From 1af8145904dfe7868e23c21c07ada4a21af91707 Mon Sep 17 00:00:00 2001 From: Mari Wahl Date: Wed, 27 Aug 2014 22:34:33 -0400 Subject: [PATCH] fix few details, transversals --- book/book_second_edition.pdf | Bin 4748087 -> 4743375 bytes src/trees/binary_tree.py | 9 +- src/trees/transversal_BST_ancestor.py | 42 ++ src/trees/transversal_BST_iteratively.py | 91 ++++ src/trees/transversal_BST_recursively.py | 88 ++++ src/trees/traversals/BST.py | 68 --- src/trees/traversals/BST_ancestor.py | 46 -- src/trees/traversals/BST_traversal.py | 88 ---- .../traversals/BST_with_Nodes_traversal.py | 68 --- .../traversals/BST_with_extra_methods.py | 95 ---- src/trees/traversals/__init__.py | 0 src/trees/traversals/binary_tree.py | 464 ------------------ src/trees/traversals/traversals.py | 131 ----- 13 files changed, 227 insertions(+), 963 deletions(-) create mode 100644 src/trees/transversal_BST_ancestor.py create mode 100644 src/trees/transversal_BST_iteratively.py create mode 100644 src/trees/transversal_BST_recursively.py delete mode 100644 src/trees/traversals/BST.py delete mode 100644 src/trees/traversals/BST_ancestor.py delete mode 100644 src/trees/traversals/BST_traversal.py delete mode 100644 src/trees/traversals/BST_with_Nodes_traversal.py delete mode 100644 src/trees/traversals/BST_with_extra_methods.py delete mode 100644 src/trees/traversals/__init__.py delete mode 100644 src/trees/traversals/binary_tree.py delete mode 100644 src/trees/traversals/traversals.py diff --git a/book/book_second_edition.pdf b/book/book_second_edition.pdf index 23a8b8b6e1cc50416f58df604749869b80150f15..c52833d726ca7525e78ac831381a8fbfafbd622d 100644 GIT binary patch delta 181263 zcmZs?Wl){58Z`=R+}+)sjk~+MLveQ~E*rPvwsCiNcc-`(mr|@~(EOu%pi-#X4g8M1WEC`KO>S)_b5`E-`f>=0p=r^jI1CJv(p=f4Nwz5RRttV9 zYsDzkd30q9bmV1PA1Vy@`n>AjlW+fOiiOoKg|?3I)yc!fuYr;h27lxuzo(&EGVc<} z(~8Z}H=7p6(Kw7s5y-BYp<+$R{@(0w!@*BfFItuzutzfY$UU)BQOt>3 zuyhVKufdQKPr{Dz1rm>m&|}EeCQ!pMDT(FgJ`y)X(;!(mK&Q4iDkX3b=>z`V#P)Fc 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zUod;zE&BP@d{rr~x^4EO@{DDaFEfekgdb}W=xJpPBE-#W0APCOd*>3TQdF{FcSb|of9H79_E8GPoxwb|wC3?EzjrM+jP6cRax&84M*iBJp~bqs zLGM~RhzqAl;9rlEd{bS!R9uUnh9eb$zd1C*g7wv$@cxI*@!#mcAo#0#)?3V$r7>}< z_ArmZF}gFhRcuWN_-DiZXQO~MHT!2Gm3c5DXig*iK@WkA|X@pPEqo4Ew1KG7A+*Ka* z^;q!JtnI}=c0@w)ZH^$bf79$zn>f3`2jp4Wsl+oU#W?-%-X>6-5ZH0w5^s2LEAtu&_fPXgZe>MvEH_HB?g{@e4-y`rdZD(mT^S$wB zfBtsy%8TAPrB9BJI;1CdTNJms{HA$Yv1JvaqT~EoG@);6^S@m^;P!Qlp0dZ{;`y{>iC67xRbzQ3q_W!@H;VSDYVqs{5w= zxsgYShS!q>&tNPCUzmwkqlw?3bMMFL-s)bO>OVBwLEF?h4LN-g z>QHsB#pbOBI7CSu9PrN@AXgilB(EN{&1=o(6etdd@PeuT(*~*q@=O7TgD-IPX9%yg z8(@jtet+_YMt8^QN({eOQ0{98eXX(G_Ww9@d){^^ap;Mp6eNU0(L zL(losH?I%RoOLgPydM_V^k63FF^$lLV#k?CLw==R)em(l9~vY-fcAIeuM&0A5)C~Q z0J}L|HR-kCOtP0&lAuYI7OGh|%+Y7DqK%@%vpj)1@6 Uft2FX($>`8ASY*PZMNb60kkT_jQ{`u diff --git a/src/trees/binary_tree.py b/src/trees/binary_tree.py index d8cd56f..fc33a52 100644 --- a/src/trees/binary_tree.py +++ b/src/trees/binary_tree.py @@ -115,7 +115,7 @@ class NodeBT(object): else: return False else: - raise Exception('Tree is empty') + print('Tree is empty') @@ -136,14 +136,17 @@ class BinaryTree(object): def isLeaf(self, value): node = self.root._searchForNode(value) - return node._isLeaf() + if node: + return node._isLeaf() + else: + print "Node not found." def getNodeLevel(self, item): node = self.root._searchForNode(item) if node: return node.level else: - raise Exception('Node not found') + print('Node not found') def isRoot(self, value): return self.root.item == value diff --git a/src/trees/transversal_BST_ancestor.py b/src/trees/transversal_BST_ancestor.py new file mode 100644 index 0000000..51288cf --- /dev/null +++ b/src/trees/transversal_BST_ancestor.py @@ -0,0 +1,42 @@ +#!