From ea2aa8d2a670af4717a23c8099290258d87e6e6c Mon Sep 17 00:00:00 2001 From: Medium Fries Date: Fri, 15 Mar 2019 01:26:26 -0700 Subject: [PATCH] yote --- 370/.gitignore | 1 + 370/notes/1.md | 6 ++++ 370/notes/2.md | 13 +++++++ 370/notes/adj-list.md | 38 +++++++++++++++++++++ 370/notes/avl-trees.md | 32 ++++++++++++++++++ 370/notes/big-o.md | 60 +++++++++++++++++++++++++++++++++ 370/notes/complex.md | 27 +++++++++++++++ 370/notes/graphs.md | 3 ++ 370/notes/sorts.md | 20 +++++++++++ 370/notes/space.md | 16 +++++++++ 370/notes/tries.md | 20 +++++++++++ 370/past-midterms/m1.md | 57 +++++++++++++++++++++++++++++++ 370/past-midterms/midterm1.pdf | Bin 0 -> 116708 bytes 370/samples/adj-matrix.py | 0 370/samples/graph.py | 53 +++++++++++++++++++++++++++++ 370/samples/tree.py | 37 ++++++++++++++++++++ 370/samples/trie.py | 32 ++++++++++++++++++ 17 files changed, 415 insertions(+) create mode 100644 370/.gitignore create mode 100644 370/notes/1.md create mode 100644 370/notes/2.md create mode 100644 370/notes/adj-list.md create mode 100644 370/notes/avl-trees.md create mode 100644 370/notes/big-o.md create mode 100644 370/notes/complex.md create mode 100644 370/notes/graphs.md create mode 100644 370/notes/sorts.md create mode 100644 370/notes/space.md create mode 100644 370/notes/tries.md create mode 100644 370/past-midterms/m1.md create mode 100644 370/past-midterms/midterm1.pdf create mode 100644 370/samples/adj-matrix.py create mode 100755 370/samples/graph.py create mode 100644 370/samples/tree.py create mode 100644 370/samples/trie.py diff --git a/370/.gitignore b/370/.gitignore new file mode 100644 index 0000000..d9568ca --- /dev/null +++ b/370/.gitignore @@ -0,0 +1 @@ +*swp diff --git a/370/notes/1.md b/370/notes/1.md new file mode 100644 index 0000000..a48d448 --- /dev/null +++ b/370/notes/1.md @@ -0,0 +1,6 @@ +# lec1 +> trees & tree heaps +> also: ilearn still busted but theres a survey to fill out + +bin search trees +max/min/heap trees diff --git a/370/notes/2.md b/370/notes/2.md new file mode 100644 index 0000000..6425e74 --- /dev/null +++ b/370/notes/2.md @@ -0,0 +1,13 @@ +# Divide and Conquer + +Make big problem into smaller problems to solve + +## Merge Sort + +_yote_ + +1. find midpoint of list +2. split into two smaller lists +3. keep splitting smaller lists until we have a bunch of 1/2 size lists +4. sort each using the _smaller_ already sorted values against each other into a new sub-list +5. combine and sort each thing diff --git a/370/notes/adj-list.md b/370/notes/adj-list.md new file mode 100644 index 0000000..cbd3ad9 --- /dev/null +++ b/370/notes/adj-list.md @@ -0,0 +1,38 @@ +# Adjacency list + +Imagine 8 nodes with no connections + +To store this data in an _adjacency list_ we need __n__ items to store them. +We'll have 0 __e__dges however so in total our space is (n+e) == (n) + +# Adjacency matrix + +space: O(n^2) +The convention for notation btw is [x,y] meaning: + * _from x to y_ + +# Breadth first search + +add neighbors of current to queue +go through current's neighbors and add their neighbors to queue +add neighbor's neighbors + keep going until there are no more neighbors to add +go through queue and start popping members out of the queue + +# Depth first search + +Here we're going deeper into the neighbors + +_once we have a starting point_ + +_available just means that node has a non-visited neighbor_ +if available go to a neighbor +if no neighbors available visit +goto 1 + +# Kahn Sort + + +# Graph Coloring + +When figuring out how many colors we need for the graph, we should note the degree of the graph diff --git a/370/notes/avl-trees.md b/370/notes/avl-trees.md new file mode 100644 index 0000000..53832ac --- /dev/null +++ b/370/notes/avl-trees.md @@ -0,0 +1,32 @@ +# Self balancing trees aka AVL trees + +_time complexity will be in terms of height_ + +> Height: + distance from nulls