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Factors of a number (#1493)
* 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
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himanshujain171
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Christian Clauss
Christian Clauss
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f8e97aa597
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@ -1,7 +1,6 @@
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"""
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Binomial Heap
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Reference: Advanced Data Structures, Peter Brass
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Binomial Heap
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Reference: Advanced Data Structures, Peter Brass
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"""
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@ -10,7 +9,7 @@ class Node:
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Node in a doubly-linked binomial tree, containing:
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- value
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- size of left subtree
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- link to left, right and parent nodes
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- link to left, right and parent nodes
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"""
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def __init__(self, val):
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@ -23,8 +22,8 @@ class Node:
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def mergeTrees(self, other):
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"""
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In-place merge of two binomial trees of equal size.
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Returns the root of the resulting tree
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In-place merge of two binomial trees of equal size.
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Returns the root of the resulting tree
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"""
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assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"
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@ -47,83 +46,79 @@ class Node:
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class BinomialHeap:
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"""
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Min-oriented priority queue implemented with the Binomial Heap data
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structure implemented with the BinomialHeap class. It supports:
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r"""
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Min-oriented priority queue implemented with the Binomial Heap data
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structure implemented with the BinomialHeap class. It supports:
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- Insert element in a heap with n elemnts: Guaranteed logn, amoratized 1
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- Merge (meld) heaps of size m and n: O(logn + logm)
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- Delete Min: O(logn)
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- Delete Min: O(logn)
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- Peek (return min without deleting it): O(1)
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Example:
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Create a random permutation of 30 integers to be inserted and
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19 of them deleted
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>>> import numpy as np
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>>> permutation = np.random.permutation(list(range(30)))
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Create a Heap and insert the 30 integers
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__init__() test
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>>> first_heap = BinomialHeap()
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Example:
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30 inserts - insert() test
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>>> for number in permutation:
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... first_heap.insert(number)
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Size test
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>>> print(first_heap.size)
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30
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Deleting - delete() test
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>>> for i in range(25):
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... print(first_heap.deleteMin(), end=" ")
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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
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Create a random permutation of 30 integers to be inserted and 19 of them deleted
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>>> import numpy as np
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>>> permutation = np.random.permutation(list(range(30)))
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Create a new Heap
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>>> second_heap = BinomialHeap()
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>>> vals = [17, 20, 31, 34]
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>>> for value in vals:
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... second_heap.insert(value)
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The heap should have the following structure:
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17
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/ \
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# 31
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/ \
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20 34
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/ \ / \
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# # # #
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preOrder() test
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>>> print(second_heap.preOrder())
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[(17, 0), ('#', 1), (31, 1), (20, 2), ('#', 3), ('#', 3), (34, 2), ('#', 3), ('#', 3)]
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printing Heap - __str__() test
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>>> print(second_heap)
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17
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-#
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-31
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--20
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---#
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---#
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--34
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---#
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---#
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Create a Heap and insert the 30 integers
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__init__() test
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>>> first_heap = BinomialHeap()
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mergeHeaps() test
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>>> merged = second_heap.mergeHeaps(first_heap)
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>>> merged.peek()
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17
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values in merged heap; (merge is inplace)
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>>> while not first_heap.isEmpty():
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... print(first_heap.deleteMin(), end=" ")
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17 20 25 26 27 28 29 31 34
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30 inserts - insert() test
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>>> for number in permutation:
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... first_heap.insert(number)
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Size test
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>>> print(first_heap.size)
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30
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Deleting - delete() test
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>>> for i in range(25):
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... print(first_heap.deleteMin(), end=" ")
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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
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Create a new Heap
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>>> second_heap = BinomialHeap()
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>>> vals = [17, 20, 31, 34]
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>>> for value in vals:
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... second_heap.insert(value)
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The heap should have the following structure:
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17
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/ \
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# 31
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/ \
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20 34
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/ \ / \
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# # # #
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preOrder() test
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>>> print(second_heap.preOrder())
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[(17, 0), ('#', 1), (31, 1), (20, 2), ('#', 3), ('#', 3), (34, 2), ('#', 3), ('#', 3)]
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printing Heap - __str__() test
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>>> print(second_heap)
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17
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-#
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-31
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--20
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---#
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---#
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--34
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---#
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---#
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mergeHeaps() test
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>>> merged = second_heap.mergeHeaps(first_heap)
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>>> merged.peek()
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17
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values in merged heap; (merge is inplace)
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>>> while not first_heap.isEmpty():
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... print(first_heap.deleteMin(), end=" ")
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17 20 25 26 27 28 29 31 34
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"""
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def __init__(self, bottom_root=None, min_node=None, heap_size=0):
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@ -133,8 +128,8 @@ class BinomialHeap:
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def mergeHeaps(self, other):
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"""
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In-place merge of two binomial heaps.
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Both of them become the resulting merged heap
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In-place merge of two binomial heaps.
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Both of them become the resulting merged heap
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"""
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# Empty heaps corner cases
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@ -209,7 +204,7 @@ class BinomialHeap:
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def insert(self, val):
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"""
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insert a value in the heap
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insert a value in the heap
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"""
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if self.size == 0:
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self.bottom_root = Node(val)
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@ -251,7 +246,7 @@ class BinomialHeap:
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def peek(self):
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"""
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return min element without deleting it
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return min element without deleting it
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"""
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return self.min_node.val
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@ -260,7 +255,7 @@ class BinomialHeap:
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def deleteMin(self):
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"""
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delete min element and return it
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delete min element and return it
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"""
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# assert not self.isEmpty(), "Empty Heap"
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@ -363,9 +358,9 @@ class BinomialHeap:
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def preOrder(self):
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"""
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Returns the Pre-order representation of the heap including
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values of nodes plus their level distance from the root;
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Empty nodes appear as #
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Returns the Pre-order representation of the heap including
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values of nodes plus their level distance from the root;
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Empty nodes appear as #
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"""
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# Find top root
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top_root = self.bottom_root
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@ -378,7 +373,7 @@ class BinomialHeap:
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def __traversal(self, curr_node, preorder, level=0):
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"""
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Pre-order traversal of nodes
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Pre-order traversal of nodes
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"""
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if curr_node:
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preorder.append((curr_node.val, level))
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@ -389,8 +384,8 @@ class BinomialHeap:
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def __str__(self):
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"""
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Overwriting str for a pre-order print of nodes in heap;
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Performance is poor, so use only for small examples
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Overwriting str for a pre-order print of nodes in heap;
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Performance is poor, so use only for small examples
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"""
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if self.isEmpty():
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return ""
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