Add Regular Expression Matching algorithm with DP implementation

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

@@ -0,0 +1,179 @@
+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * Implements regular expression matching with support for '.' and '*'.
+ * 
+ * <p>
+ * The regular expression matching problem involves determining if a given string
+ * matches a pattern containing special characters '.' and '*'. The '.' matches
+ * any single character, while '*' matches zero or more of the preceding element.
+ * 
+ * <p>
+ * This solution uses dynamic programming with memoization for efficient computation.
+ * 
+ * <p>
+ * For more information:
+ * @see <a href="https://en.wikipedia.org/wiki/Regular_expression">Regular Expression</a>
+ * @see <a href="https://leetcode.com/problems/regular-expression-matching/">LeetCode Problem 10</a>
+ * 
+ * <p>
+ * Example:
+ * <pre>
+ * Input: s = "aa", p = "a" → Output: false
+ * Input: s = "aa", p = "a*" → Output: true  
+ * Input: s = "ab", p = ".*" → Output: true
+ * </pre>
+ * 
+ * <p>
+ * Time Complexity: O(m * n) where m is length of s and n is length of p
+ * Space Complexity: O(m * n) for the memoization table
+ */
+public final class RegularExpressionMatching {
+    private RegularExpressionMatching() {
+        // Private constructor to prevent instantiation
+    }
+
+    /**
+     * Determines if the input string matches the given pattern.
+     *
+     * @param inputString the input string to match (contains only lowercase English letters)
+     * @param pattern the pattern (contains lowercase English letters, '.', and '*')
+     * @return true if the entire string matches the pattern, false otherwise
+     * @throws IllegalArgumentException if input strings are null or pattern is invalid
+     */
+    public static boolean isMatch(String inputString, String pattern) {
+        if (inputString == null || pattern == null) {
+            throw new IllegalArgumentException("Input strings cannot be null");
+        }
+
+        if (!isValidPattern(pattern)) {
+            throw new IllegalArgumentException("Invalid pattern format");
+        }
+
+        Boolean[][] memo = new Boolean[inputString.length() + 1][pattern.length() + 1];
+        return dynamicProgramming(0, 0, inputString, pattern, memo);
+    }
+
+    /**
+     * Helper method that performs the actual dynamic programming computation.
+     *
+     * @param stringIndex current index in string s
+     * @param patternIndex current index in pattern p  
+     * @param inputString the input string
+     * @param pattern the pattern
+     * @param memo memoization table storing computed results
+     * @return true if s[i:] matches p[j:], false otherwise
+     */
+    private static boolean dynamicProgramming(int stringIndex, int patternIndex, 
+                                             String inputString, String pattern, 
+                                             Boolean[][] memo) {
+        if (memo[stringIndex][patternIndex] != null) {
+            return memo[stringIndex][patternIndex];
+        }
+
+        boolean result;
+
+        if (patternIndex == pattern.length()) {
+            result = (stringIndex == inputString.length());
+        } else {
+            boolean currentMatch = stringIndex < inputString.length() && 
+                                  (pattern.charAt(patternIndex) == '.' || 
+                                   pattern.charAt(patternIndex) == inputString.charAt(stringIndex));
+
+            if (patternIndex + 1 < pattern.length() && pattern.charAt(patternIndex + 1) == '*') {
+                result = dynamicProgramming(stringIndex, patternIndex + 2, inputString, pattern, memo) || 
+                        (currentMatch && dynamicProgramming(stringIndex + 1, patternIndex, inputString, pattern, memo));
+            } else {
+                result = currentMatch && dynamicProgramming(stringIndex + 1, patternIndex + 1, inputString, pattern, memo);
+            }
+        }
+
+        memo[stringIndex][patternIndex] = result;
+        return result;
+    }
+
+    /**
+     * Validates that the pattern follows the constraints.
+     *
+     * @param pattern the pattern to validate
+     * @return true if pattern is valid, false otherwise
+     */
+    private static boolean isValidPattern(String pattern) {
+        if (pattern.isEmpty()) {
+            return true;
+        }
+
+        if (pattern.charAt(0) == '*') {
+            return false;
+        }
+
+        for (int i = 0; i < pattern.length(); i++) {
+            char currentChar = pattern.charAt(i);
+            if (!isValidPatternChar(currentChar)) {
+                return false;
+            }
+
+            if (currentChar == '*' && (i == 0 || pattern.charAt(i - 1) == '*')) {
+                return false;
+            }
+        }
+
+        return true;
+    }
+
+    /**
+     * Checks if a character is valid in a pattern.
