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Factors of a number (#1493)

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* Factors of a number

* Update factors.py

* Fix mypy issue in basic_maths.py

* Fix mypy error in perceptron.py

* def primes(max: int) -> List[int]:

* Update binomial_heap.py

* Add a space

* Remove a space

* Add a space
This commit is contained in:
himanshujain171 2019-10-30 04:24:31 +05:30 committed by Christian Clauss
parent f8e97aa597
commit 53ff735701
5 changed files with 105 additions and 95 deletions
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169
data_structures/heap/binomial_heap.py
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@ -1,7 +1,6 @@
"""
Binomial Heap
Reference: Advanced Data Structures, Peter Brass
Binomial Heap
Reference: Advanced Data Structures, Peter Brass
"""
@ -10,7 +9,7 @@ class Node:
Node in a doubly-linked binomial tree, containing:
- value
- size of left subtree
- link to left, right and parent nodes
- link to left, right and parent nodes
"""
def __init__(self, val):
@ -23,8 +22,8 @@ class Node:
def mergeTrees(self, other):
"""
In-place merge of two binomial trees of equal size.
Returns the root of the resulting tree
In-place merge of two binomial trees of equal size.
Returns the root of the resulting tree
"""
assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"
@ -47,83 +46,79 @@ class Node:
class BinomialHeap:
"""
Min-oriented priority queue implemented with the Binomial Heap data
structure implemented with the BinomialHeap class. It supports:
r"""
Min-oriented priority queue implemented with the Binomial Heap data
structure implemented with the BinomialHeap class. It supports:
- Insert element in a heap with n elemnts: Guaranteed logn, amoratized 1
- Merge (meld) heaps of size m and n: O(logn + logm)
- Delete Min: O(logn)
- Delete Min: O(logn)
- Peek (return min without deleting it): O(1)
Example:
Create a random permutation of 30 integers to be inserted and
19 of them deleted
>>> import numpy as np
>>> permutation = np.random.permutation(list(range(30)))
Create a Heap and insert the 30 integers
__init__() test
>>> first_heap = BinomialHeap()
Example:
30 inserts - insert() test
>>> for number in permutation:
... first_heap.insert(number)
Size test
>>> print(first_heap.size)
30
Deleting - delete() test
>>> for i in range(25):
... print(first_heap.deleteMin(), end=" ")
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Create a random permutation of 30 integers to be inserted and 19 of them deleted
>>> import numpy as np
>>> permutation = np.random.permutation(list(range(30)))
Create a new Heap
>>> second_heap = BinomialHeap()
>>> vals = [17, 20, 31, 34]
>>> for value in vals:
... second_heap.insert(value)
The heap should have the following structure:
17
/ \
# 31
/ \
20 34
/ \ / \
# # # #
preOrder() test
>>> print(second_heap.preOrder())
[(17, 0), ('#', 1), (31, 1), (20, 2), ('#', 3), ('#', 3), (34, 2), ('#', 3), ('#', 3)]
printing Heap - __str__() test
>>> print(second_heap)
17
-#
-31
--20
---#
---#
--34
---#
---#
Create a Heap and insert the 30 integers
__init__() test
>>> first_heap = BinomialHeap()
mergeHeaps() test
>>> merged = second_heap.mergeHeaps(first_heap)
>>> merged.peek()
17
values in merged heap; (merge is inplace)
>>> while not first_heap.isEmpty():
... print(first_heap.deleteMin(), end=" ")
17 20 25 26 27 28 29 31 34
30 inserts - insert() test
>>> for number in permutation:
... first_heap.insert(number)
Size test
>>> print(first_heap.size)
30
Deleting - delete() test
>>> for i in range(25):
... print(first_heap.deleteMin(), end=" ")
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Create a new Heap
>>> second_heap = BinomialHeap()
>>> vals = [17, 20, 31, 34]
>>> for value in vals:
... second_heap.insert(value)
The heap should have the following structure:
17
/ \
# 31
/ \
20 34
/ \ / \
# # # #
preOrder() test
>>> print(second_heap.preOrder())
[(17, 0), ('#', 1), (31, 1), (20, 2), ('#', 3), ('#', 3), (34, 2), ('#', 3), ('#', 3)]
printing Heap - __str__() test
>>> print(second_heap)
17
-#
-31
--20
---#
---#
--34
---#
---#
mergeHeaps() test
>>> merged = second_heap.mergeHeaps(first_heap)
>>> merged.peek()
17
values in merged heap; (merge is inplace)
>>> while not first_heap.isEmpty():
... print(first_heap.deleteMin(), end=" ")
17 20 25 26 27 28 29 31 34
"""
def __init__(self, bottom_root=None, min_node=None, heap_size=0):
@ -133,8 +128,8 @@ class BinomialHeap:
def mergeHeaps(self, other):
"""
In-place merge of two binomial heaps.
Both of them become the resulting merged heap
In-place merge of two binomial heaps.
Both of them become the resulting merged heap
"""
# Empty heaps corner cases
@ -209,7 +204,7 @@ class BinomialHeap:
def insert(self, val):
"""
insert a value in the heap
insert a value in the heap
"""
if self.size == 0:
self.bottom_root = Node(val)
@ -251,7 +246,7 @@ class BinomialHeap:
def peek(self):
"""
return min element without deleting it
return min element without deleting it
"""
return self.min_node.val
@ -260,7 +255,7 @@ class BinomialHeap:
def deleteMin(self):
"""
delete min element and return it
delete min element and return it
"""
# assert not self.isEmpty(), "Empty Heap"
@ -363,9 +358,9 @@ class BinomialHeap:
def preOrder(self):
"""
Returns the Pre-order representation of the heap including
values of nodes plus their level distance from the root;
Empty nodes appear as #
Returns the Pre-order representation of the heap including
values of nodes plus their level distance from the root;
Empty nodes appear as #
"""
# Find top root
top_root = self.bottom_root
@ -378,7 +373,7 @@ class BinomialHeap:
def __traversal(self, curr_node, preorder, level=0):
"""
Pre-order traversal of nodes
Pre-order traversal of nodes
"""
if curr_node:
preorder.append((curr_node.val, level))
@ -389,8 +384,8 @@ class BinomialHeap:
def __str__(self):
"""
Overwriting str for a pre-order print of nodes in heap;
Performance is poor, so use only for small examples
Overwriting str for a pre-order print of nodes in heap;
Performance is poor, so use only for small examples
"""
if self.isEmpty():
return ""

