The Big O with Python

The Big O with Python
Learn how to analyze code for efﬁciency
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Presented by: Dennis Wainaina
Position: Senior Software Engineer

What’s Big O?
- How your code performs as you process more data
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What’s Big O?
- It’s NOT running time
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What’s Big O?
- General trend of performance over time
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What’s Big O?
- General trend of performance over time
- A way of ranking the efﬁciency of an algorithm
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Why Care?
- Provides a formal way to talk about how your code
performs in comparison to your data
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Why Care?
- Discussing trade-offs between different approaches
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Why Care?
- When you notice your code is slowing down and want
to ﬁnd the bottlenecks
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Why Care?
- When you notice your code is slowing down and want
to ﬁnd the bottlenecks
- INTERVIEWS 😂
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Terminology
- O stands for “Order of”
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Terminology
- O stands for “Order of”
- N represents how much data you got
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Some Examples
Write a function that calculates the sum of integers from 1
to n
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Some Examples
def add_one_to_n(n):
total = 0
i = 1
while i <= n:
total += i
i += 1
return total
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Some Examples
def add_one_to_n_mathematical(n):
return n * (n + 1) / 2
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So, which one is better?
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Instead of timing, we can count the number of operations
performed by each piece of code

Let’s count the steps
return n * (n + 1) / 2
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1 multiplication
1 addition
1 division

return n * (n + 1) / 2
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1 multiplication
1 addition
1 division
3 steps regardless of the
size of n

def add_one_to_n(n):
total = 0
i = 1
while i <= n:
total += i
i += 1
return total
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n additions
1 assignment
1 assignment
n comparisons

- 2n ?
- 3n + 2 ?
- 5n + 2 ?
😩 22

Big O!
- 2n -> O(n)
- 3n + 2 -> O(n)
- 5n + 2 -> O(n)
- O(3) -> O(1)
- O(n + n2
) -> O(n2
)
- O(7n4
+ 2n2
+ 5) -> ???
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Big O!
So, add_one_to_n_mathematical is O(1) and
add_one_to_n is O(n)
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A O(n2
) Example
def pairs(n):
for i in range(n):
for j in range(n):
print(i, j)
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A O(n2
) Example
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def pairs(n):
for i in range(n): O(n)
for j in range(n):
O(n)
print(i, j)

A O(n2
) Example
def pairs(n):
for i in range(n): O(n)
for j in range(n):
O(n)
print(i, j)
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Nested O(n)
operations!!!
O(n * n) = O(n2
)

A O(log n) Example
def binary_search(arr, elem):
start = 0
end = len(arr) - 1
middle = math.floor((start + end) / 2)
while arr[middle] != elem:
if elem < arr[middle]:
end = middle - 1
else:
start = middle + 1
if start >= end:
return -1
middle = math.floor((start + end) / 2)
return middle
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Common Python Operations
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Lists
my_list.appen
d(a)
O(1)
my_list[i] O(1)
val in my_list O(1)
for val in
my_list
O(n)
my_list.sort() O(nlogn)
Sets
my_set.add(va
l)
O(1)
For val in
my_set
O(n)
val in my_set O(1)

Common Python Operations
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Dicts
my_dict[key] = val O(1)
my_dict[key] O(1)
key in my_dict O(1)
for key in my_dict O(n)

The Big O with Python

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