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boruvka.py: A few simplifications and f-strings (#4660)
* boruvka.py: A few simplifications and f-strings Python f-strings simplify the code and [should speed up execution](https://www.scivision.dev/python-f-string-speed). @srkchowdary2000 Your review, please. * updating DIRECTORY.md * fixup! Streamline the test Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
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Christian Clauss
GitHub
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10
DIRECTORY.md
10
DIRECTORY.md
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@ -97,6 +97,7 @@
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* [Peak Signal To Noise Ratio](https://github.com/TheAlgorithms/Python/blob/master/compression/peak_signal_to_noise_ratio.py)
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## Computer Vision
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* [Cnn Classification](https://github.com/TheAlgorithms/Python/blob/master/computer_vision/cnn_classification.py)
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* [Harris Corner](https://github.com/TheAlgorithms/Python/blob/master/computer_vision/harris_corner.py)
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* [Mean Threshold](https://github.com/TheAlgorithms/Python/blob/master/computer_vision/mean_threshold.py)
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@ -300,6 +301,7 @@
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* [Bfs Zero One Shortest Path](https://github.com/TheAlgorithms/Python/blob/master/graphs/bfs_zero_one_shortest_path.py)
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* [Bidirectional A Star](https://github.com/TheAlgorithms/Python/blob/master/graphs/bidirectional_a_star.py)
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* [Bidirectional Breadth First Search](https://github.com/TheAlgorithms/Python/blob/master/graphs/bidirectional_breadth_first_search.py)
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* [Boruvka](https://github.com/TheAlgorithms/Python/blob/master/graphs/boruvka.py)
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* [Breadth First Search](https://github.com/TheAlgorithms/Python/blob/master/graphs/breadth_first_search.py)
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* [Breadth First Search 2](https://github.com/TheAlgorithms/Python/blob/master/graphs/breadth_first_search_2.py)
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* [Breadth First Search Shortest Path](https://github.com/TheAlgorithms/Python/blob/master/graphs/breadth_first_search_shortest_path.py)
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@ -349,6 +351,7 @@
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* [Djb2](https://github.com/TheAlgorithms/Python/blob/master/hashes/djb2.py)
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* [Enigma Machine](https://github.com/TheAlgorithms/Python/blob/master/hashes/enigma_machine.py)
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* [Hamming Code](https://github.com/TheAlgorithms/Python/blob/master/hashes/hamming_code.py)
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* [Luhn](https://github.com/TheAlgorithms/Python/blob/master/hashes/luhn.py)
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* [Md5](https://github.com/TheAlgorithms/Python/blob/master/hashes/md5.py)
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* [Sdbm](https://github.com/TheAlgorithms/Python/blob/master/hashes/sdbm.py)
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* [Sha1](https://github.com/TheAlgorithms/Python/blob/master/hashes/sha1.py)
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@ -421,10 +424,12 @@
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* [Binomial Distribution](https://github.com/TheAlgorithms/Python/blob/master/maths/binomial_distribution.py)
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* [Bisection](https://github.com/TheAlgorithms/Python/blob/master/maths/bisection.py)
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* [Ceil](https://github.com/TheAlgorithms/Python/blob/master/maths/ceil.py)
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* [Check Valid Ip Address](https://github.com/TheAlgorithms/Python/blob/master/maths/check_valid_ip_address.py)
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* [Chudnovsky Algorithm](https://github.com/TheAlgorithms/Python/blob/master/maths/chudnovsky_algorithm.py)
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* [Collatz Sequence](https://github.com/TheAlgorithms/Python/blob/master/maths/collatz_sequence.py)
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* [Combinations](https://github.com/TheAlgorithms/Python/blob/master/maths/combinations.py)
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* [Decimal Isolate](https://github.com/TheAlgorithms/Python/blob/master/maths/decimal_isolate.py)
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* [Double Factorial Recursive](https://github.com/TheAlgorithms/Python/blob/master/maths/double_factorial_recursive.py)
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* [Entropy](https://github.com/TheAlgorithms/Python/blob/master/maths/entropy.py)
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* [Euclidean Distance](https://github.com/TheAlgorithms/Python/blob/master/maths/euclidean_distance.py)
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* [Euclidean Gcd](https://github.com/TheAlgorithms/Python/blob/master/maths/euclidean_gcd.py)
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@ -539,6 +544,7 @@
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## Other
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* [Activity Selection](https://github.com/TheAlgorithms/Python/blob/master/other/activity_selection.py)
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* [Date To Weekday](https://github.com/TheAlgorithms/Python/blob/master/other/date_to_weekday.py)
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* [Davis–Putnam–Logemann–Loveland](https://github.com/TheAlgorithms/Python/blob/master/other/davis–putnam–logemann–loveland.py)
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* [Dijkstra Bankers Algorithm](https://github.com/TheAlgorithms/Python/blob/master/other/dijkstra_bankers_algorithm.py)
