fundamental of algorithms lecture 1 notes

{a0,a1,…,an-1}

Denotes a set of elements

X = {}

denotes an empty set or list

∈

denotes a variable or value in an element of a given set

∉

denotes a variable or value is not an element of a given set

⊆

denotes a given variable or value or set is a subset of a given set

⊂

denotes a given variable or value or set is a proper subset of a given set

(x,y)

denotes a pair of values

(X0,x1,….,xn-1)

denotes an ordered n tuple or list

|x|

denotes the size of a given set or list x

y[I]

denotes the ith element of a given list y where I = 0, 1…., |y| - 1

⌊π⌋

denotes floor value of a given value or variable

⌈π⌉

smallest integer greater than or equal to x

Mod ( % )

remainder after one integer is divided by another

Σ

finite non empty set

Lexicographic order

order on strings induced by order on letter and denoted by the same symbol

log(a) + log(b)

log(ab)

log(a) - log(b)

log(a/b)

log(n^k)

k log(n)

log(2^n)

n

2^log(n)

n