after leaves + * impl: _root will typically have the largest height value_ + +> Balance: + | left_height - right_height | + we can discard the || if we want negative balance vals but it really shouldn't matter + basically: we want the balance for each node to be 1 or 0. + +# Self balancing part + +We maintain balance through the tree's lifetime as we insert/delete things into the tree + +> Insertion/Deletion + * just like BST but we balance starting from the new node + +# Restoring balance + +There are 4 special cases when dealing with restoring balance: + + 1. left-left + 2. left-right + 3. right-left + 4. right-right + +# Tries + + diff --git a/370/notes/big-o.md b/370/notes/big-o.md new file mode 100644 index 0000000..a77eff7 --- /dev/null +++ b/370/notes/big-o.md @@ -0,0 +1,60 @@ +# Calculating Big O + +Suppose we have the following function + +``` +func(x): + if cond1 + O(n^2) + elif cond2 + O(n) + else + O(1) +``` + +How do we define the _average_ time complexity: +* any input which isn't setup to be _special_ + 1. linear search which always finds the first elementO(1) + 2. linear search that doen't find anything/last elementO(n) + +With linear searches: finding an average item in the middle(somwhere) we have to cover: + * x% of the n size list + +Since we drop the constants in time complexity expressions we thus end up with O(n). + +## Heap Sort + +Time Complexity Exercise + +* Best: +* Average: +* Worst: +* Space: + +## Insertion Sort + +Time Complexity Exercise + +* Best: + * Already sorted meaning we go through the whole list once + * O(n) - because we'll do the check into our left sub-list but we don't go into it leaving us as constant time spent per item ie c\*n + +* Average: + * Pretty close to n^2 just for the sake of + * O(n^2) + +* Worst: + * Going through the whole list sorting everything(backwards) + * O(n^2) + + * must go through N items for each item +* Space: + +# Notation + +Time Complexity: O(n) + +Space Complexity: OMEGA(n) + +Both Complexity: THETA(n) + * such a complexity only exists if O(n) == OMEGA(n) diff --git a/370/notes/complex.md b/370/notes/complex.md new file mode 100644 index 0000000..1492b96 --- /dev/null +++ b/370/notes/complex.md @@ -0,0 +1,27 @@ +# Complexities + +yote we talkin about space and time complexity + +* Space + +How much space this shit takin up + +* Time + +How fast something it's gonna take + +* Both time/space complexity notation + +_O(?)_: this notation is used for both space and time complexity + +# Scale of Complexity + +O(n) we refer as a linear because the higheset order exponent is /1/ + +The higher the max order of the expression the higher order the overall complexity(duh). + +Non-polynomial expressions are just non-polynomial expressions(yote). + +In other words the part most people care about is the highest order exponential value in the function/expression, since everything else _will_ be faster than that. + +If you want to jam jargon in there go ahead but don't overthink this tbh famalamasham. diff --git a/370/notes/graphs.md b/370/notes/graphs.md new file mode 100644 index 0000000..06708cf --- /dev/null +++ b/370/notes/graphs.md @@ -0,0 +1,3 @@ +# Graph + +_First of a few pages on graphs_ diff --git a/370/notes/sorts.md b/370/notes/sorts.md new file mode 100644 index 0000000..ba15ccc --- /dev/null +++ b/370/notes/sorts.md @@ -0,0 +1,20 @@ +# Cheatsheet for sorts + +_using pythonic terminology for these cases_ + +> Bubble + * take the largest value and buble it to the top/front of the list + +> Insertion + +> Selection + * take smallest value and drop it to the front + +> Merge + * split the hell out of things and sort from the inside out + * goes from side to side + +> Heap + * grab max item and append it to a heap + +> Quick diff --git a/370/notes/space.md b/370/notes/space.md new file mode 100644 index 0000000..7e305b4 --- /dev/null +++ b/370/notes/space.md @@ -0,0 +1,16 @@ +# Space complexity + +With function calls there is explicit space used. + +Implicit space used is about how much work is done to take up space + +# Binary recursive search + +> Explicit space: O(c) + +This is the amount of space taken per call. +We know how much space has to be allocated every call so we can say it would likely be constant + +> Implicit: O(log(n)) + +Because again we will likely take up log(n) times to reach our destination an this comes from our rekked stackspace. diff --git a/370/notes/tries.md b/370/notes/tries.md new file mode 100644 index 0000000..2a9442d --- /dev/null +++ b/370/notes/tries.md @@ -0,0 +1,20 @@ +# Tries - Prefix Trees(syntax trees in disguise) + +We can build grammers from symbols where symbols follow a set of rules to build on each other. +Kinda like linguistic sytax trees but, exactly the same. +_Individual syntaxes are combined to build grammers combine to build phrases, etc. etc._ + +Instead of symbols we use _prefixes_ as our terminology, to build _words_. +Terminally sequenced symbols are denoted by a _leaf_ flag. + +# Deletion + +We don't actually remove things for trivial cases. +Instead we turn off the leaf flag in the end target node + +if we have /bathe/ and /bathes/ as valid phrases and wanted to remaove /bathe/ from our language + * All we have to do is set the /e/ to off as a valid leaf. + +If instead we wanted to remove /bathes/ instead we would go to /s/ and then set it to off like before. + * The problem now is that /s/ is hanging and it doesn't have any children so we can remove it entirely + * If a toggled off node has children it means that it necessarily is part of a valid prefix so it can not be removed diff --git a/370/past-midterms/m1.md b/370/past-midterms/m1.md new file mode 100644 index 0000000..689b275 --- /dev/null +++ b/370/past-midterms/m1.md @@ -0,0 +1,57 @@ +# Practice things +_just going through the practice midterm problems_ + + +1. Identifying sorting algorithms based on progression(_conceptual_) + +_bubble sort_: the bigger the value = the bigger the bubble + * compare two values from the start always, bubble up the bigger value + keep compmaring two adjacent values till you get to the end of the list + * kinda like gladiator m&m's + +_insertion sort_: we have the left sublist which maintains a ordered state always + * we walk along the unsorted list and try to drop our current value into the currently sorted left-hand sublist. + * Key points: + left hand ordered sublist + +_quick sort_: here we push things up to the top immediately where they are then sorted against the left hand sub-list + +_heap sort_: make a giant heap(list) and just take the largest/smallest value and prepend/append to the """heap""" + +__reponse__: insertion sort +Left side of progression is always sorted while the right isn't +Left side also get progressively larger + +2. How you know if a graph is undirected given a matrix(_code_) + +_empirically_: check the upper right half of the matrix and check if each coord pair is reflected across the main axis + + 1. Take a coords pair value(_say True_) + 2. Flip the (x,y) so we have /x,y/ + 3. If the /x,y/ value is the same as (x,y) then those two nodes are bidrectional(i.e. undirected) + +The _trick_ here is making sure we don't bother check the divisor axis or below by accident. + +3. Binary tree lookup(_code_) + +Recursion is the smollest way of doing this so just go with that. + +4. Quick sort partition(_code_) + + * Just splitting lists again + * Checking for partition results as well + +5. Graph traversal(_code_) + +DFS/BFS is fair game +List/matrix meme allowed so don't even bother with other trash + +6. Emperical Graph Traversal(_conceptual_) + +Time complexity of either dfs/bfs will be /v\*e/ or something like that + +7. 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