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Commit 033b6a0a authored by Renato Alves's avatar Renato Alves :seedling:
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No parenthesis needed on return 

In Python, return is a keyword not a function
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%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# Defensive Programming # Defensive Programming
Defensive programming describes concepts and approaches we can use to ensure that... Defensive programming describes concepts and approaches we can use to ensure that...
* Code does what we think it does (i.e. is free of bugs) * Code does what we think it does (i.e. is free of bugs)
* Our programs fail when they should... * Our programs fail when they should...
* ... and do so with informative error messages (throwback to last session) * ... and do so with informative error messages (throwback to last session)
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Let's say we want a function that takes in a list and computes the mean of all elements in that list Let's say we want a function that takes in a list and computes the mean of all elements in that list
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# Assert statement # Assert statement
The simplest tool we have to ensure that our functions are doing what we intend them to do are assert statements The simplest tool we have to ensure that our functions are doing what we intend them to do are assert statements
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def get_sum_of_numbers(alist): def get_sum_of_numbers(alist):
tmp = None tmp = None
for element in alist: for element in alist:
if tmp == None: if tmp == None:
tmp = element tmp = element
else: else:
tmp = tmp + element tmp = tmp + element
return(tmp) return tmp
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([1,2,3,4,5]) get_sum_of_numbers([1,2,3,4,5])
``` ```
%% Output %% Output
15 15
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers(["a", "b", "c", "d", "e"]) get_sum_of_numbers(["a", "b", "c", "d", "e"])
``` ```
%% Output %% Output
'abcde' 'abcde'
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def get_sum_of_numbers(alist): def get_sum_of_numbers(alist):
assert all([isinstance(element, int) for element in alist]), "Not all elements are integers" assert all([isinstance(element, int) for element in alist]), "Not all elements are integers"
tmp = None tmp = None
for element in alist: for element in alist:
if tmp == None: if tmp == None:
tmp = element tmp = element
else: else:
tmp = tmp + element tmp = tmp + element
return(tmp) return tmp
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([1,2,3,4,5]) get_sum_of_numbers([1,2,3,4,5])
``` ```
%% Output %% Output
15 15
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers(["a", "b", "c", "d", "e"]) get_sum_of_numbers(["a", "b", "c", "d", "e"])
``` ```
%% Output %% Output
--------------------------------------------------------------------------- ---------------------------------------------------------------------------
AssertionError Traceback (most recent call last) AssertionError Traceback (most recent call last)
<ipython-input-90-7bd3d4f8528b> in <module> <ipython-input-90-7bd3d4f8528b> in <module>
----> 1 get_sum_of_numbers(["a", "b", "c", "d", "e"]) ----> 1 get_sum_of_numbers(["a", "b", "c", "d", "e"])
<ipython-input-88-a16d13d448b4> in get_sum_of_numbers(alist) <ipython-input-88-a16d13d448b4> in get_sum_of_numbers(alist)
1 def get_sum_of_numbers(alist): 1 def get_sum_of_numbers(alist):
----> 2 assert all([isinstance(element, int) for element in alist]), "Not all elements are integers" ----> 2 assert all([isinstance(element, int) for element in alist]), "Not all elements are integers"
3 tmp = None 3 tmp = None
4 for element in alist: 4 for element in alist:
5 if tmp == None: 5 if tmp == None:
AssertionError: Not all elements are integers AssertionError: Not all elements are integers
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([1,2,3,4,5.01]) get_sum_of_numbers([1,2,3,4,5.01])
``` ```
%% Output %% Output
--------------------------------------------------------------------------- ---------------------------------------------------------------------------
AssertionError Traceback (most recent call last) AssertionError Traceback (most recent call last)
<ipython-input-91-d71b6bf3bcf6> in <module> <ipython-input-91-d71b6bf3bcf6> in <module>
----> 1 get_sum_of_numbers([1,2,3,4,5.01]) ----> 1 get_sum_of_numbers([1,2,3,4,5.01])
<ipython-input-88-a16d13d448b4> in get_sum_of_numbers(alist) <ipython-input-88-a16d13d448b4> in get_sum_of_numbers(alist)
1 def get_sum_of_numbers(alist): 1 def get_sum_of_numbers(alist):
----> 2 assert all([isinstance(element, int) for element in alist]), "Not all elements are integers" ----> 2 assert all([isinstance(element, int) for element in alist]), "Not all elements are integers"
3 tmp = None 3 tmp = None
4 for element in alist: 4 for element in alist:
5 if tmp == None: 5 if tmp == None:
AssertionError: Not all elements are integers AssertionError: Not all elements are integers
