Enhance comments & improve readability in LongestCommonSubsequence.java (#5523)

src/main/java/com/thealgorithms/dynamicprogramming/LongestCommonSubsequence.java

@@ -1,73 +1,98 @@
 package com.thealgorithms.dynamicprogramming;
 
+/**
+ * This class implements the Longest Common Subsequence (LCS) problem.
+ * The LCS of two sequences is the longest sequence that appears in both
+ * sequences
+ * in the same order, but not necessarily consecutively.
+ *
+ * This implementation uses dynamic programming to find the LCS of two strings.
+ */
 final class LongestCommonSubsequence {
+
     private LongestCommonSubsequence() {
     }
 
+    /**
+     * Returns the Longest Common Subsequence (LCS) of two given strings.
+     *
+     * @param str1 The first string.
+     * @param str2 The second string.
+     * @return The LCS of the two strings, or null if one of the strings is null.
+     */
     public static String getLCS(String str1, String str2) {
-        // At least one string is null
+        // If either string is null, return null as LCS can't be computed.
         if (str1 == null || str2 == null) {
             return null;
         }
-
-        // At least one string is empty
+        // If either string is empty, return an empty string as LCS.
         if (str1.length() == 0 || str2.length() == 0) {
             return "";
         }
 
+        // Convert the strings into arrays of characters
         String[] arr1 = str1.split("");
         String[] arr2 = str2.split("");
 
-        // lcsMatrix[i][j]  = LCS of first i elements of arr1 and first j characters of arr2
+        // lcsMatrix[i][j] = LCS(first i characters of str1, first j characters of str2)
         int[][] lcsMatrix = new int[arr1.length + 1][arr2.length + 1];
 
+        // Base Case: Fill the LCS matrix 0th row & 0th column with 0s
+        // as LCS of any string with an empty string is 0.
         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;
         }
+
+        // Build the LCS matrix by comparing characters of str1 & str2
         for (int i = 1; i < arr1.length + 1; i++) {
             for (int j = 1; j < arr2.length + 1; j++) {
+                // If characters match, the LCS increases by 1
                 if (arr1[i - 1].equals(arr2[j - 1])) {
                     lcsMatrix[i][j] = lcsMatrix[i - 1][j - 1] + 1;
                 } else {
+                    // Otherwise, take the maximum of the left or above values
                     lcsMatrix[i][j] = Math.max(lcsMatrix[i - 1][j], lcsMatrix[i][j - 1]);
                 }
             }
         }
+
+        // Call helper function to reconstruct the LCS from the matrix
         return lcsString(str1, str2, lcsMatrix);
     }
 
+    /**
+     * Reconstructs the LCS string from the LCS matrix.
+     *
+     * @param str1      The first string.
+     * @param str2      The second string.
+     * @param lcsMatrix The matrix storing the lengths of LCSs
+     *                  of substrings of str1 and str2.
+     * @return The LCS string.
+     */
     public static String lcsString(String str1, String str2, int[][] lcsMatrix) {
-        StringBuilder lcs = new StringBuilder();
-        int i = str1.length();
-        int j = str2.length();
+        StringBuilder lcs = new StringBuilder(); // Hold the LCS characters.
+        int i = str1.length(); // Start from the end of str1.
+        int j = str2.length(); // Start from the end of str2.
+
+        // Trace back through the LCS matrix to reconstruct the LCS
         while (i > 0 && j > 0) {
+            // If characters match, add to the LCS and move diagonally in the matrix
             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]) {
+                // If the value above is larger, move up
                 i--;
             } else {
+                // If the value to the left is larger, move left
                 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());
-        }
+        return lcs.reverse().toString(); // LCS built in reverse, so reverse it back
     }
 }