AdvancedAdvanced
Bit Manipulation
Use bitwise operations (AND, OR, XOR, shift) for efficient computation on integers.
Problem: Single Number
Find the number that appears once in [4, 1, 2, 1, 2]. Use XOR: a ^ a = 0, a ^ 0 = a
Array: [4, 1, 2, 1, 2]
4:
0
1
0
0
1:
0
0
0
1
2:
0
0
1
0
1:
0
0
0
1
2:
0
0
1
0
Active Bit
Result Bit
Step 1/8
Speed:
When to Use
- Find single/unique number
- Power of two checks
- Subset generation using bitmasks
- Efficient integer operations
Key Indicators
- XOR to find unique element
- Power of two
- Bitmask for subsets
- Binary representation
Complexity
Time
O(n) or O(1)
Space
O(1)
Common Problems
Single NumberNumber of 1 BitsCounting BitsMissing NumberPower of Two
Code
# Find single number (all others appear twice)
result = 0
for num in arr:
result ^= num # XOR cancels pairs
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