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UWI Comp2211 - Analysis of Algorithms Cheat Sheet by

This course covers the fundamental concepts of computer algorithms, including time and space complexity analysis, algorithm design techniques, and data structures. Students will learn how to develop efficient algorithms to solve complex problems and how to evaluate their performance. The course requires a strong background in mathematics and programming, and students can expect to spend a significant amount of time studying and practicing algorithms.

Summations - Closed Forms

Summations - Rules

Logarithm Rules

  

Asymptotic Analysis - Common Orders of Growth

Master Theorem Shortcut

Case
Condition
Result
1
k < E
nᴱ
2
k == E
nᴷ lg(n)
3
k > E
nᴷ
 

Fermat's Little Theorem

For any prime p, for any x:
xᵖ ≡ x (mod p)
Altern­ati­vely, for any x ≠ 0:
xᵖ⁻¹ ≡ 1 (mod p)

Mod Operations

(x + y) mod n = ((x mod n) + (y mod n)) mod n
(xy) mod n = ((x mod n) × (y mod n)) mod n
(x − y) mod n = ((x mod n) − (y mod n)) mod n
 

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  • Published: 24th April, 2023

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