Merge pull request TheAlgorithms#188 from rahul1995/master

Add Longest Common Subsequence algorithm (DP)

Author: varunu28

Dynamic Programming/LongestCommonSubsequence.java

@@ -0,0 +1,66 @@
+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());
+		}
+	}
+}