Merge pull request #1 from TheAlgorithms/master

pull from master

Author: itsvinayak

Diff for: Travis_CI_tests_are_failing.md

@@ -0,0 +1,9 @@
+# Travis CI test are failing
+### How do I find out what is wrong with my pull request?
+1. In your PR look for the failing test and click the `Details` link: ![Travis_CI_fail_1.png](images/Travis_CI_fail_1.png)
+2. On the next page, click `The build failed` link: ![Travis_CI_fail_2.png](images/Travis_CI_fail_2.png)
+3. Now scroll down and look for `red` text describing the error(s) in the test log.
+
+Pull requests will __not__ be merged if the Travis CI tests are failing.
+
+If anything is unclear, please read through [CONTRIBUTING.md](CONTRIBUTING.md) and attempt to run the failing tests on your computer before asking for assistance.

Diff for: arithmetic_analysis/secant_method.py

@@ -0,0 +1,28 @@
+# Implementing Secant method in Python
+# Author: dimgrichr
+
+
+from math import exp
+
+
+def f(x):
+    """
+    >>> f(5)
+    39.98652410600183
+    """
+    return 8 * x - 2 * exp(-x)
+
+
+def SecantMethod(lower_bound, upper_bound, repeats):
+    """
+    >>> SecantMethod(1, 3, 2)
+    0.2139409276214589
+    """
+    x0 = lower_bound
+    x1 = upper_bound
+    for i in range(0, repeats):
+        x0, x1 = x1, x1 - (f(x1) * (x1 - x0)) / (f(x1) - f(x0))
+    return x1
+
+
+print(f"The solution is: {SecantMethod(1, 3, 2)}")

Diff for: ciphers/diffie.py

@@ -0,0 +1,26 @@
+def find_primitive(n):
+    for r in range(1, n):
+        li = []
+        for x in range(n-1):
+            val = pow(r,x,n)
+            if val in li:
+                break
+            li.append(val)
+        else:
+            return r
+
+
+if __name__ == "__main__":
+    q = int(input('Enter a prime number q: '))
+    a = find_primitive(q)
+    a_private = int(input('Enter private key of A: '))
+    a_public = pow(a, a_private, q)
+    b_private = int(input('Enter private key of B: '))
+    b_public = pow(a, b_private, q)
+
+    a_secret = pow(b_public, a_private, q)
+    b_secret = pow(a_public, b_private, q)
+
+    print('The key value generated by A is: ', a_secret)
+    print('The key value generated by B is: ', b_secret)
+    

Diff for: ciphers/mixed_keyword_cypher.py

@@ -0,0 +1,71 @@
+def mixed_keyword(key="college", pt="UNIVERSITY"):
+    """
+
+    For key:hello
+
+    H E L O
+    A B C D
+    F G I J
+    K M N P
+    Q R S T
+    U V W X
+    Y Z
+    and map vertically
+
+    >>> mixed_keyword("college", "UNIVERSITY")  # doctest: +NORMALIZE_WHITESPACE
+    {'A': 'C', 'B': 'A', 'C': 'I', 'D': 'P', 'E': 'U', 'F': 'Z', 'G': 'O', 'H': 'B',
+     'I': 'J', 'J': 'Q', 'K': 'V', 'L': 'L', 'M': 'D', 'N': 'K', 'O': 'R', 'P': 'W',
+     'Q': 'E', 'R': 'F', 'S': 'M', 'T': 'S', 'U': 'X', 'V': 'G', 'W': 'H', 'X': 'N',
+     'Y': 'T', 'Z': 'Y'}
+    'XKJGUFMJST'
+    """
+    key = key.upper()
+    pt = pt.upper()
+    temp = []
+    for i in key:
+        if i not in temp:
+            temp.append(i)
+    l = len(temp)
+    # print(temp)
+    alpha = []
+    modalpha = []
+    # modalpha.append(temp)
+    dic = dict()
+    c = 0
+    for i in range(65, 91):
+        t = chr(i)
+        alpha.append(t)
+        if t not in temp:
+            temp.append(t)
+    # print(temp)
+    r = int(26 / 4)
+    # print(r)
+    k = 0
+    for i in range(r):
+        t = []
+        for j in range(l):
+            t.append(temp[k])
+            if not (k < 25):
+                break
+            k += 1
+        modalpha.append(t)
+    # print(modalpha)
+    d = dict()
+    j = 0
+    k = 0
+    for j in range(l):
+        for i in modalpha:
+            if not (len(i) - 1 >= j):
+                break
+            d[alpha[k]] = i[j]
+            if not k < 25:
+                break
+            k += 1
+    print(d)
+    cypher = ""
+    for i in pt:
+        cypher += d[i]
+    return cypher
+
+
+print(mixed_keyword("college", "UNIVERSITY"))

Diff for: data_structures/heap/binomial_heap.py

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