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--git a/data_structures_and_algorithms/data_structures/tree/resd.md b/data_structures_and_algorithms/data_structures/tree/resd.md new file mode 100644 index 0000000..e216d2e --- /dev/null +++ b/data_structures_and_algorithms/data_structures/tree/resd.md @@ -0,0 +1,76 @@ +Tree Traversals (Inorder, Preorder and Postorder) +Unlike linear data structures (Array, Linked List, Queues, Stacks, etc) which have only one logical way to traverse them, trees can be traversed in different ways. Following are the generally used ways for traversing trees. + + + +Depth First Traversals: +(a) Inorder (Left, Root, Right) : 4 2 5 1 3 +(b) Preorder (Root, Left, Right) : 1 2 4 5 3 +(c) Postorder (Left, Right, Root) : 4 5 2 3 1 + +Breadth First or Level Order Traversal : 1 2 3 4 5 +Please see this post for Breadth First Traversal. + +Inorder Traversal : + +Algorithm Inorder(tree) + 1. Traverse the left subtree, i.e., call Inorder(left-subtree) + 2. Visit the root. + 3. Traverse the right subtree, i.e., call Inorder(right-subtree) +Uses of Inorder +In case of binary search trees (BST), Inorder traversal gives nodes in non-decreasing order. To get nodes of BST in non-increasing order, a variation of Inorder traversal where Inorder traversal s reversed can be used. + + +Preorder Traversal : + +Algorithm Preorder(tree) + 1. Visit the root. + 2. Traverse the left subtree, i.e., call Preorder(left-subtree) + 3. Traverse the right subtree, i.e., call Preorder(right-subtree) +Uses of Preorder +Preorder traversal is used to create a copy of the tree. Preorder traversal is also used to get prefix expression on of an expression tree. + +Postorder Traversal : + +Algorithm Postorder(tree) + 1. Traverse the left subtree, i.e., call Postorder(left-subtree) + 2. Traverse the right subtree, i.e., call Postorder(right-subtree) + 3. Visit the root. +Uses of Postorder +Postorder traversal is used to delete the tree. Please see the question for deletion of tree for details. Postorder traversal is also useful to get the postfix expression of an expression tree. + + +Time Complexity: O(n) +Complexity function T(n) — for all problem where tree traversal is involved — can be defined as: + +T(n) = T(k) + T(n – k – 1) + c + +Where k is the number of nodes on one side of root and n-k-1 on the other side. + +Let’s do an analysis of boundary conditions + +Case 1: Skewed tree (One of the subtrees is empty and other subtree is non-empty ) + +k is 0 in this case. +T(n) = T(0) + T(n-1) + c +T(n) = 2T(0) + T(n-2) + 2c +T(n) = 3T(0) + T(n-3) + 3c +T(n) = 4T(0) + T(n-4) + 4c + +………………………………………… +…………………………………………. +T(n) = (n-1)T(0) + T(1) + (n-1)c +T(n) = nT(0) + (n)c + +Value of T(0) will be some constant say d. (traversing a empty tree will take some constants time) + +T(n) = n(c+d) +T(n) = Θ(n) (Theta of n) + +Case 2: Both left and right subtrees have equal number of nodes. + +T(n) = 2T(|_n/2_|) + c + +This recursive function is in the standard form (T(n) = aT(n/b) + (-)(n) ) + +Auxiliary Space : If we don’t consider size of stack for function calls then O(1) otherwise O(n). \ No newline at end of file diff --git a/data_structures_and_algorithms/data_structures/tree/tree.py b/data_structures_and_algorithms/data_structures/tree/tree.py new file mode 100644 index 0000000..47cbe49 --- /dev/null +++ b/data_structures_and_algorithms/data_structures/tree/tree.py @@ -0,0 +1,125 @@ +class Node: + """Node class definition.""" + + def __init__(self, val=None): + """Create an instance of Node object.""" + self.val = val + self.children = [] + self._next = next + + def __repr__(self): + """Node class representation.""" + return ''.format(self.val) + + def __str__(self): + """Node class string printout.""" + return 'Node Val: {}'.format(self.val) + +class Queue: + def __init__(self, iter=[]): + self.front = None + self.back = None + self._length = 0 + + if not isinstance(iter, (list, dict, tuple)): + """ check for iterable """ + raise TypeError('It is not iterable.') + for i in iter: + self.enqueue(i) + + def enqueue(self, val): + """ add a value, increase size by 1""" + node = Node(val) + if self._length == 0: + self.front = self.back = node + self._length += 1 + return node + self.back.next = node + self.back = node + self._length += 1 + return node + + def dequeue(self): + """ remove node from the front of queue """ + if self._length == 0: + raise IndexError('You cannot dequeue() when front is empty') + + temp = self.front + self.front = temp.next + self._length -= 1 + return temp + +class KTree: + """Ktree class definition.""" + + def __init__(self): + """Create an instance of KTree object.""" + self.root = None + + def __repr__(self): + """Ktree class representation.""" + return ''.format(self.root.val) + + def __str__(self): + """Ktree class string printout.""" + return 'KTree Root Val: {}'.format(self.root.val) + + def pre_order(self, operation): + """Ktree pre_order traversal.""" + def _walk(node=None): + if node is None: + return + + operation(node) + + for child in node.children: + _walk(child) + + _walk(self.root) + + def post_order(self, operation): + """Ktree post_order traversal.""" + def _walk(node=None): + if node is None: + return + + for child in node.children: + _walk(child) + + operation(node) + + _walk(self.root) + + def breadth_first_traversal(self, operation): + """Ktree breadth_first_traversal.""" + queue = Queue() + queue.enqueue(self.root) + while queue._length > 0: + current = queue.dequeue() + operation(current) + for child in current.children: + queue.enqueue(child) + + def insert(self, val, parent=None): + """Insert a value at first instance of given parent.""" + if parent is None: + if self.root is None: + self.root = Node(val) + return self.root + raise ValueError('parent node is none.') + + node = Node(val) + + def _walk(curr=None): + if curr is None: + return + + if curr.val == parent: + curr.children.append(node) + return + + for child in curr.children: + _walk(child) + if node in child.children: + return + _walk(self.root) \ No newline at end of file From 7c36bc5ff5304fed4005e0fc229d958d4b8a3e22 Mon Sep 17 00:00:00 2001 From: MsDiala Date: Sun, 3 Jan 2021 22:50:52 +0200 Subject: [PATCH 3/4] gg --- .../.vscode/settings.json | 4 ++ .../challenges/.vscode/settings.json | 4 ++ .../challenges/Insertion_Sort/README.rst | 0 .../Insertion_Sort/insertion_sort/__init__.py | 1 + .../insertion_sort/insertion.py | 15 ++++ .../Insertion_Sort/insertion_sort/read.md | 67 ++++++++++++++++++ .../challenges/Insertion_Sort/pyproject.toml | 15 ++++ .../Insertion_Sort/tests/__init__.py | 0 .../tests/test_insertion_sort.py | 5 ++ .../challenges/selection-sort GIF.gif | Bin 0 -> 3875060 bytes 10 files changed, 111 insertions(+) create mode 100644 data_structures_and_algorithms/.vscode/settings.json create mode 100644 data_structures_and_algorithms/challenges/.vscode/settings.json create mode 100644 data_structures_and_algorithms/challenges/Insertion_Sort/README.rst create mode 100644 data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/__init__.py create mode 100644 data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/insertion.py create mode 100644 data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/read.md create mode 100644 data_structures_and_algorithms/challenges/Insertion_Sort/pyproject.toml create mode 100644 data_structures_and_algorithms/challenges/Insertion_Sort/tests/__init__.py create mode 100644 data_structures_and_algorithms/challenges/Insertion_Sort/tests/test_insertion_sort.py create mode 100644 data_structures_and_algorithms/challenges/selection-sort GIF.gif diff --git a/data_structures_and_algorithms/.vscode/settings.json b/data_structures_and_algorithms/.vscode/settings.json new file mode 100644 index 0000000..506fdf7 --- /dev/null +++ b/data_structures_and_algorithms/.vscode/settings.json @@ -0,0 +1,4 @@ +{ + "ponicode.testSettings.testLocation.locationType": "Same folder as source file", + "ponicode.testSettings.testLocation.path": "{rootDir}/{filePath}/{fileName}.test.{ext}" +} \ No newline at end of file diff --git a/data_structures_and_algorithms/challenges/.vscode/settings.json b/data_structures_and_algorithms/challenges/.vscode/settings.json new file mode 100644 index 0000000..506fdf7 --- /dev/null +++ b/data_structures_and_algorithms/challenges/.vscode/settings.json @@ -0,0 +1,4 @@ +{ + "ponicode.testSettings.testLocation.locationType": "Same folder as source file", + "ponicode.testSettings.testLocation.path": "{rootDir}/{filePath}/{fileName}.test.