/usr/bin/python + +__author__ = "Mari Wahl" +__email__ = "marina.w4hl@gmail.com" + +''' find the lowest ancestor in a BST ''' + +from transversal_BST_recursively import BSTwithTransversalRecursively + + + +def find_ancestor(path, low_value, high_value): + while path: + current_value = path[0] + if current_value < low_value: + try: + path = path[2:] + except: + return current_value + elif current_value > high_value: + try: + path = path[1:] + except: + return current_value + elif low_value <= current_value <= high_value: + return current_value + + + + +if __name__ == '__main__': + bst = BSTwithTransversalRecursively() + l = [10, 5, 15, 1, 6, 11, 50] + for i in l: + bst.addNode(i) + path = bst.preorder() + print("The path inorder: ", path) + + print("The path between 1 and 6 is :", find_ancestor(path, 1, 6)) + print("The path between 1 and 11 is: ", find_ancestor(path, 1, 11)) + print("The path between 11 and 50 is: ", find_ancestor(path, 11, 50)) + print("The path between 5 and 15 is: ", find_ancestor(path, 5, 15)) \ No newline at end of file diff --git a/src/trees/transversal_BST_iteratively.py b/src/trees/transversal_BST_iteratively.py new file mode 100644 index 0000000..4cbba51 --- /dev/null +++ b/src/trees/transversal_BST_iteratively.py @@ -0,0 +1,91 @@ +#!/usr/bin/python + +__author__ = "Mari Wahl" +__email__ = "marina.w4hl@gmail.com" + + +from collections import deque +from binary_search_tree import BinarySearchTree, NodeBST + + + +class BSTwithTransversalIterative(BinarySearchTree): + + def inorder(self): + current = self.root + nodes, stack = [], [] + while stack or current: + if current: + stack.append(current) + current = current.left + else: + current = stack.pop() + nodes.append(current.item) # thats what change + current = current.right + return nodes + + + def preorder(self): + current = self.root + nodes, stack = [], [] + while stack or current: + if current: + nodes.append(current.item) # thats what change + stack.append(current) + current = current.left + else: + current = stack.pop() + current = current.right + return nodes + + + def preorder2(self): + nodes = [] + stack = [self.root] + while stack: + current = stack.pop() + if current: + nodes.append(current.item) + stack.append(current.right) + stack.append(current.left) + return nodes + + + def BFT(self): + current = self.root + nodes = [] + queue = deque() + queue.append(current) + while queue: + current = queue.popleft() + nodes.append(current.item) + if current.left: + queue.append(current.left) # LEFT FIRST! + if current.right: + queue.append(current.right) + return nodes + + + + + + +if __name__ == '__main__': + + bst = BSTwithTransversalIterative() + l = [10, 5, 6, 3, 8, 2, 1, 11, 9, 4] + for i in l: + bst.addNode(i) + + print "Is 8 a leaf? ", bst.isLeaf(8) + print "Whats the level of node 8? ", bst.getNodeLevel(8) + print "Is node 10 a root? ", bst.isRoot(10) + print "Is node 1 a root? ", bst.isRoot(1) + print "Whats the tree height? ", bst.getHeight() + print "Is this tree BST? ", bst.isBST() + print "Is this tree balanced? ", bst.isBalanced() + + print("Pre-order I: ", bst.preorder()) + print("Pre-order II: ", bst.preorder2()) + print("In-order: ", bst.inorder()) + print("BFT: ", bst.BFT()) diff --git a/src/trees/transversal_BST_recursively.py b/src/trees/transversal_BST_recursively.py new file mode 100644 index 0000000..a2512f3 --- /dev/null +++ b/src/trees/transversal_BST_recursively.py @@ -0,0 +1,88 @@ +#!