Chapter 1: Introduction

General performance tips

Use C++! 80% of comp programmers use it
Use g++ -std=c++11 -O2 -Wall test.cpp -o test
- -O2 is optimizer flag
- -Wall shows warnings
Use #include <bits/stdc++.h>to include all STL
Use ios::sync_with_stdio(0); cin.tie(0); to make cin and cout faster!
Use freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); to set redirect stdout/in
Use macros to do things faster (typedefs, #defines). Kinda advanced.

Arithmetic progression = Sequence of numbers where difference between 2 adjacent is the same.
- Formula: n(a+b)/2 where n = length, a = first num, b = last num
Geometric progression = Sequence of numbers where ratio between 2 adjacent is the same (Ex: 1, 2, 4, 8)
- Formula: (bk-a)/(k-1) where k = constant ratio
Harmonic sum = 1 + (1/2) + (1/3) + ... + (1/n) = O(log₂(n)+1)
\ = difference between sets (i.e. A \ B)
N = natural numbers (1-oo), Z = integers (whole nums), Q = rational nums (nums w/o infinite decimal), R = real nums (any num)
Predicate = something that is T/F based on parameter(s) ex: P(0)
Upside down A = "for all", backwards E = "there is"
There is a closed form for Fibonnaci sequence! Called Binet's formula
A logarithm of x with base b is how many times x needs to be divided by b to get to 1