} else if (mB[i][j] == 2) {
			getLCSequence(str, i - 1, j);
		} else {
			getLCSequence(str, i, j - 1);
		}
	}

	public void printMatrix(int[][] in) {
		for (int i = 0; i < in.length; i++) {
			for (int j = 0; j < in[i].length; j++) {
				System.out.print(in[i][j] + "   ");
			}
			System.out.println();
		}
	}

	public void printMatrix(char[][] in) {
		for (int i = 0; i < in.length; i++) {
			for (int j = 0; j < in[i].length; j++) {
				System.out.print(in[i][j] + "   ");
			}
			System.out.println();
		}
	}

	public static void main(String[] args) {
		String one = "abcbdab";
		String two = "bdcaba";
		LCSequence mLcSequence = new LCSequence(one, two);
		mLcSequence.generateMatrix();
		mLcSequence.printMatrix(mLcSequence.mMatrix);
		System.out.println("------------------------");
		mLcSequence.printMatrix(mLcSequence.mB);
		mLcSequence.getLCSequence(one, one.length(), two.length());
		System.out.println(mLcSequence.mResult);
	}
}

【数据结构与算法】LCS（不连续）