🧩 DSA Sheet – Day 34: Miscellaneous

This section covers mixed problems involving bit manipulation, recursion, simulation, and observations. These questions are often used to test your problem-solving intuition.

📊 Progress Tracker

Progress: 0 / 5 Completed

Done	Problem	Practice	Level	Companies
	Power Set	Solve	Medium	Google, Uber
	Maximum XOR of Two Numbers	Solve	Medium	Amazon, Google
	Power of Two	Solve	Easy	Apple, TCS
	XOR Beauty of Array	Solve	Medium	Amazon
	Watering Plants II	Solve	Medium	Amazon

🧠 Key Approaches

• Power Set: Backtracking OR bitmasking
• Maximum XOR: Trie OR greedy bit manipulation
• Power of Two: Bit trick → n & (n-1)
• XOR Beauty: Reduce expression using XOR properties
• Watering Plants: Two pointers + simulation

⚡ Quick Cheatsheet

Power of Two

return n > 0 && (n & (n - 1)) == 0;
    

Power Set (Bitmask)

for(int i = 0; i < (1 << n); i++){
  for(int j = 0; j < n; j++){
    if(i & (1 << j)){
      // include nums[j]
    }
  }
}
    

Maximum XOR (Concept)

// try to match opposite bit (1 ↔ 0)
// maximize XOR using Trie
    

🔥 Pro Tip

These problems test your thinking, not memorization:

• Use bit manipulation wherever possible
• Look for mathematical simplifications
• Simulate when logic is complex

If you understand XOR deeply → many problems become easy.

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