Add explanation and solution for LeetCode problem 290 (Word Pattern)

Author: romankurnovskii

explanations/290/en.md

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+## 290. Word Pattern [Easy]
+
+https://leetcode.com/problems/word-pattern
+
+## Description
+Given a `pattern` and a string `s`, find if `s` follows the same pattern.
+
+Here **follow** means a full match, such that there is a bijection between a letter in `pattern` and a **non-empty** word in `s`. Specifically:
+
+- Each letter in `pattern` maps to **exactly** one unique word in `s`.
+- Each unique word in `s` maps to **exactly** one letter in `pattern`.
+- No two letters map to the same word, and no two words map to the same letter.
+
+**Examples**
+
+```tex
+Example 1:
+Input: pattern = "abba", s = "dog cat cat dog"
+Output: true
+Explanation:
+The bijection can be established as:
+- 'a' maps to "dog".
+- 'b' maps to "cat".
+
+Example 2:
+Input: pattern = "abba", s = "dog cat cat fish"
+Output: false
+
+Example 3:
+Input: pattern = "aaaa", s = "dog cat cat dog"
+Output: false
+```
+
+**Constraints**
+```tex
+- 1 <= pattern.length <= 300
+- pattern contains only lower-case English letters
+- 1 <= s.length <= 3000
+- s contains only lowercase English letters and spaces ' '
+- s does not contain any leading or trailing spaces
+- All the words in s are separated by a single space
+```
+
+## Explanation
+
+### Strategy
+Let's restate the problem: You're given a pattern string (like "abba") and a string of words (like "dog cat cat dog"), and you need to determine if the words follow the same pattern. This means there should be a one-to-one mapping between letters in the pattern and words in the string.
+
+This is a **hash table problem** that requires tracking bidirectional mappings between pattern characters and words, similar to the isomorphic strings problem but with words instead of individual characters.
+
+**What is given?** A pattern string and a string of space-separated words.
+
+**What is being asked?** Determine if the words follow the same pattern as the given pattern string.
+
+**Constraints:** The pattern can be up to 300 characters, and the string can be up to 3000 characters with words separated by single spaces.
+
+**Edge cases:** 
+- Pattern and words have different lengths
+- Empty pattern or empty string
+- Pattern with repeated characters
+- String with repeated words
+
+**High-level approach:**
+The solution involves using two hash maps to track character-to-word and word-to-character mappings, ensuring that the bijection property is maintained.
+
+**Decomposition:**
+1. **Split the string into words**: Convert the space-separated string into a list of words
+2. **Check length consistency**: If pattern length doesn't match word count, return false
+3. **Create mapping dictionaries**: Track character-to-word and word-to-character mappings
+4. **Verify bijection**: Ensure each character maps to exactly one word and vice versa
+
+**Brute force vs. optimized strategy:**
+- **Brute force**: Try all possible mappings. This is extremely inefficient.
+- **Optimized**: Use hash tables to track mappings in a single pass. This takes O(n) time.
+
+### Steps
+Let's walk through the solution step by step using the first example: `pattern = "abba"`, `s = "dog cat cat dog"`
+
+**Step 1: Split the string into words**
+- `s = "dog cat cat dog"`
+- `words = ["dog", "cat", "cat", "dog"]`
+
+**Step 2: Check length consistency**
+- `pattern.length = 4`
+- `words.length = 4`
+- Lengths match ✓
+
+**Step 3: Initialize mapping dictionaries**
+- `char_to_word = {}` (maps pattern characters to words)
+- `word_to_char = {}` (maps words to pattern characters)
+
+**Step 4: Check first character-word pair**
+- `pattern[0] = 'a'`, `words[0] = "dog"`
+- Check if 'a' is already mapped: No
+- Check if "dog" is already mapped: No
+- Add mappings: `char_to_word['a'] = "dog"`, `word_to_char["dog"] = 'a'`
+
+**Step 5: Check second character-word pair**
+- `pattern[1] = 'b'`, `words[1] = "cat"`
+- Check if 'b' is already mapped: No
+- Check if "cat" is already mapped: No
+- Add mappings: `char_to_word['b'] = "cat"`, `word_to_char["cat"] = 'b'`
+
+**Step 6: Check third character-word pair**
+- `pattern[2] = 'b'`, `words[2] = "cat"`
+- Check if 'b' is already mapped: Yes, to "cat"
+- Verify consistency: `char_to_word['b'] == "cat"` ✓
+- Check if "cat" is already mapped: Yes, to 'b'
+- Verify consistency: `word_to_char["cat"] == 'b'` ✓
+
+**Step 7: Check fourth character-word pair**
+- `pattern[3] = 'a'`, `words[3] = "dog"`
+- Check if 'a' is already mapped: Yes, to "dog"
+- Verify consistency: `char_to_word['a'] == "dog"` ✓
+- Check if "dog" is already mapped: Yes, to 'a'
+- Verify consistency: `word_to_char["dog"] == 'a'` ✓
+
+**Step 8: Result**
+- All character-word pairs are consistent
+- Pattern is followed: `true`
+
+**Why this works:**
+By maintaining mappings in both directions, we ensure that:
+1. Each character in the pattern maps to exactly one word
+2. Each word maps to exactly one character
+3. The bijection property is maintained throughout the pattern
+
+> **Note:** The key insight is using bidirectional mapping to ensure the bijection property. This is similar to the isomorphic strings problem but operates on words instead of individual characters.
+
+**Time Complexity:** O(n) - we visit each character/word once  
+**Space Complexity:** O(k) - where k is the number of unique characters/words

solutions/290/01.py

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+def wordPattern(pattern, s):
+    """
+    Determine if the string s follows the given pattern.
+    
+    Args:
+        pattern: str - The pattern string to match against
+        s: str - The string of space-separated words
+        
+    Returns:
+        bool - True if s follows the pattern, False otherwise
+    """
+    # Split the string into words
+    words = s.split()
+    
+    # Check if pattern length matches word count
+    if len(pattern) != len(words):
+        return False
+    
+    # Create mapping dictionaries for both directions
+    char_to_word = {}  # maps pattern characters to words
+    word_to_char = {}  # maps words to pattern characters
+    
+    # Check each character-word pair
+    for i in range(len(pattern)):
+        char = pattern[i]
+        word = words[i]
+        
+        # Check if char is already mapped
+        if char in char_to_word:
+            # Verify the mapping is consistent
+            if char_to_word[char] != word:
+                return False
+        else:
+            # Check if word is already mapped to by another character
+            if word in word_to_char:
+                return False
+            
+            # Add new mapping
+            char_to_word[char] = word
+            word_to_char[word] = char
+    
+    return True