Merge pull request #1 from TheAlgorithms/master

Update from master

Author: parth-paradkar

README.md

@@ -10,18 +10,6 @@
 
 These implementations are for learning purposes. They may be less efficient than the implementations in the Python standard library.
 
-## Owners
-
-Anup Kumar Panwar
-  [[Gmail](mailto:[email protected]?Subject=The%20Algorithms%20-%20Python)
-  [GitHub](https://github.com/anupkumarpanwar)
-  [LinkedIn](https://www.linkedin.com/in/anupkumarpanwar/)]
-
-Chetan Kaushik
-  [[Gmail](mailto:[email protected]?Subject=The%20Algorithms%20-%20Python)
-  [GitHub](https://github.com/dynamitechetan)
-  [LinkedIn](https://www.linkedin.com/in/chetankaushik/)]
-
 ## Contribution Guidelines
 
 Read our [Contribution Guidelines](CONTRIBUTING.md) before you contribute.

arithmetic_analysis/bisection.py

@@ -1,21 +1,25 @@
 import math
 
 
-def bisection(function, a, b):  # finds where the function becomes 0 in [a,b] using bolzano
+def bisection(
+    function, a, b
+):  # finds where the function becomes 0 in [a,b] using bolzano
 
     start = a
     end = b
     if function(a) == 0:  # one of the a or b is a root for the function
         return a
     elif function(b) == 0:
         return b
-    elif function(a) * function(b) > 0:  # if none of these are root and they are both positive or negative,
+    elif (
+        function(a) * function(b) > 0
+    ):  # if none of these are root and they are both positive or negative,
         # then his algorithm can't find the root
         print("couldn't find root in [a,b]")
         return
     else:
         mid = start + (end - start) / 2.0
-        while abs(start - mid) > 10**-7:  # until we achieve precise equals to 10^-7
+        while abs(start - mid) > 10 ** -7:  # until we achieve precise equals to 10^-7
             if function(mid) == 0:
                 return mid
             elif function(mid) * function(start) < 0:
@@ -27,7 +31,8 @@ def bisection(function, a, b):  # finds where the function becomes 0 in [a,b] us
 
 
 def f(x):
-    return math.pow(x, 3) - 2*x - 5
+    return math.pow(x, 3) - 2 * x - 5
+
 
 if __name__ == "__main__":
     print(bisection(f, 1, 1000))

arithmetic_analysis/in_static_equilibrium.py

@@ -54,11 +54,8 @@ def in_static_equilibrium(
 if __name__ == "__main__":
     # Test to check if it works
     forces = array(
-        [
-            polar_force(718.4, 180 - 30),
-            polar_force(879.54, 45),
-            polar_force(100, -90)
-        ])
+        [polar_force(718.4, 180 - 30), polar_force(879.54, 45), polar_force(100, -90)]
+    )
 
     location = array([[0, 0], [0, 0], [0, 0]])
 

arithmetic_analysis/intersection.py

@@ -1,17 +1,24 @@
 import math
 
-def intersection(function,x0,x1): #function is the f we want to find its root and x0 and x1 are two random starting points
+
+def intersection(
+    function, x0, x1
+):  # function is the f we want to find its root and x0 and x1 are two random starting points
     x_n = x0
     x_n1 = x1
     while True:
-        x_n2 = x_n1-(function(x_n1)/((function(x_n1)-function(x_n))/(x_n1-x_n)))
-        if abs(x_n2 - x_n1) < 10**-5:
+        x_n2 = x_n1 - (
+            function(x_n1) / ((function(x_n1) - function(x_n)) / (x_n1 - x_n))
+        )
+        if abs(x_n2 - x_n1) < 10 ** -5:
             return x_n2
-        x_n=x_n1
-        x_n1=x_n2
+        x_n = x_n1
+        x_n1 = x_n2
+
 
 def f(x):
-    return math.pow(x , 3) - (2 * x) -5
+    return math.pow(x, 3) - (2 * x) - 5
+
 
 if __name__ == "__main__":
-    print(intersection(f,3,3.5))
+    print(intersection(f, 3, 3.5))

arithmetic_analysis/lu_decomposition.py

@@ -28,9 +28,7 @@ def LUDecompose(table):
 
 
 if __name__ == "__main__":
-    matrix = numpy.array([[2, -2, 1],
-                          [0, 1, 2],
-                          [5, 3, 1]])
+    matrix = numpy.array([[2, -2, 1], [0, 1, 2], [5, 3, 1]])
     L, U = LUDecompose(matrix)
     print(L)
     print(U)

