update folder structure

algorithms/Python/README.md

@@ -1,6 +1,7 @@
 # Python
 
 ## Arrays
+
 - [Count Inversions](arrays/counting_inversions.py)
 - [Majority Element](arrays/majority_element.py)
 - [Rotate Array](arrays/rotate_array.py)
@@ -10,31 +11,36 @@
 - [Max Sub Array Sum](arrays/max_sub_array_sum.py)
 
 ## Linked Lists
+
 - [Doubly](linked_lists/doubly.py)
 - [Singly](linked_lists/singly.py)
 - [Reverse List](linked_lists/reverse-linkedlist.py)
 - [Middle Node](linked_lists/middle-node-linkedlist.py)
 - [Cycle Detection and Removal](linked_lists/cycle-detection-and-removal-linkedlist.py)
 
-
 ## Dictionaries
+
 - [Two Sum](dictionaries/two-sum.py)
 
 ## Multiplication
+
 - [Karatsuba](multiplication/karatsuba_algorithm.py)
 
 ## Recursion
+
 - [Factorial](recursion/factorial.py)
 - [n-th Fibonacci number](recursion/nth_fibonacci_number.py)
 - [Recursive Insertion Sort](recursion/recursive_insertion_sort.py)
 - [Recursive Sum of n numbers](recursion/recursive-sum-of-n-numbers.py)
 - [GCD by Euclid's Algorithm](recursion/gcd_using_recursion.py)
-
+- [Levenshtein distance](recursion/levenshtein_distance.py)
 
 ## Scheduling
+
 - [Interval Scheduling](scheduling/interval_scheduling.py)
 
 ## Searching
+
 - [Binary Search](searching/binary_search.py)
 - [Jump Search](searching/jump_search.py)
 - [Linear Search](searching/linear_search.py)
@@ -44,6 +50,7 @@
 - [Breath First Search](searching/breadth-first-search.py)
 
 ## Sorting
+
 - [Bubble Sort](sorting/bubble_sort.py)
 - [Comb Sort](sorting/comb_sort.py)
 - [Count Sort](sorting/count-sort.py)
@@ -56,6 +63,7 @@
 - [Merge sort](sorting/merge_sort.py)
 
 ## Strings
+
 - [Is Good Str](strings/is_good_str.py)
 - [Palindrome](strings/palindrome.py)
 - [Word Count](strings/word_count.py)
@@ -69,6 +77,7 @@
 - [Roman to Int](strings/roman-to-int.py)
 
 ## Dynamic Programming
+
 - [Print Fibonacci Series Up To N-th Term](dynamic_programming/fibonacci_series.py)
 - [Sum Up To N-th Term Of Fibonacci Series](dynamic_programming/fibonacci_series_sum.py)
 - [N-th Term Of Fibonacci Series](dynamic_programming/fibonacci_series_nth_term.py)
@@ -77,16 +86,20 @@
 - [Levenshtein distance](dynamic_programming/levenshtein_distance.py)
 
 ## Graphs
+
 - [Simple Graph](graphs/graph.py)
 - [BFS SEQUENCE](graphs/bfs-sequence.py)
 - [Depth First Search](graphs/depth-first-search.py)
 
 ## Trees
+
 - [Binary Tree](trees/binary_tree.py)
 - [Binary Search Tree](trees/binary_search_tree.py)
 
 ## Queues
+
 - [First in First out Queue](queues/fifo-queue.py)
 
 ## Number Theory
+
 - [Prime Number Checker](number_theory/prime_number.py)

algorithms/Python/dynamic_programming/levenshtein_distance.py

@@ -1,41 +1,27 @@
-# The Levenshtein distance (Edit distance) Problem
 
-# Informally, the Levenshtein distance between two words is
+def edit_distance(w1, w2):
-# the minimum number of single-character edits (insertions, deletions or substitutions)
+    """
-# required to change one word into the other.
+    Find edit distance (minimum number of changes) required to convert string w1 to string w2. 
+    """
 
-# For example, the Levenshtein distance between kitten and sitting is 3.
+    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)]
-# The minimal edit script that transforms the former into the latter is:
 
