Week 37 of 43
CP Track
WEEK 37 LEARNING MODULE
Bitwise Operations & Bit Manipulation
Opens Phase 3 (Competitive Programming) with bitwise operators, binary representations, bitmask tricks (LSB, clear bit, power of two), XOR properties, and subset generation.
6 Practice Problems4 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master bitwise operators: AND (`&`), OR (`|`), XOR (`^`), NOT (`~`), Left Shift (`<<`), Right Shift (`>>`).
- ✓Apply bit manipulation idioms: check set bit, set bit, clear bit, toggle bit, extract lowest set bit (`n & -n`), clear lowest set bit (`n & (n - 1)`).
- ✓Leverage XOR algebraic properties ($a \oplus a = 0, a \oplus 0 = a$) for single number problems.
- ✓Generate all $2^n$ subsets iteratively using integer bitmasks.
Core Concepts
Bitwise Primitive Operators
O(1)Performing bit-level logical operations directly in CPU hardware registers in O(1) time.
Lowest Set Bit (LSB) Extraction
O(1)Using two's complement identity n & -n to isolate the lowest 1-bit.
Brian Kernighan’s Algorithm
O(set bits)Counting set bits in O(set bits) time by repeatedly executing n = n & (n - 1).
Bitmask Power Set Generation
O(n * 2^n)Iterating integer mask from 0 to 2^n - 1 to represent element inclusions in O(n * 2^n) time.
Algorithms Covered
Brian Kernighan's Bit CountingSingle Number via XORBitmask Subset Generation ($O(2^n)$)Binary Addition SimulationBitmask Equation Matching
Data Structures Applied
Integers / Bitmasks
“The greatest glory in living lies not in never falling, but in rising every time we fall.”
— Nelson Mandela