{ext}" +} \ No newline at end of file diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/README.rst b/data_structures_and_algorithms/challenges/Insertion_Sort/README.rst new file mode 100644 index 0000000..e69de29 diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/__init__.py b/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/__init__.py new file mode 100644 index 0000000..b794fd4 --- /dev/null +++ b/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/__init__.py @@ -0,0 +1 @@ +__version__ = '0.1.0' diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/insertion.py b/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/insertion.py new file mode 100644 index 0000000..ed22c93 --- /dev/null +++ b/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/insertion.py @@ -0,0 +1,15 @@ +def selection_sort(list_a): + indexing_length = range(0,len(list_a)-1) + + for i in indexing_length: + min_value = i + + for j in range(i+1,len(list_a)): + if list_a[j] < list_a[min_value]: + min_value = j + if min_value != i: + list_a[min_value] = list_a[i], + return list_a + + +print(selection_sort([3,1,6,5,9,4,2,8])) \ No newline at end of file diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/read.md b/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/read.md new file mode 100644 index 0000000..b3af14f --- /dev/null +++ b/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/read.md @@ -0,0 +1,67 @@ +# SELECTION-SORT + + We divide the array into two parts: sorted and unsorted. The left part is sorted subarray and the right part is unsorted subarray. Initially, sorted subarray is empty and unsorted array is the complete given array. + or +Selection sort is an algorithm that selects the smallest element from an unsorted list in each iteration and places that element at the beginning of the unsorted list. + +# Visualization +![Getting Started](selection-sort GIF.gif) + +# Pseudocode +SelectionSort(int[] arr) + DECLARE n <-- arr.Length; + FOR i = 0; i to n - 1 + DECLARE min <-- i; + FOR j = i + 1 to n + if (arr[j] < arr[min]) + min <-- j; + + DECLARE temp <-- arr[min]; + arr[min] <-- arr[i]; + arr[i] <-- temp; + +# APPROACH FOR SELECTION SORT + +1.Set the first element as minimum. + +2.Compare minimum with the second element. If the second element is smaller than minimum, assign the second element as minimum. + +Compare minimum with the third element. Again, if the third element is smaller, then assign minimum to the third element otherwise do nothing. The process goes on until the last element. + +3.After each iteration, minimum is placed in the front of the unsorted list + +4.For each iteration, indexing starts from the first unsorted element. They are repeated until all the elements are placed at their correct positions. + +# steps +![Getting Started](selection-sort GIF.gif) +![Getting Started](selection-sort GIF.gif) +![Getting Started](selection-sort GIF.gif) +![Getting Started](selection-sort GIF.gif) +![Getting Started](selection-sort GIF.gif) + +# COMPLEXITY: O(n2) + +Also, we can analyze the complexity by simply observing the number of loops. There are 2 loops so the complexity is n*n = n2. + +## Time Complexities: + +# Worst Case Complexity: O(n2) +If we want to sort in ascending order and the array is in descending order then, the worst case occurs. +# Best Case Complexity: O(n2) +It occurs when the array is already sorted +# Average Case Complexity: O(n2) +It occurs when the elements of the array are neither ascending nor descending. + + +The time complexity of the selection sort is the same in all cases. At every step, you have to find the minimum element and put it in the right place. The minimum element is not known until the end of the array is not reached. + + +# Space Complexity: + +Space complexity is O(1) because an extra variable temp is used. + + + +# LINK FOR REFERENCE +mycodeschool:- +https://www.youtube.com/watch?v=GUDLRan2DWM diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/pyproject.toml b/data_structures_and_algorithms/challenges/Insertion_Sort/pyproject.toml new file mode 100644 index 0000000..b597208 --- /dev/null +++ b/data_structures_and_algorithms/challenges/Insertion_Sort/pyproject.toml @@ -0,0 +1,15 @@ +[tool.poetry] +name = "Insertion_Sort" +version = "0.1.0" +description = "" +authors = ["MsDiala "] + +[tool.poetry.dependencies] +python = "^3.9" + +[tool.poetry.dev-dependencies] +pytest = "^5.2" + +[build-system] +requires = ["poetry-core>=1.0.0"] +build-backend = "poetry.core.masonry.api" diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/tests/__init__.py b/data_structures_and_algorithms/challenges/Insertion_Sort/tests/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/tests/test_insertion_sort.py b/data_structures_and_algorithms/challenges/Insertion_Sort/tests/test_insertion_sort.py new file mode 100644 index 0000000..169059c --- /dev/null +++ b/data_structures_and_algorithms/challenges/Insertion_Sort/tests/test_insertion_sort.py @@ -0,0 +1,5 @@ +from insertion_sort import __version__ + + +def test_version(): + assert __version__ == '0.1.0' diff --git a/data_structures_and_algorithms/challenges/selection-sort GIF.gif b/data_structures_and_algorithms/challenges/selection-sort GIF.gif new file mode 100644 index 0000000000000000000000000000000000000000..c0e330d0c27c03a70a742bcc94f9b6ce6a541166 GIT binary patch literal 3875060 zcmeFaWmH>jqplkRg1bwh1qzfRZE0~Sw73^3(gHQy3N7B?5L}BB+}%C6y9amoQas(f z-*@&WYn`#j8vCrX&yT|#_ef^uoOzNT$unkVu5n+|vak6C3`@b7z%u}#cyi@7MSo?r 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a/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/insertion.py b/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/insertion.py index ed22c93..3b72e7f 100644 --- a/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/insertion.py +++ b/data_structures_and_algorithms/challenges/Insertion_Sort/insertion_sort/insertion.py @@ -1,15 +1,20 @@ -def selection_sort(list_a): - indexing_length = range(0,len(list_a)-1) - - for i in indexing_length: - min_value = i - - for j in range(i+1,len(list_a)): - if list_a[j] < list_a[min_value]: - min_value = j - if min_value != i: - list_a[min_value] = list_a[i], - return list_a - - -print(selection_sort([3,1,6,5,9,4,2,8])) \ No newline at end of file +def insertion_sort(arr): + # for each char in the array + if len(arr) < 1: + return "Not a valid input" + if len(arr) == 1: + return arr + for char in range(1, len(arr)): + # set check_char to 0 + check_char = char - 1 + # set temp to arr at 1 + temp = arr[char] + # iterate through the array and check if temp is < arr[check] + while check_char >= 0 and temp < arr[check_char]: + # move a the check_char +1 to the check_char position + arr[check_char + 1] = arr[check_char] + # set check_char to check_char minus 1 + check_char = check_char - 1 + # set temp to the position after check_char + arr[check_char + 1] = temp + return arr \ No newline at end of file diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/tests/__init__.py b/data_structures_and_algorithms/challenges/Insertion_Sort/tests/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/data_structures_and_algorithms/challenges/Insertion_Sort/tests/test_insertion_sort.py b/data_structures_and_algorithms/challenges/Insertion_Sort/tests/test_insertion_sort.py deleted file mode 100644 index 169059c..0000000 --- a/data_structures_and_algorithms/challenges/Insertion_Sort/tests/test_insertion_sort.py +++ /dev/null @@ -1,5 +0,0 @@ -from 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b/tests/challenges/test_insertion_sort.py new file mode 100644 index 0000000..ffea7db --- /dev/null +++ b/tests/challenges/test_insertion_sort.py @@ -0,0 +1,46 @@ +from insertion_sort.insertion_sort.insertion import insertion_sort + + +# test 0 one two and many + + +def test_zero(): + z = [] + actual = insertion_sort(z) + expected = "Not a valid input" + assert actual == expected + + +def test_one(): + z = [1] + actual = insertion_sort(z) + expected = [1] + assert actual == expected + + +def test_many(): + z = [8, 4, 23, 42, 16, 15] + actual = insertion_sort(z) + expected = [4, 8, 15, 16, 23, 42] + assert actual == expected + + +def test_many1(): + z = [20, 18, 12, 8, 5, -2] + actual = insertion_sort(z) + expected = [-2, 5, 8, 12, 18, 20] + assert actual == expected + + +def test_many2(): + z = [5, 12, 7, 5, 5, 7] + actual = insertion_sort(z) + expected = [5, 5, 5, 7, 7, 12] + assert actual == expected + + +def test_many3(): + z = [2, 3, 5, 7, 13, 11] + actual = insertion_sort(z) + 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