-# kitten —> sitten (substitution of s for k)
+    for i in range(1,len(w1) + 1):
-# sitten —> sittin (substitution of i for e)
+        m[i][0] = i 
-# sittin —> sitting (insertion of g at the end)
+    for j in range(1, len(w2) + 1):
+        m[0][j] = j 
     
-def levenshtein_distance(word_1, chars_1, word_2, chars_2):
+    for i in range(1, len(w1) + 1):
-    # base case if the strings are empty
+        for j in range(1, len(w2) + 1):
-    if chars_1 == 0:
+            m[i][j] = min(
-        return chars_2
+                m[i-1][j-1] + int(w1[i-1] != w2[j-1]),
-    if chars_2 == 0:
+                m[i-1][j] + 1,
-        return chars_1
+                m[i][j-1] + 1
+            )
     
-    # if last characters of the string match, the cost of
+    return m
-    # operations is 0, i.e. no changes are made
-    if word_1[chars_1 - 1] == word_2[chars_2 - 1]:
-        cost = 0
-    else:
-        cost = 1
 
-    # calculating the numbers of operations recursively
-    deletion =  levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2) + 1
-    insertion = levenshtein_distance(word_1, chars_1, word_2, chars_2 - 1) + 1
-    substitution = levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2 - 1) + cost
 
-    return min(deletion, insertion, substitution)
+if __name__ == "__main__":
+    print(edit_distance("sitting", "kitten"))
 
-# driving script
-if __name__ == '__main__':
-    word_1 = 'plain'
-    word_2 = 'plane'
-
-    print('The Levenshtein distance is:')
-    print(levenshtein_distance(word_1, len(word_1), word_2, len(word_2)))

algorithms/Python/dynamic_programming/levenshtein_distance_dp.py

@@ -1,27 +0,0 @@
-
-def edit_distance(w1, w2):
-    """
-    Find edit distance (minimum number of changes) required to convert string w1 to string w2. 
-    """
-
-    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)]
-
-    for i in range(1,len(w1) + 1):
-        m[i][0] = i 
-    for j in range(1, len(w2) + 1):
-        m[0][j] = j 
-    
-    for i in range(1, len(w1) + 1):
-        for j in range(1, len(w2) + 1):
-            m[i][j] = min(
-                m[i-1][j-1] + int(w1[i-1] != w2[j-1]),
-                m[i-1][j] + 1,
-                m[i][j-1] + 1
-            )
-    
-    return m
-
-
-if __name__ == "__main__":
-    print(edit_distance("sitting", "kitten"))
-

algorithms/Python/recursion/levenshtein_distance.py

@@ -0,0 +1,41 @@
+# The Levenshtein distance (Edit distance) Problem
+
+# Informally, the Levenshtein distance between two words is
+# the minimum number of single-character edits (insertions, deletions or substitutions)
+# required to change one word into the other.
+
+# For example, the Levenshtein distance between kitten and sitting is 3.
+# The minimal edit script that transforms the former into the latter is:
+
+# kitten —> sitten (substitution of s for k)
+# sitten —> sittin (substitution of i for e)
+# sittin —> sitting (insertion of g at the end)
+
+def levenshtein_distance(word_1, chars_1, word_2, chars_2):
+    # base case if the strings are empty
+    if chars_1 == 0:
+        return chars_2
+    if chars_2 == 0:
+        return chars_1
+
+    # if last characters of the string match, the cost of
+    # operations is 0, i.e. no changes are made
+    if word_1[chars_1 - 1] == word_2[chars_2 - 1]:
+        cost = 0
+    else:
+        cost = 1
+
+    # calculating the numbers of operations recursively
+    deletion =  levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2) + 1
+    insertion = levenshtein_distance(word_1, chars_1, word_2, chars_2 - 1) + 1
+    substitution = levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2 - 1) + cost
+
+    return min(deletion, insertion, substitution)
+
+# driving script
+if __name__ == '__main__':
+    word_1 = 'plain'
+    word_2 = 'plane'
+
+    print('The Levenshtein distance is:')
+    print(levenshtein_distance(word_1, len(word_1), word_2, len(word_2)))