cs exam 2 review slides
what is the basic process of quicksort
- pick pivot - move all numbers less than pivot to beginning - move all numbers greater or equal to pivot to end - quicksort the numbers less than - quicksort the numbers greater than
why is hash collision a problem
- put keys in slots determined by hash function - collision means natural choice slot is taken - cannot replace k1 with k2 because the jeys are differeny - so where do we put k2
best and average case time complexity of quicksort
O n log n
what is the time complexity for mergesort
O n log n
what is the time complexity of recursion
O(2^n)
a tree of function calls is a single chain of length at most what time
O(log n)
what is the timing of insertion sort if the array is sorted or exactly one item is out of place
O(n)
best-case performance of bubble sort
O(n) comparisons, O(1) swaps
what does memoization do to time complexity
O(n) memoization
worst case performance of bubble sort
O(n2) comparisons and swaps
worst case time complexity of quick sort
O(n2) when list is sorted or reverse sorted order
best case performance of insertion sort
On comparisons , O1 swaps
what is the timing for merging
On time because we only need to do a comparison and some assignment for each item that gets added to the final list
average performance of bubble sort
On2 comparisons and swaps
average performance of insertion sort
On2 comparisons and swaps
worst case performance of insertion sort
On2 comparisons and swaps
best case performance of selection sort
On2 comparisons, O1 swaps
average performance of selection sort
On2 comparisons, On swaps
worst case performance of selection sort
On2 comparisons, On swaps
what does having a greedy algorithm mean
algorithm picls the best solution at the moment without regard for consequences - picls the best immediate output, but does not consider the big picture
what is a greedy algorithm
algorithmic strategy makes the best optimal choice at each small stage with goal of eventually leading to a globally optimum solution
what is mapping
association between two sets of things - key value pairs
running time for quick select
average - On worst - On2 but by random pivot, worst case can be avoided in most cases
what is one the most important things to have in recursive function
base case - where recursion stops
what are hashable objects
bool , int, long, float, string, tuple
how to use recursion in a function
call function inside of function
what is a hash collision
case when two different keys have the same hash value
what is memoization recursion
collapse repeated nodes and don't do the same work twice - but otherwise treat it like the same recursive algorithm
what is separate chaining
collisions are resolved by storing all colliding keys in the same slot (using list or some other data structure)
what is one of several powerful techniques for algorithm design
divide and conquer
divide and conquer paradigm includes three steps
divide the problem into subproblems til a base base conquer the subproblems by solving recursively combine subproblem solutions
the mapping between a key and bucket is alled
hash function
the information to be retrieved in stored in a ________ which is best thought of as an array of m locations called ______
hash table buckets
python hash()
hash(object) - only takes one parameter - object whose hash value is to be returned - only immutable objects can be hashed
what is rehashing
increase the number of buckets - not just by appending more, but have to reinsert all the items in mapping so that they can be found when we next get them
what is different about quickselect
instead of recursive into both sides, quickselect only recurses into one side - the side with the element it is searching for
what is insertion sort
iterates over a progressively growing sorted section of the list - bubbles the next unsorted item into place - like deck of cards
what is the basic definition of what bubble sort does
iterates over every pair in collection, swaps out of order pairs
what is the basic definition of selection sort
iterates over every unsorted item in collection, selects the next biggest(or smallest)
what is the first step of merge sort
keep tract of smallest element in each sorted half - insert smallest of two elements into temporary array - repeat until done
how long would the time be if we used slicing
linear time
what are non hashable objects
lists, sets, dictionary
what does the load factor do
measure that decides when to increase the hashmap capacity to maintain the get() and put() operation complexity of O1
does a greedy strategy produce an optimal solution in many problems?
no
why is binary search time O(log n)
number of times you can cut n in half before it gets down to 1
what is recursion
problem solving technique that involves breaking up a problem into smaller instances of the same problem (also called subproblems) until we get a small enough subproblem having a trivial solution
what is the time to store and retrive data
proportional to the time to compute the hash function
what is load factor
ratio of number of entries in the table to the table size
what is better about timing of selection sort than bubble sort
selection sort is always performed at most On swaps no matter how the input list is arranged
what is a strategy to handle hash collision
separate chaining(open hashing)
what is the main idea of insertion sort
sort as you go
what is tabulation (iterative)
step 1: identify solution to problem with respect to smaller subproblems step 2: bottom up - start with solutions to smallest problems and build solutions to the larger problems
what x calls, what items have been sorted using bubble sort
the last x items
after x calls, how many items have been sorted using selection sort
the last x items are sorted and in their final position
after x calls what items are sorted for insertion sort
the last x items are sorted relative to each other
what is the best case scenario for using bubble sort
the list is already sorted
what is the most direct application of the divide and conquer paradigm to the sorting problem
the mergesort algorithm
what does it mean that keys must be unique
there can only be one value associated with a given key
what is quickselect
uses the same overall approach as quicksort - select one element as pivot - partition data in two based on pivot
what is the main idea of the selection. sort
with every inner loop, select the next highest item and move it to the end