+     */
+    private static boolean isValidPatternChar(char character) {
+        return (character >= 'a' && character <= 'z') || character == '.' || character == '*';
+    }
+
+    /**
+     * Alternative iterative DP solution (bottom-up approach).
+     *
+     * @param inputString the input string
+     * @param pattern the pattern
+     * @return true if string matches pattern, false otherwise
+     */
+    public static boolean isMatchIterative(String inputString, String pattern) {
+        if (inputString == null || pattern == null) {
+            throw new IllegalArgumentException("Input strings cannot be null");
+        }
+
+        if (!isValidPattern(pattern)) {
+            throw new IllegalArgumentException("Invalid pattern format");
+        }
+
+        int stringLength = inputString.length();
+        int patternLength = pattern.length();
+
+        boolean[][] dp = new boolean[stringLength + 1][patternLength + 1];
+
+        dp[0][0] = true;
+
+        for (int j = 2; j <= patternLength; j++) {
+            if (pattern.charAt(j - 1) == '*') {
+                dp[0][j] = dp[0][j - 2];
+            }
+        }
+
+        for (int i = 1; i <= stringLength; i++) {
+            for (int j = 1; j <= patternLength; j++) {
+                char stringChar = inputString.charAt(i - 1);
+                char patternChar = pattern.charAt(j - 1);
+
+                if (patternChar == '.' || patternChar == stringChar) {
+                    dp[i][j] = dp[i - 1][j - 1];
+                } else if (patternChar == '*') {
+                    char previousChar = pattern.charAt(j - 2);
+                    dp[i][j] = dp[i][j - 2];
+                    if (previousChar == '.' || previousChar == stringChar) {
+                        dp[i][j] = dp[i][j] || dp[i - 1][j];
+                    }
+                }
+            }
+        }
+
+        return dp[stringLength][patternLength];
+    }
+}

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

@@ -0,0 +1,122 @@
+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for RegularExpressionMatching algorithm.
+ * 
+ * <p>
+ * For more information about regular expression matching:
+ * @see <a href="https://en.wikipedia.org/wiki/Regular_expression">Regular Expression</a>
+ * @see <a href="https://leetcode.com/problems/regular-expression-matching/">LeetCode Problem 10</a>
+ */
+class RegularExpressionMatchingTest {
+
+    @Test
+    void testBasicMatching() {
+        assertTrue(RegularExpressionMatching.isMatch("abc", "abc"));
+        assertFalse(RegularExpressionMatching.isMatch("abc", "abcd"));
+        assertFalse(RegularExpressionMatching.isMatch("abcd", "abc"));
+    }
+
+    @Test
+    void testDotWildcard() {
+        assertTrue(RegularExpressionMatching.isMatch("abc", "a.c"));
+        assertTrue(RegularExpressionMatching.isMatch("axc", "a.c"));
+        assertFalse(RegularExpressionMatching.isMatch("abc", "a.."));
+        assertTrue(RegularExpressionMatching.isMatch("abc", "..."));
+        assertFalse(RegularExpressionMatching.isMatch("ab", "..."));
+    }
+
+    @Test
+    void testStarQuantifier() {
+        assertTrue(RegularExpressionMatching.isMatch("aa", "a*"));
+        assertTrue(RegularExpressionMatching.isMatch("aaa", "a*"));
+        assertTrue(RegularExpressionMatching.isMatch("", "a*"));
+        assertFalse(RegularExpressionMatching.isMatch("b", "a*"));
+        assertTrue(RegularExpressionMatching.isMatch("aab", "c*a*b"));
+        assertTrue(RegularExpressionMatching.isMatch("b", "c*a*b"));
+    }
+
+    @Test
+    void testDotStarCombination() {
+        assertTrue(RegularExpressionMatching.isMatch("abc", ".*"));
+        assertTrue(RegularExpressionMatching.isMatch("xyz", ".*"));
