Big O notation (O) permalink
- for describing the running time of algorithms (how many steps max will it take)
O(n)- on the order of n
🤔 And what's in the opposite end of Big O?
ΩGreek Omega letter used to describe the best-case scenario (Ω of ...)
- They are both approximations
Linear search permalink
- Iterate across the array from left to right, trying to find the target element.
for i from 0 to n-1
If i-th element is "value you are looking for"
Binary search permalink
- Given a sorted array, divide and conquer by systematically eliminating half of the remaining elements (phone book) in the search for the target element.
if no items
if middle item is "value you are looking for"
else if "value you are looking for" < middle item
search left half
else if "value you are looking for" > middle item
search right half
- In C you can't use
==to compare two strings (yes for
intand yes for
- instead you have to use a function like
🤔 What's a hertz?
- something that is done once per second
- if your computer's CPU is 1 gigahertz, that means that it can do 1 billion things at a time
Custom types permalink
🤔 What is a struct? It's a container inside which you can put multiple other data types.
// define the struct
// initialize the array people with length of two
// using the person struct
// assign value
people.name = "Eva";
people.number = "123-456-789";
Selection sort permalink
- Find the smallest unsorted element in an array and swap it with the first unsorted element of that array.
- The amount of work will decrease with each iteration.
- However, you can't short circuit and quit the work even if all the elements are already swapped
for i from 0 to n-1
find smallest item between i'th item and last item
swap the smallest item with the i'th item
Bubble sort permalink
- Swap the adjacent pairs of elements if they are out of order, effectively bubbling larger elements to the right and smaller ones to the left.
Repeat n-1 times
for i from 0 to n-2
if i'th and i+1'th elements out of order
if no swaps
Merge sort permalink
- Split the full array into subarrays, then merge those subarrays back together in the correct order.
- Meaning that in an array of size 8, you'll start with 8 lists of size 1
- You'll need some temporary arrays to help you with sorting, meaning you'll be needing at least twice as much space
if only one item
sort left half of items
sort right half of items
merge sorted halves
Insertion sort permalink
- Proceed once through the array from left to right, shifting elements as necessary to insert each element into its correct place.
🤔 How do the algorithms compare In terms of running time (slowest -> fastest)?
In terms of Big O:
O(n2)bubble sort, selection sort, insertion sort
O(n log n)merge sort
O(log n)binary search
In terms of Ω:
Ω(n log n)merge sort
Ω(n)bubble sort, insertion sort
Ω(1)linear search, binary search
θ Theta permalink
for describing algorithms where
Ω values are the same
θ(n log n)merge sort
A function calling itself.
Classic example is the factorial:
fact(n) = n * fact(n-1)
Every factorial has two cases:
- base case: when triggered, will terminate the recursive process
- recursive case: which is where recursion actually occurs
int fact(int n)
if (n == 1)
// With single line returns, you can take the curly braces away.
return n * fact(n-1)'