add: LongestCommonSubsequenceOptimized

Author: Jer3myYu

java/Dynamic Programming/LongestCommonSubsequenceOptimized.java

@@ -0,0 +1,30 @@
+public class LongestCommonSubsequenceOptimized {
+    public int longestCommonSubsequenceOptimized(String s1, String s2) {
+        // Initialize 'prevRow' as the DP values of the last row.
+        int[] prevRow = new int[s2.length() + 1];
+        for (int i = s1.length() - 1; i >= 0; i--) {
+            // Set the last cell of 'currRow' to 0 to set the base case for
+            // this row. This is done by initializing the entire row to 0.
+            int[] currRow = new int[s2.length() + 1];
+            for (int j = s2.length() - 1; j >= 0; j--) {
+                // If the characters match, the length of the LCS at
+                // 'currRow[j]' is 1 + the LCS length of the remaining
+                // substrings ('prevRow[j + 1]').
+                if (s1.charAt(i) == s2.charAt(j)) {
+                    currRow[j] = 1 + prevRow[j + 1];
+                }
+                // If the characters don't match, the LCS length at
+                // 'currRow[j]' can be found by either:
+                // 1. Excluding the current character of s1 ('prevRow[j]').
+                // 2. Excluding the current character of s2 ('currRow[j + 1]').
+                else {
+                    currRow[j] = Math.max(prevRow[j], currRow[j + 1]);
+                }
+            }
+            // Update 'prevRow' with 'currRow' values for the next
+            // iteration.
+            prevRow = currRow;
+        }
+        return prevRow[0];
+    }
+}