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* [Doomsday](https://github.com/TheAlgorithms/Python/blob/master/other/doomsday.py)
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@ -854,6 +860,7 @@
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* [Counting Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/counting_sort.py)
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* [Cycle Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/cycle_sort.py)
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* [Double Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/double_sort.py)
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* [Exchange Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/exchange_sort.py)
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* [External Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/external_sort.py)
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* [Gnome Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/gnome_sort.py)
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* [Heap Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/heap_sort.py)
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@ -893,6 +900,7 @@
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## Strings
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* [Aho Corasick](https://github.com/TheAlgorithms/Python/blob/master/strings/aho_corasick.py)
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* [Alternative String Arrange](https://github.com/TheAlgorithms/Python/blob/master/strings/alternative_string_arrange.py)
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* [Anagrams](https://github.com/TheAlgorithms/Python/blob/master/strings/anagrams.py)
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* [Autocomplete Using Trie](https://github.com/TheAlgorithms/Python/blob/master/strings/autocomplete_using_trie.py)
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* [Boyer Moore Search](https://github.com/TheAlgorithms/Python/blob/master/strings/boyer_moore_search.py)
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@ -902,6 +910,7 @@
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* [Check Pangram](https://github.com/TheAlgorithms/Python/blob/master/strings/check_pangram.py)
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* [Detecting English Programmatically](https://github.com/TheAlgorithms/Python/blob/master/strings/detecting_english_programmatically.py)
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* [Frequency Finder](https://github.com/TheAlgorithms/Python/blob/master/strings/frequency_finder.py)
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* [Indian Phone Validator](https://github.com/TheAlgorithms/Python/blob/master/strings/indian_phone_validator.py)
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* [Is Palindrome](https://github.com/TheAlgorithms/Python/blob/master/strings/is_palindrome.py)
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* [Jaro Winkler](https://github.com/TheAlgorithms/Python/blob/master/strings/jaro_winkler.py)
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* [Knuth Morris Pratt](https://github.com/TheAlgorithms/Python/blob/master/strings/knuth_morris_pratt.py)
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@ -941,6 +950,7 @@
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* [Instagram Crawler](https://github.com/TheAlgorithms/Python/blob/master/web_programming/instagram_crawler.py)
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* [Instagram Pic](https://github.com/TheAlgorithms/Python/blob/master/web_programming/instagram_pic.py)
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* [Instagram Video](https://github.com/TheAlgorithms/Python/blob/master/web_programming/instagram_video.py)
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* [Random Anime Character](https://github.com/TheAlgorithms/Python/blob/master/web_programming/random_anime_character.py)
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* [Recaptcha Verification](https://github.com/TheAlgorithms/Python/blob/master/web_programming/recaptcha_verification.py)
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* [Slack Message](https://github.com/TheAlgorithms/Python/blob/master/web_programming/slack_message.py)
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* [Test Fetch Github Info](https://github.com/TheAlgorithms/Python/blob/master/web_programming/test_fetch_github_info.py)
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@ -1,11 +1,12 @@
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"""Borůvka's algorithm.
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Determines the minimum spanning tree(MST) of a graph using the Borůvka's algorithm.
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Determines the minimum spanning tree (MST) of a graph using the Borůvka's algorithm.
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Borůvka's algorithm is a greedy algorithm for finding a minimum spanning tree in a
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graph,or a minimum spanning forest in the case of a graph that is not connected.
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connected graph, or a minimum spanning forest if a graph that is not connected.
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The time complexity of this algorithm is O(ELogV), where E represents the number
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of edges, while V represents the number of nodes.
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O(number_of_edges Log number_of_nodes)
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The space complexity of this algorithm is O(V + E), since we have to keep a couple
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of lists whose sizes are equal to the number of nodes, as well as keep all the
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doesn't need to presort the edges or maintain a priority queue in order to find the
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minimum spanning tree.
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Even though that doesn't help its complexity, since it still passes the edges logE
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times, it is a bit more simple to code.
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times, it is a bit simpler to code.
