Cheatography

# hopefullygood Cheat Sheet by noxlock

### 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]  ⠀⠀⠀ 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