Add Regular Expression Matching algorithm using DP with test cases

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

@@ -0,0 +1,44 @@
+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * Class for Regular Expression Matching using Dynamic Programming.
+ */
+public class RegularExpressionMatching {
+
+    /**
+     * Determines if the input string matches the given pattern.
+     *
+     * @param s the input string
+     * @param p the pattern string (may contain '.' and '*')
+     * @return true if the string matches the pattern, false otherwise
+     */
+    public boolean isMatch(final String s, final String p) {
+        final Boolean[][] memo = new Boolean[s.length() + 1][p.length() + 1];
+        return dp(0, 0, s, p, memo);
+    }
+
+    private boolean dp(final int i, final int j, final String s, final String p, final Boolean[][] memo) {
+        if (memo[i][j] != null) {
+            return memo[i][j];
+        }
+
+        final boolean ans;
+        if (j == p.length()) {
+            ans = (i == s.length());
+        } else {
+            final boolean firstMatch = (i < s.length() && (s.charAt(i) == p.charAt(j) || p.charAt(j) == '.'));
+
+            if (j + 1 < p.length() && p.charAt(j + 1) == '*') {
+                // Two options:
+                // 1. Skip the pattern with '*'
+                // 2. Use '*' to match one character
+                ans = dp(i, j + 2, s, p, memo) || (firstMatch && dp(i + 1, j, s, p, memo));
+            } else {
+                ans = firstMatch && dp(i + 1, j + 1, s, p, memo);
+            }
+        }
+
+        memo[i][j] = ans;
+        return ans;
+    }
+}

src/test/java/com/thealgorithms/dynamicprogramming/RegularExpressionMatchingTest.java

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+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Test class for RegularExpressionMatching.
+ */
+public class RegularExpressionMatchingTest {
+
+    @Test
+    public void testBasicCases() {
+        final RegularExpressionMatching matcher = new RegularExpressionMatching();
+
+        // Test cases from the problem
+        assertFalse(matcher.isMatch("aa", "a"));
+        assertTrue(matcher.isMatch("aa", "a*"));
+        assertTrue(matcher.isMatch("ab", ".*"));
+        assertFalse(matcher.isMatch("mississippi", "mis*is*p*."));
+        assertFalse(matcher.isMatch("ab", ".*c"));
+        assertTrue(matcher.isMatch("aaa", "a*a"));
+        assertTrue(matcher.isMatch("aab", "c*a*b"));
+        assertTrue(matcher.isMatch("", ".*"));
+        assertTrue(matcher.isMatch("", ""));
+        assertFalse(matcher.isMatch("abcd", "d*"));
+    }
+}