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Details: https://en.wikipedia.org/wiki/Bor%C5%AFvka%27s_algorithm
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"""
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@ -31,13 +32,13 @@ class Graph:
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Arguments:
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num_of_nodes - the number of nodes in the graph
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Attributes:
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m_v - the number of nodes in the graph.
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m_num_of_nodes - the number of nodes in the graph.
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m_edges - the list of edges.
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m_component - the dictionary which stores the index of the component which
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a node belongs to.
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"""
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self.m_v = num_of_nodes
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self.m_num_of_nodes = num_of_nodes
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self.m_edges = []
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self.m_component = {}
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@ -57,7 +58,7 @@ class Graph:
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"""Finds the component index of a given node"""
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if self.m_component[u_node] != u_node:
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for k in self.m_component.keys():
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for k in self.m_component:
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self.m_component[k] = self.find_component(k)
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def union(self, component_size: list, u_node: int, v_node: int) -> None:
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@ -82,22 +83,18 @@ class Graph:
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component_size = []
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mst_weight = 0
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minimum_weight_edge = [-1] * self.m_v
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minimum_weight_edge = [-1] * self.m_num_of_nodes
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# A list of components (initialized to all of the nodes)
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for node in range(self.m_v):
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for node in range(self.m_num_of_nodes):
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self.m_component.update({node: node})
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component_size.append(1)
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num_of_components = self.m_v
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num_of_components = self.m_num_of_nodes
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while num_of_components > 1:
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l_edges = len(self.m_edges)
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for i in range(l_edges):
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u = self.m_edges[i][0]
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v = self.m_edges[i][1]
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w = self.m_edges[i][2]
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for edge in self.m_edges:
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u, v, w = edge
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u_component = self.m_component[u]
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v_component = self.m_component[v]
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@ -113,22 +110,16 @@ class Graph:
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observing right now, we will assign the value of the edge
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we're observing to it"""
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if (
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minimum_weight_edge[u_component] == -1
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or minimum_weight_edge[u_component][2] > w
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):
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minimum_weight_edge[u_component] = [u, v, w]
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if (
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minimum_weight_edge[v_component] == -1
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or minimum_weight_edge[v_component][2] > w
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):
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minimum_weight_edge[v_component] = [u, v, w]
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for component in (u_component, v_component):
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if (
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minimum_weight_edge[component] == -1
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or minimum_weight_edge[component][2] > w
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):
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minimum_weight_edge[component] = [u, v, w]
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for node in range(self.m_v):
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if minimum_weight_edge[node] != -1:
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u = minimum_weight_edge[node][0]
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v = minimum_weight_edge[node][1]
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w = minimum_weight_edge[node][2]
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for edge in minimum_weight_edge:
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if edge != -1:
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u, v, w = edge
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u_component = self.m_component[u]
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v_component = self.m_component[v]
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@ -136,36 +127,19 @@ class Graph:
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if u_component != v_component:
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mst_weight += w
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self.union(component_size, u_component, v_component)
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print(
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"Added edge ["
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+ str(u)
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+ " - "
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+ str(v)
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+ "]\n"
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+ "Added weight: "
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+ str(w)
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+ "\n"
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)
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print(f"Added edge [{u} - {v}]\nAdded weight: {w}\n")
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num_of_components -= 1
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minimum_weight_edge = [-1] * self.m_v
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print("The total weight of the minimal spanning tree is: " + str(mst_weight))
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minimum_weight_edge = [-1] * self.m_num_of_nodes
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print(f"The total weight of the minimal spanning tree is: {mst_weight}")
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def test_vector() -> None:
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"""
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>>> g=Graph(8)
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>>> g.add_edge(0, 1, 10)
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>>> g.add_edge(0, 2, 6)
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>>> g.add_edge(0, 3, 5)
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>>> g.add_edge(1, 3, 15)
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>>> g.add_edge(2, 3, 4)
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>>> g.add_edge(3, 4, 8)
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>>> g.add_edge(4, 5, 10)
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>>> g.add_edge(4, 6, 6)
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>>> g.add_edge(4, 7, 5)
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>>> g.add_edge(5, 7, 15)
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>>> g.add_edge(6, 7, 4)
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>>> g = Graph(8)
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>>> for u_v_w in ((0, 1, 10), (0, 2, 6), (0, 3, 5), (1, 3, 15), (2, 3, 4),
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... (3, 4, 8), (4, 5, 10), (4, 6, 6), (4, 7, 5), (5, 7, 15), (6, 7, 4)):
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... g.add_edge(*u_v_w)
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>>> g.boruvka()
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Added edge [0 - 3]
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Added weight: 5
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