Add WordPatternMatcher algorithm (#5627)

src/main/java/com/thealgorithms/backtracking/WordPatternMatcher.java

@@ -0,0 +1,86 @@
+package com.thealgorithms.backtracking;
+
+import java.util.HashMap;
+import java.util.Map;
+
+/**
+ * Class to determine if a pattern matches a string using backtracking.
+ *
+ * Example:
+ * Pattern: "abab"
+ * Input String: "JavaPythonJavaPython"
+ * Output: true
+ *
+ * Pattern: "aaaa"
+ * Input String: "JavaJavaJavaJava"
+ * Output: true
+ *
+ * Pattern: "aabb"
+ * Input String: "JavaPythonPythonJava"
+ * Output: false
+ */
+public final class WordPatternMatcher {
+    private WordPatternMatcher() {
+    }
+
+    /**
+     * Determines if the given pattern matches the input string using backtracking.
+     *
+     * @param pattern The pattern to match.
+     * @param inputString The string to match against the pattern.
+     * @return True if the pattern matches the string, False otherwise.
+     */
+    public static boolean matchWordPattern(String pattern, String inputString) {
+        Map<Character, String> patternMap = new HashMap<>();
+        Map<String, Character> strMap = new HashMap<>();
+        return backtrack(pattern, inputString, 0, 0, patternMap, strMap);
+    }
+
+    /**
+     * Backtracking helper function to check if the pattern matches the string.
+     *
+     * @param pattern The pattern string.
+     * @param inputString The string to match against the pattern.
+     * @param patternIndex Current index in the pattern.
+     * @param strIndex Current index in the input string.
+     * @param patternMap Map to store pattern characters to string mappings.
+     * @param strMap Map to store string to pattern character mappings.
+     * @return True if the pattern matches, False otherwise.
+     */
+    private static boolean backtrack(String pattern, String inputString, int patternIndex, int strIndex, Map<Character, String> patternMap, Map<String, Character> strMap) {
+        if (patternIndex == pattern.length() && strIndex == inputString.length()) {
+            return true;
+        }
+        if (patternIndex == pattern.length() || strIndex == inputString.length()) {
+            return false;
+        }
+
+        char currentChar = pattern.charAt(patternIndex);
+        if (patternMap.containsKey(currentChar)) {
+            String mappedStr = patternMap.get(currentChar);
+            if (inputString.startsWith(mappedStr, strIndex)) {
+                return backtrack(pattern, inputString, patternIndex + 1, strIndex + mappedStr.length(), patternMap, strMap);
+            } else {
+                return false;
+            }
+        }
+
+        for (int end = strIndex + 1; end <= inputString.length(); end++) {
+            String substring = inputString.substring(strIndex, end);
+            if (strMap.containsKey(substring)) {
+                continue;
+            }
+
+            patternMap.put(currentChar, substring);
+            strMap.put(substring, currentChar);
+            if (backtrack(pattern, inputString, patternIndex + 1, end, patternMap, strMap)) {
+                return true;
+            }
+
+            patternMap.remove(currentChar);
+            strMap.remove(substring);
+        }
+
+        return false;
+    }
+}