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
import numbers import numbers
def get_sum_of_numbers(alist): def get_sum_of_numbers(alist):
assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers" assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers"
tmp = None tmp = None
for element in alist: for element in alist:
if tmp == None: if tmp == None:
tmp = element tmp = element
else: else:
tmp = tmp + element tmp = tmp + element
return(tmp) return tmp
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([1,2,3,4,5.01]) get_sum_of_numbers([1,2,3,4,5.01])
``` ```
%% Output %% Output
15.01 15.01
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([]) get_sum_of_numbers([])
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
import numbers import numbers
def get_sum_of_numbers(alist): def get_sum_of_numbers(alist):
assert len(alist) > 0, "List is empty" assert len(alist) > 0, "List is empty"
assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers" assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers"
tmp = None tmp = None
for element in alist: for element in alist:
if tmp == None: if tmp == None:
tmp = element tmp = element
else: else:
tmp = tmp + element tmp = tmp + element
return(tmp) return tmp
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([]) get_sum_of_numbers([])
``` ```
%% Output %% Output
--------------------------------------------------------------------------- ---------------------------------------------------------------------------
AssertionError Traceback (most recent call last) AssertionError Traceback (most recent call last)
<ipython-input-96-408adf4db5ec> in <module> <ipython-input-96-408adf4db5ec> in <module>
----> 1 get_sum_of_numbers([]) ----> 1 get_sum_of_numbers([])
<ipython-input-95-7d1e398e65a2> in get_sum_of_numbers(alist) <ipython-input-95-7d1e398e65a2> in get_sum_of_numbers(alist)
1 import numbers 1 import numbers
2 def get_sum_of_numbers(alist): 2 def get_sum_of_numbers(alist):
----> 3 assert len(alist) > 0, "List is empty" ----> 3 assert len(alist) > 0, "List is empty"
4 assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers" 4 assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers"
5 tmp = None 5 tmp = None
AssertionError: List is empty AssertionError: List is empty
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# Preconditions, postconditions and invariants # Preconditions, postconditions and invariants
Assertions can be grouped into: Assertions can be grouped into:
* Preconditions, which should be true the computional part of a function * Preconditions, which should be true the computional part of a function
* Postconditions, which should be true afterwards * Postconditions, which should be true afterwards
* (Invariants, which should be true anywhere) * (Invariants, which should be true anywhere)
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
import numbers import numbers
def get_sum_of_numbers(alist): def get_sum_of_numbers(alist):
# Preconditions # Preconditions
assert len(alist) > 0, "List is empty" assert len(alist) > 0, "List is empty"
assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers" assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers"
tmp = None tmp = None
for element in alist: for element in alist:
if tmp == None: if tmp == None:
tmp = element tmp = element
else: else:
tmp = tmp + element tmp = tmp + element
return(tmp) return tmp
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([1,2,3,4,5]) get_sum_of_numbers([1,2,3,4,5])
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def get_sum_of_numbers(alist): def get_sum_of_numbers(alist):
# Preconditions # Preconditions
assert len(alist) > 0, "Cannot compute the mean of nothing" assert len(alist) > 0, "Cannot compute the mean of nothing"
assert all([isinstance(element, int) for element in alist]), "Not all elements of your list are integer" assert all([isinstance(element, int) for element in alist]), "Not all elements of your list are integer"
tmp = None tmp = None
for element in alist: for element in alist:
if tmp == None: if tmp == None:
tmp = element tmp = element
else: else:
tmp = tmp + element tmp = tmp + element
tmp = 'Your code has been visited by an evil spirit!' tmp = 'Your code has been visited by an evil spirit!'
return(tmp) return tmp
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([1, 2, 3]) get_sum_of_numbers([1, 2, 3])
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
import numbers import numbers
def get_sum_of_numbers(alist): def get_sum_of_numbers(alist):
# Preconditions # Preconditions
assert len(alist) > 0, "List is empty" assert len(alist) > 0, "List is empty"
assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers" assert all([isinstance(element, numbers.Number) for element in alist]), "Not all elements are Numbers"
tmp = alist[0] tmp = alist[0]
for element in alist[1:]: for element in alist[1:]:
tmp = tmp + element tmp = tmp + element
tmp = 'Your code has been visited by an evil spirit!' tmp = 'Your code has been visited by an evil spirit!'