+        assertTrue(RegularExpressionMatching.isMatch("", ".*"));
+        assertTrue(RegularExpressionMatching.isMatch("abc123", ".*"));
+        assertTrue(RegularExpressionMatching.isMatch("abc", "a.*c"));
+        assertTrue(RegularExpressionMatching.isMatch("axxxc", "a.*c"));
+        assertFalse(RegularExpressionMatching.isMatch("abc", "a.*d"));
+    }
+
+    @Test
+    void testComplexPatterns() {
+        assertTrue(RegularExpressionMatching.isMatch("mississippi", "mis*is*ip*."));
+        assertTrue(RegularExpressionMatching.isMatch("mississippi", "mis*is*p*."));
+        assertFalse(RegularExpressionMatching.isMatch("mississippi", "mis*is*ip*.."));
+        assertTrue(RegularExpressionMatching.isMatch("a", "a*a*a*"));
+        assertTrue(RegularExpressionMatching.isMatch("aaa", "a*a*a*"));
+        assertTrue(RegularExpressionMatching.isMatch("", "a*b*c*"));
+    }
+
+    @Test
+    void testEdgeCases() {
+        assertTrue(RegularExpressionMatching.isMatch("", ""));
+        assertTrue(RegularExpressionMatching.isMatch("", "a*"));
+        assertTrue(RegularExpressionMatching.isMatch("", ".*"));
+        assertFalse(RegularExpressionMatching.isMatch("", "a"));
+        assertFalse(RegularExpressionMatching.isMatch("", "."));
+        assertTrue(RegularExpressionMatching.isMatch("a", "a"));
+        assertTrue(RegularExpressionMatching.isMatch("a", "."));
+        assertFalse(RegularExpressionMatching.isMatch("a", "b"));
+        assertFalse(RegularExpressionMatching.isMatch("a", "aa"));
+    }
+
+    @Test
+    void testInvalidInputs() {
+        assertThrows(IllegalArgumentException.class, 
+            () -> RegularExpressionMatching.isMatch(null, "pattern"));
+        assertThrows(IllegalArgumentException.class, 
+            () -> RegularExpressionMatching.isMatch("string", null));
+        assertThrows(IllegalArgumentException.class, 
+            () -> RegularExpressionMatching.isMatch(null, null));
+        assertThrows(IllegalArgumentException.class, 
+            () -> RegularExpressionMatching.isMatch("test", "*abc"));
+        assertThrows(IllegalArgumentException.class, 
+            () -> RegularExpressionMatching.isMatch("test", "a**b"));
+    }
+
+    @Test
+    void testIterativeImplementation() {
+        assertTrue(RegularExpressionMatching.isMatchIterative("aa", "a*"));
+        assertTrue(RegularExpressionMatching.isMatchIterative("ab", ".*"));
+        assertFalse(RegularExpressionMatching.isMatchIterative("aa", "a"));
+        assertTrue(RegularExpressionMatching.isMatchIterative("aab", "c*a*b"));
+
+        String[] testStrings = {"", "a", "aa", "ab", "aaa", "aab"};
+        String[] testPatterns = {"", "a", "a*", ".*", "a.b", "c*a*b"};
+
+        for (String string : testStrings) {
+            for (String patternString : testPatterns) {
+                if (!patternString.isEmpty() && patternString.charAt(0) != '*') {
+                    boolean recursiveResult = RegularExpressionMatching.isMatch(string, patternString);
+                    boolean iterativeResult = RegularExpressionMatching.isMatchIterative(string, patternString);
+                    assertTrue(recursiveResult == iterativeResult);
+                }
+            }
+        }
+    }
+
+    @Test
+    void testLeetCodeExamples() {
+        assertFalse(RegularExpressionMatching.isMatch("aa", "a"));
+        assertTrue(RegularExpressionMatching.isMatch("aa", "a*"));
+        assertTrue(RegularExpressionMatching.isMatch("ab", ".*"));
+        assertTrue(RegularExpressionMatching.isMatch("aab", "c*a*b"));
+        assertFalse(RegularExpressionMatching.isMatch("mississippi", "mis*is*p*."));
+    }
+}