/usr/bin/python + +__author__ = "Mari Wahl" +__email__ = "marina.w4hl@gmail.com" + + +from binary_search_tree import BinarySearchTree, NodeBST + + + +class BSTwithTransversalRecursively(BinarySearchTree): + + def __init__(self): + self.root = None + self.nodes_BFS = [] + self.nodes_pre = [] + self.nodes_post = [] + self.nodes_in = [] + + def BFT(self): + self.root.level = 0 + queue = [self.root] + current_level = self.root.level + + while len(queue) > 0: + current_node = queue.pop(0) + if current_node.level > current_level: + current_level += 1 + self.nodes_BFS.append(current_node.item) + + if current_node.left: + current_node.left.level = current_level + 1 + queue.append(current_node.left) + + if current_node.right: + current_node.right.level = current_level + 1 + queue.append(current_node.right) + + return self.nodes_BFS + + def inorder(self, node=None, level=0): + if not node and level == 0: + node = self.root + if node: + self.inorder(node.left, level+1) + self.nodes_in.append(node.item) + self.inorder(node.right, level+1) + return self.nodes_in + + def preorder(self, node=None, level=0): + if not node and level == 0: + node = self.root + if node: + self.nodes_pre.append(node.item) + self.preorder(node.left, level+1) + self.preorder(node.right, level+1) + return self.nodes_pre + + def postorder(self, node=None, level=0): + if not node and level == 0: + node = self.root + if node: + self.postorder(node.left, level+1) + self.postorder(node.right, level+1) + self.nodes_post.append(node.item) + return self.nodes_post + + + +if __name__ == '__main__': + + bst = BSTwithTransversalRecursively() + l = [10, 5, 6, 3, 8, 2, 1, 11, 9, 4] + for i in l: + bst.addNode(i) + + print "Is 8 a leaf? ", bst.isLeaf(8) + print "Whats the level of node 8? ", bst.getNodeLevel(8) + print "Is node 10 a root? ", bst.isRoot(10) + print "Is node 1 a root? ", bst.isRoot(1) + print "Whats the tree height? ", bst.getHeight() + print "Is this tree BST? ", bst.isBST() + print "Is this tree balanced? ", bst.isBalanced() + + print("Pre-order: ", bst.preorder()) + print("Post-order: ", bst.postorder()) + print("In-order: ", bst.inorder()) + print("BFT: ", bst.BFT()) \ No newline at end of file diff --git a/src/trees/traversals/BST.py b/src/trees/traversals/BST.py deleted file mode 100644 index b2384a3..0000000 --- a/src/trees/traversals/BST.py +++ /dev/null @@ -1,68 +0,0 @@ -#!/usr/bin/python3 -# mari von steinkirch @2013 -# steinkirch at gmail - -from BT import BT - -class BST(BT): - def __init__(self, value=None): - self.value = value - self.left = None - self.right = None - - def insert_left(self, new_node): - self.insert(value) - - def insert_right(self, new_node): - self.insert(value) - - - def insert(self, value): - if self.value == None: - self.value = value - else: - if value > self.value: - self.right = self.right and self.right.insert(value) or BST(value) - else: - self.left = self.left and self.left.insert(value) or BST(value) - return self - - def find(self, value): - if value == self.value: - return self - elif value > self.value and self.right: - return self.right.find(value) - elif self.left: - return self.left.find(value) - return None - - - - -def main(): - """ - BST - 4 - 2 6 - 1 3 5 7 - """ - tree = BST() - tree.insert(4) - tree.insert(2) - tree.insert(6) - tree.insert(1) - tree.insert(3) - tree.insert(7) - tree.insert(5) - print(tree.get_right()) - print(tree.get_right().get_left()) - print(tree.get_right().get_right()) - print(tree.get_left()) - print(tree.get_left().get_left()) - print(tree.get_left().get_right() == 1) - assert(tree.find(30) == None) - - -if __name__ == '__main__': - main() - diff --git a/src/trees/traversals/BST_ancestor.py b/src/trees/traversals/BST_ancestor.py deleted file mode 100644 index c61933d..0000000 --- a/src/trees/traversals/BST_ancestor.py +++ /dev/null @@ -1,46 +0,0 @@ -#!