# Postcondition # Postcondition
assert isinstance(tmp, numbers.Number), "Your sum isn't numerical..." assert isinstance(tmp, numbers.Number), "Your sum isn't numerical..."
return(tmp) return tmp
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
get_sum_of_numbers([1, 2, 3]) get_sum_of_numbers([1, 2, 3])
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# Test-Driven Development # Test-Driven Development
Some programmers write code and then test that code somehow to be confident enough that it's bug free. Some programmers write code and then test that code somehow to be confident enough that it's bug free.
Other programms create tests and then write code that has to pass these tests in an iterative manner. This approach is called test-driven development. Other programms create tests and then write code that has to pass these tests in an iterative manner. This approach is called test-driven development.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We want to write a function that calculates the largest overlap between numerical ranges. Each numerical range is a two-element tuple specifying the upper and lower boundaries. We want to write a function that calculates the largest overlap between numerical ranges. Each numerical range is a two-element tuple specifying the upper and lower boundaries.
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
![caption](python-overlapping-ranges.png) ![caption](python-overlapping-ranges.png)
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# Single range # Single range
assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
# Two overlapping ranges # Two overlapping ranges
assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0) assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)
# Three overlapping ranges # Three overlapping ranges
assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0)
# What else is missing? # What else is missing?
# Twice the same range # Twice the same range
assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0) assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0)
# Two non-overlapping ranges. What is the desired output? (0, 0)? None? # Two non-overlapping ranges. What is the desired output? (0, 0)? None?
assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None
# More than two non-overlapping ranges. See above. # More than two non-overlapping ranges. See above.
assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None
# Two intervals touching # Two intervals touching
assert range_overlap([(0, 2), (2, 4)]) == None assert range_overlap([(0, 2), (2, 4)]) == None
# empty input? # empty input?
assert range_overlap([]) == None assert range_overlap([]) == None
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def range_overlap(ranges): def range_overlap(ranges):
max_left = ranges[0][0] max_left = ranges[0][0]
min_right = ranges[0][1] min_right = ranges[0][1]
# ranges[2:] returns an empty list if len(ranges) == 1 and nothing is being looped over. # ranges[2:] returns an empty list if len(ranges) == 1 and nothing is being looped over.
for (left, right) in ranges[1:]: for (left, right) in ranges[1:]:
max_left = max(max_left, left) max_left = max(max_left, left)
min_right = min(min_right, right) min_right = min(min_right, right)
return (max_left, min_right) return (max_left, min_right)
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# Single range # Single range
assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
# Two overlapping ranges # Two overlapping ranges
assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0) assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)
# Three overlapping ranges # Three overlapping ranges
assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0)
# What else is missing? # What else is missing?
# Twice the same range # Twice the same range
assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0) assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0)
# Two non-overlapping ranges. What is the desired output? (0, 0)? None? # Two non-overlapping ranges. What is the desired output? (0, 0)? None?
assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None
# More than two non-overlapping ranges. See above. # More than two non-overlapping ranges. See above.
assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None
# Two touching intervals # Two touching intervals
assert range_overlap([(0, 2), (2, 4)]) == None assert range_overlap([(0, 2), (2, 4)]) == None
# empty input? # empty input?
assert range_overlap([]) == None assert range_overlap([]) == None
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def range_overlap(ranges): def range_overlap(ranges):
max_left = ranges[0][0] max_left = ranges[0][0]
min_right = ranges[0][1] min_right = ranges[0][1]
# ranges[2:] returns an empty list if len(ranges) == 0 and nothing is being looped over. # ranges[2:] returns an empty list if len(ranges) == 0 and nothing is being looped over.