4
maths/basic_maths.py
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@ -67,10 +67,8 @@ def euler_phi(n: int) -> int:
>>> euler_phi(100)
40
"""
l = prime_factors(n)
l = set(l)
s = n
for x in l:
for x in set(prime_factors(n)):
s *= (x - 1) / x
return int(s)

18
maths/factors.py Normal file
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@ -0,0 +1,18 @@
def factors_of_a_number(num: int) -> list:
"""
>>> factors_of_a_number(1)
[1]
>>> factors_of_a_number(5)
[1, 5]
>>> factors_of_a_number(24)
[1, 2, 3, 4, 6, 8, 12, 24]
>>> factors_of_a_number(-24)
[]
"""
return [i for i in range(1, num + 1) if num % i == 0]
if __name__ == "__main__":
num = int(input("Enter a number to find its factors: "))
factors = factors_of_a_number(num)
print(f"{num} has {len(factors)} factors: {', '.join(str(f) for f in factors)}")

6
maths/prime_numbers.py
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@ -1,9 +1,9 @@
"""Prime numbers calculation."""
from typing import List
def primes(max: int) -> int:
def primes(max: int) -> List[int]:
"""
Return a list of all primes up to max.
Return a list of all primes numbers up to max.
>>> primes(10)
[2, 3, 5, 7]
>>> primes(11)

3
neural_network/perceptron.py
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@ -95,8 +95,7 @@ class Perceptron:
...
>>> perceptron.sort([-0.6508, 0.1097, 4.0009]) # doctest: +ELLIPSIS
('Sample: ', ...)
classification: P1
classification: P...
"""
if len(self.sample) == 0:
raise AttributeError("Sample data can not be empty")