arithmetic_analysis/newton_method.py

@@ -8,17 +8,17 @@ def newton(function, function1, startingInt):
     x_n = startingInt
     while True:
         x_n1 = x_n - function(x_n) / function1(x_n)
-        if abs(x_n - x_n1) < 10**-5:
+        if abs(x_n - x_n1) < 10 ** -5:
             return x_n1
         x_n = x_n1
 
 
 def f(x):
-    return (x**3) - (2 * x) - 5
+    return (x ** 3) - (2 * x) - 5
 
 
 def f1(x):
-    return 3 * (x**2) - 2
+    return 3 * (x ** 2) - 2
 
 
 if __name__ == "__main__":

arithmetic_analysis/newton_raphson_method.py

@@ -1,32 +1,34 @@
 # Implementing Newton Raphson method in Python
 # Author: Syed Haseeb Shah (github.com/QuantumNovice)
-
+# The Newton-Raphson method (also known as Newton's method) is a way to
+# quickly find a good approximation for the root of a real-valued function
 from sympy import diff
 from decimal import Decimal
 
+
 def NewtonRaphson(func, a):
-    ''' Finds root from the point 'a' onwards by Newton-Raphson method '''
+    """ Finds root from the point 'a' onwards by Newton-Raphson method """
     while True:
-        c = Decimal(a) - ( Decimal(eval(func)) / Decimal(eval(str(diff(func)))) )
+        c = Decimal(a) - (Decimal(eval(func)) / Decimal(eval(str(diff(func)))))
 
         a = c
 
         # This number dictates the accuracy of the answer
-        if  abs(eval(func)) < 10**-15:
-            return  c
+        if abs(eval(func)) < 10 ** -15:
+            return c
 
 
 # Let's Execute
-if __name__ == '__main__':
+if __name__ == "__main__":
     # Find root of trigonometric function
     # Find value of pi
-    print('sin(x) = 0', NewtonRaphson('sin(x)', 2))
+    print("sin(x) = 0", NewtonRaphson("sin(x)", 2))
 
     # Find root of polynomial
-    print('x**2 - 5*x +2 = 0', NewtonRaphson('x**2 - 5*x +2', 0.4))
+    print("x**2 - 5*x +2 = 0", NewtonRaphson("x**2 - 5*x +2", 0.4))
 
     # Find Square Root of 5
-    print('x**2 - 5 = 0', NewtonRaphson('x**2 - 5', 0.1))
+    print("x**2 - 5 = 0", NewtonRaphson("x**2 - 5", 0.1))
 
     # Exponential Roots
-    print('exp(x) - 1 = 0', NewtonRaphson('exp(x) - 1', 0))
+    print("exp(x) - 1 = 0", NewtonRaphson("exp(x) - 1", 0))

backtracking/all_combinations.py

@@ -12,7 +12,7 @@ def generate_all_combinations(n: int, k: int) -> [[int]]:
     >>> generate_all_combinations(n=4, k=2)
     [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
     """
-    
+
     result = []
     create_all_state(1, n, k, [], result)
     return result
@@ -34,7 +34,7 @@ def print_all_state(total_list):
         print(*i)
 
 
-if __name__ == '__main__':
+if __name__ == "__main__":
     n = 4
     k = 2
     total_list = generate_all_combinations(n, k)

backtracking/all_permutations.py

@@ -1,42 +1,42 @@
-'''
+"""
 	In this problem, we want to determine all possible permutations
 	of the given sequence. We use backtracking to solve this problem.
 
 	Time complexity: O(n! * n),
 	where n denotes the length of the given sequence.
-'''
+"""
 
 
 def generate_all_permutations(sequence):
-	create_state_space_tree(sequence, [], 0, [0 for i in range(len(sequence))])
+    create_state_space_tree(sequence, [], 0, [0 for i in range(len(sequence))])
 
 
 def create_state_space_tree(sequence, current_sequence, index, index_used):
-	'''
+    """
 	Creates a state space tree to iterate through each branch using DFS.
 	We know that each state has exactly len(sequence) - index children.
 	It terminates when it reaches the end of the given sequence.
-	'''
+	"""
 
-	if index == len(sequence):
-		print(current_sequence)
-		return
+    if index == len(sequence):
+        print(current_sequence)
+        return
 