for (left, right) in ranges[1:]: for (left, right) in ranges[1:]:
max_left = max(max_left, left) max_left = max(max_left, left)
min_right = min(min_right, right) min_right = min(min_right, right)
if max_left > min_right: if max_left > min_right:
return(None) return(None)
return (max_left, min_right) return (max_left, min_right)
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# Single range # Single range
assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
# Two overlapping ranges # Two overlapping ranges
assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0) assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)
# Three overlapping ranges # Three overlapping ranges
assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0)
# What else is missing? # What else is missing?
# Twice the same range # Twice the same range
assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0) assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0)
# Two non-overlapping ranges. What is the desired output? (0, 0)? None? # Two non-overlapping ranges. What is the desired output? (0, 0)? None?
assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None
# More than two non-overlapping ranges. See above. # More than two non-overlapping ranges. See above.
assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None
# Two touching intervals # Two touching intervals
assert range_overlap([(0, 2), (2, 4)]) == None assert range_overlap([(0, 2), (2, 4)]) == None
# empty input? # empty input?
assert range_overlap([]) == None assert range_overlap([]) == None
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def range_overlap(ranges): def range_overlap(ranges):
max_left = ranges[0][0] max_left = ranges[0][0]
min_right = ranges[0][1] min_right = ranges[0][1]
# ranges[2:] returns an empty list if len(ranges) == 1 and nothing is being looped over. # ranges[2:] returns an empty list if len(ranges) == 1 and nothing is being looped over.
for (left, right) in ranges[1:]: for (left, right) in ranges[1:]:
max_left = max(max_left, left) max_left = max(max_left, left)
min_right = min(min_right, right) min_right = min(min_right, right)
if max_left >= min_right: if max_left >= min_right:
return(None) return(None)
return (max_left, min_right) return (max_left, min_right)
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# Single range # Single range
assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
# Two overlapping ranges # Two overlapping ranges
assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0) assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)
# Three overlapping ranges # Three overlapping ranges
assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0)
# What else is missing? # What else is missing?
# Twice the same range # Twice the same range
assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0) assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0)
# Two non-overlapping ranges. What is the desired output? (0, 0)? None? # Two non-overlapping ranges. What is the desired output? (0, 0)? None?
assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None
# More than two non-overlapping ranges. See above. # More than two non-overlapping ranges. See above.
assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None
# Two touching intervals # Two touching intervals
assert range_overlap([(0, 2), (2, 4)]) == None assert range_overlap([(0, 2), (2, 4)]) == None
# empty input? # empty input?
assert range_overlap([]) == None assert range_overlap([]) == None
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
def range_overlap(ranges): def range_overlap(ranges):
if len(ranges) == 0: if len(ranges) == 0:
return(None) return(None)
max_left = ranges[0][0] max_left = ranges[0][0]
min_right = ranges[0][1] min_right = ranges[0][1]
# ranges[2:] returns an empty list if len(ranges) == 1 and nothing is being looped over. # ranges[2:] returns an empty list if len(ranges) == 1 and nothing is being looped over.
for (left, right) in ranges[1:]: for (left, right) in ranges[1:]:
max_left = max(max_left, left) max_left = max(max_left, left)
min_right = min(min_right, right) min_right = min(min_right, right)
if max_left >= min_right: if max_left >= min_right:
return(None) return(None)
return (max_left, min_right) return (max_left, min_right)
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
# Single range # Single range
assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
# Two overlapping ranges # Two overlapping ranges
assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0) assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)
# Three overlapping ranges # Three overlapping ranges
assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0) assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0)
# What else is missing? # What else is missing?
# Twice the same range # Twice the same range
assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0) assert range_overlap([(0, 2), (0, 2)]) == (0.0, 2.0)
# Two non-overlapping ranges. What is the desired output? (0, 0)? None? # Two non-overlapping ranges. What is the desired output? (0, 0)? None?
assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0) ]) == None
# More than two non-overlapping ranges. See above. # More than two non-overlapping ranges. See above.
assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None assert range_overlap([ (0.1, 1.0), (3.0, 4.0), (10, 12) ]) == None
# Two touching intervals # Two touching intervals
assert range_overlap([(0, 2), (2, 4)]) == None assert range_overlap([(0, 2), (2, 4)]) == None
# empty input? # empty input?
assert range_overlap([]) == None assert range_overlap([]) == None
``` ```
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