math bit Pattern
Pattern hubs are for building transferable solving frames. Learn the recognition signals first, then drill state definition, update rules, and edge explanation until the pattern feels stable.
Pattern brief
Recognize first
They expect you to replace repeated subtraction with doubling or left shifts, not brute force loops.
Solve rhythm
State the active state and invariant first, explain how each update preserves them, then pressure-test with counterexamples.
Most common miss
Taking abs(INT_MIN) in a 32-bit type and silently overflowing before the real logic even starts.
Recognition signals
- They expect you to replace repeated subtraction with doubling or left shifts, not brute force loops.
- They are checking whether you know why INT_MIN cannot be safely negated in 32-bit signed arithmetic.
- Clarifies whether negative numbers and zero should return false.
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Taking abs(INT_MIN) in a 32-bit type and silently overflowing before the real logic even starts.
- Not handling zero and negative inputs correctly, returning true incorrectly.
- Checking only n > 0 or n & (n - 1) without verifying bit position can misidentify powers of two as powers of four.
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