Math mind map
Number theory, combinatorics, and arithmetic tricks.
Core idea: Replace simulation with an invariant, identity, or cycle.
Mnemonic: Model → reduce → prove · Cost: Shrink work with structure
Reduce: GCD, primes & factors
Signal: The property is divisibility or repeated common structure.
Move: Use Euclid, sieve candidates once, or enumerate factors only through the square root.
Examples: Greatest Common Divisor, Count Primes, Fraction Addition
Cycle: Modular arithmetic
Signal: Numbers grow huge or states repeat on a fixed clock.
Move: Reduce after each operation; exponentiate by squaring and detect repeated remainders.
Examples: Pow(x,n), Super Pow, Clock Cycles
Bits: XOR & masks
Signal: Boolean membership, cancellation, or a compact subset state fits in bits.
Move: Use XOR for paired cancellation and masks for set, test, and enumerate operations.
Examples: Single Number, Missing Number, Subset Masks
Digits: Base & combinatorics
Signal: The answer follows carry, digit extraction, or direct counting.
Move: Use divmod for representation; count arrangements instead of generating them when possible.
Examples: Add Strings, Happy Number, Pascal Triangle