dsa3 min read
Matrix Exponentiation: Fibonacci and Linear Recurrences
Solve linear recurrences like Fibonacci in O(log n) using matrix exponentiation. Essential for DP optimization on large n.
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Number Theory: Perfect Numbers, Abundant, and Digit Problems
Explore digit manipulation, perfect/abundant numbers, Armstrong numbers, and common math interview patterns.
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Combinatorics: nCr, Pascal's Triangle, and Catalan Numbers
Compute combinations nCr efficiently with precomputed factorials, Pascal's triangle for small n, and Catalan numbers for tree/parenthesis counting.
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dsa3 min read
Euler's Totient Function and Applications
Compute Euler's totient phi(n) for cryptography and modular inverse applications. Sieve variant for all values up to n.
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Prime Factorization: Trial Division and Pollard's Rho
Factor integers efficiently with trial division O(sqrt n), SPF sieve O(log n), and understand when each approach is optimal.
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