Time complexity in Ruby programs
Chennai.rb meet-up 25-june-2016
@h6165
Abhishek Yadav
ரூபீ ப்ரோக்ராமர்
Co-organizer: Chennai.rb
Topics covered
- Search and binary search
- Big O notation
- Time complexity
- Example-2
- Accidentally quadratic
- Space complexity
- Example-3
Search and binary search
## Search an element in the given, sorted array
def search1(arr, input)
i = 0
while i < arr.size do
return i if arr[i] == input
i += 1
end
end
input = 73
arr = [3, 10, 22, 72, 100, 344]
search1(73, arr)
Sequencial search
In the worst case it has to go ever the whole array
Search and binary search
## Search an element in the given, sorted array
def bsearch(arr, input, start=0, finish=arr.size-1)
if start == finish
return arr[start] == input ? start : nil
end
mid = start + (finish - start)/2
case
when input == arr[mid] then return mid
when input < arr[mid] then return bsearch(arr, input, start, mid)
when input > arr[mid] then return bsearch(arr, input, mid+1, finish)
end
end
input = 73
arr = [3, 10, 22, 72, 100, 344]
search1(73, arr)
Binary search
Search and binary search
Binary search
visualization: searching 33
Search and binary search
Binary search
- It has to traverse a tree like path
- In the worst case, it can be depth of the tree
- Which is log(n) : n = array size
- Hence: O(log n)
Big O notation
- Time taken by algorithm is expressed as a function of size of input
-
Sequencial search: O(n)
- For an list sized n, it may have to traverse all the elements.
-
Binary search: O(log n)
- For a list sized n, it may have to traverse upto log n elements.
-
Selection sort: O(n^2)
- It may have to traverse the whole list twice. Hence squared
-
O(1)
- Constant time: doesn't depend on size of input
Selection sort
# Selection sort (very slow on large lists)
a = [9,8,6,1,2,5,4,3,9,50,12,11]
n = a.size - 1
n.times do |i|
index_min = i
(i + 1).upto(n) do |j|
index_min = j if a[j] < a[index_min]
end
# Yep, in ruby I can do that, no aux variable. w00t!
a[i], a[index_min] = a[index_min], a[i] if index_min != i
end
## Credit: https://gist.github.com/brianstorti/953310
Big O notation
- Big-O values may be different with different datasets
- Worst case and average case scenarios must be considered
- Quick-sort has O(nlogn), better than others in worst case
Optimization
- Time complexity can be sometimes improved by using space complexity
- Use the Ruby hash
Optimization
users = User.where(active: true).to_a
## TODO
Quiz
# What is the time complexity here?
def foo(arr)
1.upto(100).each do |i|
1.upto(1000).each do |j|
puts arr[i] + arr[j]
end
end
end
Time and space complexity with Ruby
By Abhishek Yadav
Time and space complexity with Ruby
- 1,215