-	for i in range(len(sequence)):
-		if not index_used[i]:
-			current_sequence.append(sequence[i])
-			index_used[i] = True
-			create_state_space_tree(sequence, current_sequence, index + 1, index_used)
-			current_sequence.pop()
-			index_used[i] = False
+    for i in range(len(sequence)):
+        if not index_used[i]:
+            current_sequence.append(sequence[i])
+            index_used[i] = True
+            create_state_space_tree(sequence, current_sequence, index + 1, index_used)
+            current_sequence.pop()
+            index_used[i] = False
 
 
-'''
+"""
 remove the comment to take an input from the user 
 
 print("Enter the elements")
 sequence = list(map(int, input().split()))
-'''
+"""
 
 sequence = [3, 1, 2, 4]
 generate_all_permutations(sequence)

backtracking/all_subsequences.py

@@ -1,39 +1,39 @@
-'''
+"""
 	In this problem, we want to determine all possible subsequences
 	of the given sequence. We use backtracking to solve this problem.
 
 	Time complexity: O(2^n),
 	where n denotes the length of the given sequence.
-'''
+"""
 
 
 def generate_all_subsequences(sequence):
-	create_state_space_tree(sequence, [], 0)
+    create_state_space_tree(sequence, [], 0)
 
 
 def create_state_space_tree(sequence, current_subsequence, index):
-	'''
+    """
 	Creates a state space tree to iterate through each branch using DFS.
 	We know that each state has exactly two children.
 	It terminates when it reaches the end of the given sequence.
-	'''
+	"""
 
-	if index == len(sequence):
-		print(current_subsequence)
-		return
+    if index == len(sequence):
+        print(current_subsequence)
+        return
 
-	create_state_space_tree(sequence, current_subsequence, index + 1)
-	current_subsequence.append(sequence[index])
-	create_state_space_tree(sequence, current_subsequence, index + 1)
-	current_subsequence.pop()
+    create_state_space_tree(sequence, current_subsequence, index + 1)
+    current_subsequence.append(sequence[index])
+    create_state_space_tree(sequence, current_subsequence, index + 1)
+    current_subsequence.pop()
 
 
-'''
+"""
 remove the comment to take an input from the user 
 
 print("Enter the elements")
 sequence = list(map(int, input().split()))
-'''
+"""
 
 sequence = [3, 1, 2, 4]
 generate_all_subsequences(sequence)

backtracking/minimax.py

@@ -1,28 +1,34 @@
-import math 
+import math
 
-''' Minimax helps to achieve maximum score in a game by checking all possible moves
+""" Minimax helps to achieve maximum score in a game by checking all possible moves
     depth is current depth in game tree. 
     nodeIndex is index of current node in scores[].
     if move is of maximizer return true else false
     leaves of game tree is stored in scores[]  
     height is maximum height of Game tree
-'''
+"""
 
-def minimax (Depth, nodeIndex, isMax, scores, height):  
 
-    if Depth == height:  
-        return scores[nodeIndex] 
+def minimax(Depth, nodeIndex, isMax, scores, height):
 
-    if isMax: 
-        return (max(minimax(Depth + 1, nodeIndex * 2, False, scores, height),
-                    minimax(Depth + 1, nodeIndex * 2 + 1, False, scores, height))) 
-    return (min(minimax(Depth + 1, nodeIndex * 2, True, scores, height), 
-               minimax(Depth + 1, nodeIndex * 2 + 1, True, scores, height))) 
+    if Depth == height:
+        return scores[nodeIndex]
 
-if __name__ == "__main__": 
- 
-    scores = [90, 23, 6, 33, 21, 65, 123, 34423] 
-    height = math.log(len(scores), 2) 
+    if isMax:
+        return max(
+            minimax(Depth + 1, nodeIndex * 2, False, scores, height),
+            minimax(Depth + 1, nodeIndex * 2 + 1, False, scores, height),
+        )
+    return min(
+        minimax(Depth + 1, nodeIndex * 2, True, scores, height),
+        minimax(Depth + 1, nodeIndex * 2 + 1, True, scores, height),
+    )
 
-    print("Optimal value : ", end = "") 
-    print(minimax(0, 0, True, scores, height)) 
+
+if __name__ == "__main__":
+
+    scores = [90, 23, 6, 33, 21, 65, 123, 34423]
+    height = math.log(len(scores), 2)
+
+    print("Optimal value : ", end="")
+    print(minimax(0, 0, True, scores, height))