Dynamic Programming/LongestCommonSubsequence.java

class LongestCommonSubsequence {

	public static String getLCS(String str1, String str2) {

		//At least one string is null
		if(str1 == null || str2 == null)
			return null;

		//At least one string is empty
		if(str1.length() == 0 || str2.length() == 0)
			return "";

		String[] arr1 = str1.split("");
		String[] arr2 = str2.split("");

		//lcsMatrix[i][j]  = LCS of first i elements of arr1 and first j characters of arr2
		int[][] lcsMatrix = new int[arr1.length + 1][arr2.length + 1];

		for(int i = 0; i < arr1.length + 1; i++)
			lcsMatrix[i][0] = 0;
		for(int j = 1; j < arr2.length + 1; j++)
			lcsMatrix[0][j] = 0;
		for(int i = 1; i < arr1.length + 1; i++) {
			for(int j = 1; j < arr2.length + 1; j++) {
				if(arr1[i-1].equals(arr2[j-1])) {
					lcsMatrix[i][j] = lcsMatrix[i-1][j-1] + 1;
				} else {
					lcsMatrix[i][j] = lcsMatrix[i-1][j] > lcsMatrix[i][j-1] ? lcsMatrix[i-1][j] : lcsMatrix[i][j-1];
				}
			}
		}
		return lcsString(str1, str2, lcsMatrix);
	}

	public static String lcsString (String str1, String str2, int[][] lcsMatrix) {
		StringBuilder lcs = new StringBuilder();
		int i = str1.length(),
			j = str2.length();
		while(i > 0  && j > 0) {
			if(str1.charAt(i-1) == str2.charAt(j-1)) {
				lcs.append(str1.charAt(i-1));
				i--;
				j--;
			} else if(lcsMatrix[i-1][j] > lcsMatrix[i][j-1]) {
				i--;
			} else {
				j--;
			}
		}
		return lcs.reverse().toString();
	}

	public static void main(String[] args) {
		String str1 = "DSGSHSRGSRHTRD";
		String str2 = "DATRGAGTSHS";
		String lcs = getLCS(str1, str2);
		
		//Print LCS
		if(lcs != null) {
			System.out.println("String 1: " + str1);
			System.out.println("String 2: " + str2);
			System.out.println("LCS: " + lcs);
			System.out.println("LCS length: " + lcs.length());
		}
	}
}