add: LongestCommonSubsequence

Author: Jer3myYu

java/Dynamic Programming/LongestCommonSubsequence.java

@@ -0,0 +1,26 @@
+public class LongestCommonSubsequence {
+    public int longestCommonSubsequence(String s1, String s2) {
+        // Base case: Set the last row and last column to 0 by
+        // initializing the entire DP table with 0s.
+        int[][] dp = new int[s1.length() + 1][s2.length() + 1];
+        // Populate the DP table.
+        for (int i = s1.length() - 1; i >= 0; i--) {
+            for (int j = s2.length() - 1; j >= 0; j--) {
+                // If the characters match, the length of the LCS at
+                // 'dp[i][j]' is 1 + the LCS length of the remaining
+                // substrings.
+                if (s1.charAt(i) == s2.charAt(j)) {
+                    dp[i][j] = 1 + dp[i + 1][j + 1];
+                }
+                // If the characters don't match, the LCS length at
+                // 'dp[i][j]' can be found by either:
+                // 1. Excluding the current character of s1.
+                // 2. Excluding the current character of s2.
+                else {
+                    dp[i][j] = Math.max(dp[i + 1][j], dp[i][j + 1]);
+                }
+            }
+        }
+        return dp[0][0];
+    }
+}