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Bases

0x0F > 0000 1111
Convert by each byte for bitstr­ings.

1100 + 11 =
1100 + 0011
Pad from the left.

0x0F + 0x0A
15 + 10 = 25

REMEMBER TO CONVERT BASES BACK UNLESS STATED OTHERWISE

Logic

p
implies
q
0
0
1
0
1
1
1
0
0
1
1
1
 
p
or
q
0
0
0
0
1
1
1
0
1
1
1
1
 
p
and
q
0
0
0
0
1
0
1
0
0
1
1
1
 

Sets

Sets have no duplic­ates, and are unordered.

set('john, stop')
= {'j', 'o', 'h', 'n', ',' '', 's', 't', 'o', 'p'}
commas and spaces count as characters

A = {j, o, h, n}, B = {s, t, o , p}

A ⋃ B = {j, o, h, n, s, t , o, p}

A ⋂ B = {o}

A - B = {j, h, n}

Symdiff = A ⋃ B - A ⋂ B =
{j, h, n, s, t, p}
= XOR

Graphs

For (v, w) ∈ E => (w, v) ∈ E to be true...
It must be an undirected graph.
(v,w) is an edge in the set of all edges E

Trees are graphs but cannot have cycles.

Edge list: (NODE, COST, NODE)
 

Big O

Most Efficient
O(1)
O(logn)
O(n)
O(nlogn)
O(n^2)
O(n!)
Least Efficient

logn is hopping halfway between

Functions

Domain = Source­/Left
Range = Result­/Right

A relation can be thought of as a set that contains every pair which maps from
an element in the domain to an element in the range.

For a function, every element in the range is mapped to from a
unique element in the domain. This is to say, that an element on the left of this diagram can ONLY map to ONE
element on the right.
 

Matrices

1 x 2 2 x 1
[5, 7] [3]
⠀⠀⠀[4]

If the two inside numbers are the same, dot product can be performed, the resulting matrix is the rows x column

Relations

Domain­/Range is the same
RELATIONS CAN MAP MULTIPLE DOMAIN ELEMENTS TO A RANGE ELEMENT

Transitive
Triangle line.
I'm taller than Pramod, who is taller than Alex, therefore, I'm taller than Alex.
x>y, y>z => x>z

Reflexive
Diagonal line
I know myself
x=x

Symmetric
Diagonal with identical results mirrored.
They're sitting across from me, therefore I'm sitting across from them.
x+y /2 = y => x=y
 

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