update folder structure
Sean Leishman
parent
b84dd0a187
commit
603f184c61
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# Python
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## Arrays
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- [Count Inversions](arrays/counting_inversions.py)
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- [Majority Element](arrays/majority_element.py)
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- [Rotate Array](arrays/rotate_array.py)
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- [Max Sub Array Sum](arrays/max_sub_array_sum.py)
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## Linked Lists
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- [Doubly](linked_lists/doubly.py)
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- [Singly](linked_lists/singly.py)
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- [Reverse List](linked_lists/reverse-linkedlist.py)
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- [Middle Node](linked_lists/middle-node-linkedlist.py)
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- [Cycle Detection and Removal](linked_lists/cycle-detection-and-removal-linkedlist.py)
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## Dictionaries
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- [Two Sum](dictionaries/two-sum.py)
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## Multiplication
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- [Karatsuba](multiplication/karatsuba_algorithm.py)
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## Recursion
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- [Factorial](recursion/factorial.py)
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- [n-th Fibonacci number](recursion/nth_fibonacci_number.py)
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- [Recursive Insertion Sort](recursion/recursive_insertion_sort.py)
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- [Recursive Sum of n numbers](recursion/recursive-sum-of-n-numbers.py)
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- [GCD by Euclid's Algorithm](recursion/gcd_using_recursion.py)
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- [Levenshtein distance](recursion/levenshtein_distance.py)
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## Scheduling
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- [Interval Scheduling](scheduling/interval_scheduling.py)
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## Searching
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- [Binary Search](searching/binary_search.py)
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- [Jump Search](searching/jump_search.py)
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- [Linear Search](searching/linear_search.py)
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@ -44,6 +50,7 @@
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- [Breath First Search](searching/breadth-first-search.py)
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## Sorting
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- [Bubble Sort](sorting/bubble_sort.py)
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- [Comb Sort](sorting/comb_sort.py)
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- [Count Sort](sorting/count-sort.py)
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- [Merge sort](sorting/merge_sort.py)
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## Strings
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- [Is Good Str](strings/is_good_str.py)
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- [Palindrome](strings/palindrome.py)
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- [Word Count](strings/word_count.py)
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- [Roman to Int](strings/roman-to-int.py)
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## Dynamic Programming
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- [Print Fibonacci Series Up To N-th Term](dynamic_programming/fibonacci_series.py)
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- [Sum Up To N-th Term Of Fibonacci Series](dynamic_programming/fibonacci_series_sum.py)
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- [N-th Term Of Fibonacci Series](dynamic_programming/fibonacci_series_nth_term.py)
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- [Levenshtein distance](dynamic_programming/levenshtein_distance.py)
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## Graphs
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- [Simple Graph](graphs/graph.py)
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- [BFS SEQUENCE](graphs/bfs-sequence.py)
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- [Depth First Search](graphs/depth-first-search.py)
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## Trees
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- [Binary Tree](trees/binary_tree.py)
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- [Binary Search Tree](trees/binary_search_tree.py)
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## Queues
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- [First in First out Queue](queues/fifo-queue.py)
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## Number Theory
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- [Prime Number Checker](number_theory/prime_number.py)
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# The Levenshtein distance (Edit distance) Problem
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# Informally, the Levenshtein distance between two words is
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# the minimum number of single-character edits (insertions, deletions or substitutions)
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# required to change one word into the other.
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def edit_distance(w1, w2):
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"""
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Find edit distance (minimum number of changes) required to convert string w1 to string w2.
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"""
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# For example, the Levenshtein distance between kitten and sitting is 3.
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# The minimal edit script that transforms the former into the latter is:
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m = [[0 if x != 0 else y if y != 0 else x for x in range(len(w2) + 1)] for y in range(len(w1) + 1)]
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# kitten —> sitten (substitution of s for k)
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# sitten —> sittin (substitution of i for e)
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# sittin —> sitting (insertion of g at the end)
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for i in range(1,len(w1) + 1):
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m[i][0] = i
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for j in range(1, len(w2) + 1):
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m[0][j] = j
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for i in range(1, len(w1) + 1):
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for j in range(1, len(w2) + 1):
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m[i][j] = min(
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m[i-1][j-1] + int(w1[i-1] != w2[j-1]),
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m[i-1][j] + 1,
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m[i][j-1] + 1
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)
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return m
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def levenshtein_distance(word_1, chars_1, word_2, chars_2):
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# base case if the strings are empty
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if chars_1 == 0:
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return chars_2
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if chars_2 == 0:
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return chars_1
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# if last characters of the string match, the cost of
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# operations is 0, i.e. no changes are made
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if word_1[chars_1 - 1] == word_2[chars_2 - 1]:
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cost = 0
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else:
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cost = 1
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if __name__ == "__main__":
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print(edit_distance("sitting", "kitten"))
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# calculating the numbers of operations recursively
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deletion = levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2) + 1
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insertion = levenshtein_distance(word_1, chars_1, word_2, chars_2 - 1) + 1
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substitution = levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2 - 1) + cost
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return min(deletion, insertion, substitution)
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# driving script
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if __name__ == '__main__':
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word_1 = 'plain'
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word_2 = 'plane'
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print('The Levenshtein distance is:')
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print(levenshtein_distance(word_1, len(word_1), word_2, len(word_2)))
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def edit_distance(w1, w2):
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"""
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Find edit distance (minimum number of changes) required to convert string w1 to string w2.
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"""
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m = [[0 if x != 0 else y if y != 0 else x for x in range(len(w2) + 1)] for y in range(len(w1) + 1)]
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for i in range(1,len(w1) + 1):
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m[i][0] = i
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for j in range(1, len(w2) + 1):
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m[0][j] = j
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for i in range(1, len(w1) + 1):
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for j in range(1, len(w2) + 1):
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m[i][j] = min(
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m[i-1][j-1] + int(w1[i-1] != w2[j-1]),
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m[i-1][j] + 1,
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m[i][j-1] + 1
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)
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return m
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if __name__ == "__main__":
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print(edit_distance("sitting", "kitten"))
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# The Levenshtein distance (Edit distance) Problem
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# Informally, the Levenshtein distance between two words is
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# the minimum number of single-character edits (insertions, deletions or substitutions)
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# required to change one word into the other.
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# For example, the Levenshtein distance between kitten and sitting is 3.
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# The minimal edit script that transforms the former into the latter is:
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# kitten —> sitten (substitution of s for k)
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# sitten —> sittin (substitution of i for e)
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# sittin —> sitting (insertion of g at the end)
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def levenshtein_distance(word_1, chars_1, word_2, chars_2):
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# base case if the strings are empty
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if chars_1 == 0:
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return chars_2
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if chars_2 == 0:
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return chars_1
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# if last characters of the string match, the cost of
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# operations is 0, i.e. no changes are made
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if word_1[chars_1 - 1] == word_2[chars_2 - 1]:
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cost = 0
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else:
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cost = 1
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# calculating the numbers of operations recursively
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deletion = levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2) + 1
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insertion = levenshtein_distance(word_1, chars_1, word_2, chars_2 - 1) + 1
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substitution = levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2 - 1) + cost
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return min(deletion, insertion, substitution)
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# driving script
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if __name__ == '__main__':
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word_1 = 'plain'
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word_2 = 'plane'
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print('The Levenshtein distance is:')
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print(levenshtein_distance(word_1, len(word_1), word_2, len(word_2)))
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