🚀 Given two strings like "listen" and "silent", determine if they contain exactly the same characters in different order (Anagram)

🧩 THE CHALLENGE

Given two strings like "listen" and "silent", determine if they contain exactly the same characters in different order.

Examples:

• ✅ "listen" ↔ "silent" → TRUE

• ✅ "evil" ↔ "vile" → TRUE

• ❌ "hello" ↔ "world" → FALSE

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💡 THE OPTIMAL SOLUTION

Here's the breakthrough algorithm that achieves O(n) time and O(1) space:

public Boolean isAnagram(String s1, String s2) {

  int[] frequency = new int[26];  // Fixed array for a-z letters
    
    // Different lengths? Not anagrams!
    if (s1.length() != s2.length()) return false;
    
    // Process both strings in ONE loop - O(n)
    for (int i = 0; i < s1.length(); i++) {
        frequency[s1.charAt(i) - 'a']++;  // Count letters in s1
        frequency[s2.charAt(i) - 'a']--;  // Subtract letters in s2
    }
    
    // If all counters are zero = perfect match!
    for (int count : frequency) {
        if (count != 0) return false;
    }
    
    return true;
}

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🔬 THE GENIUS BEHIND THE CODE

Character to Index Magic:

'a' - 'a' = 0  →  Array position 0
'b' - 'a' = 1  →  Array position 1
'l' - 'a' = 11 →  Array position 11
'z' - 'a' = 25 →  Array position 25

The Balancing Algorithm:

1. Add +1 for each character in string 1

2. Subtract -1 for each character in string 2

3. Result = 0 everywhere? → Perfect anagram! ✅

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📊 STEP-BY-STEP EXAMPLE: "cat" vs "act"

Final Result: All zeros → ANAGRAM! 🎉

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⚡ WHY THIS SOLUTION DOMINATES

*k = number of unique characters

Key Advantages:

• 🚀 Single pass through both strings

• 💾 Constant space - only 26 integers

• ⚡ Cache-friendly - array access beats HashMap

• 🎯 Theoretically optimal - can't do better than O(n)

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🧠 THE ALGORITHM INSIGHTS

✅ Think Arrays Over HashMaps - When dealing with limited character sets
✅ Process Simultaneously - Why make two passes when one suffices?
✅ Character Arithmetic - c - 'a' is a powerful mapping technique
✅ Early Termination - Check length first, save computation
✅ Balance Principle - Add and subtract to detect mismatches