/usr/bin/python3 -# mari von steinkirch @2013 -# steinkirch at gmail - -from BST_traversal import TranversalBST - -def find_ancestor(path, low_value, high_value): - ''' find the lowest ancestor in a BST ''' - while path: - current_value = path[0] - if current_value < low_value: - try: - path = path[2:] - except: - return current_value - elif current_value > high_value: - try: - path = path[1:] - except: - return current_value - elif low_value <= current_value <= high_value: - return current_value - return None - - -def test_find_ancestor(): - """ - 10 - 5 15 - 1 6 11 50 - """ - t = TranversalBST() - l1 = [10, 5, 15, 1, 6, 11, 50] - for i in l1: t.insert(i) - path = t.preorder() - assert(find_ancestor(path, 1, 6) == 5) - assert(find_ancestor(path, 1, 11) == 10) - assert(find_ancestor(path, 11, 50) == 15) - assert(find_ancestor(path, 5, 15) == 10) - - - print("Tests passsed!") - -if __name__ == '__main__': - test_find_ancestor() - diff --git a/src/trees/traversals/BST_traversal.py b/src/trees/traversals/BST_traversal.py deleted file mode 100644 index 8a6b21b..0000000 --- a/src/trees/traversals/BST_traversal.py +++ /dev/null @@ -1,88 +0,0 @@ -#!/usr/bin/python3 -# mari von steinkirch @2013 -# steinkirch at gmail - -from BST import BST - -class TranversalBST(object): - def __init__(self): - self.bst = BST(None) - self.nodes = [] - - def insert(self, value): - if not self.bst.value: - self.bst.value = value - else: - self.bst.insert(value) - - def contains(self, value): - return bool(self.bst.find(value)) - - def get(self, index): - for i, value in enumerate(self.inorder()): - if i == index: - return value - - def inorder(self): - current = self.bst - self.nodes = [] - stack = [] - while len(stack) > 0 or current is not None: - if current is not None: - stack.append(current) - current = current.left - else: - current = stack.pop() - self.nodes.append(current.value) - current = current.right - return self.nodes - - - def preorder(self): - self.nodes = [] - stack = [self.bst] - while len(stack) > 0: - curr = stack.pop() - if curr is not None: - self.nodes.append(curr.value) - stack.append(curr.right) - stack.append(curr.left) - return self.nodes - - - def preorder2(self): - self.nodes = [] - current = self.bst - stack = [] - while len(stack) > 0 or current is not None: - if current is not None: - self.nodes.append(current.value) - stack.append(current) - current = current.left - else: - current = stack.pop() - current = current.right - return self.nodes - - - -def main(): - """ - 10 - 5 15 - 1 6 11 50 - """ - t = TranversalBST() - t.insert(10) - t.insert(5) - t.insert(15) - t.insert(1) - t.insert(6) - t.insert(11) - t.insert(50) - print(t.preorder()) - print(t.preorder2()) - print(t.inorder()) - -if __name__ == '__main__': - main() diff --git a/src/trees/traversals/BST_with_Nodes_traversal.py b/src/trees/traversals/BST_with_Nodes_traversal.py deleted file mode 100644 index f443753..0000000 --- a/src/trees/traversals/BST_with_Nodes_traversal.py +++ /dev/null @@ -1,68 +0,0 @@ -#!/usr/bin/python3 -# mari von steinkirch @2013 -# steinkirch at gmail - -from BST_with_Nodes import BSTwithNodes, Node - -class BSTTraversal(BSTwithNodes): - def __init__(self): - self.root = None - self.nodes_BFS = [] - self.nodes_DFS_pre = [] - self.nodes_DFS_post = [] - self.nodes_DFS_in = [] - - def BFS(self): - self.root.level = 0 - queue = [self.root] - current_level = self.root.level - - while len(queue) > 0: - current_node = queue.pop(0) - if current_node.level > current_level: - current_level += 1 - self.nodes_BFS.append(current_node.value) - - if current_node.left: - current_node.left.level = current_level + 1 - queue.append(current_node.left) - - if current_node.right: - current_node.right.level = current_level + 1 - queue.append(current_node.right) - - return self.nodes_BFS - - def DFS_inorder(self, node): - if node is not None: - self.DFS_inorder(node.left) - self.nodes_DFS_in.append(node.value) - self.DFS_inorder(node.right) - return self.nodes_DFS_in - - def DFS_preorder(self, node): - if node is not None: - self.nodes_DFS_pre.append(node.value) - self.DFS_preorder(node.left) - self.DFS_preorder(node.right) - return self.nodes_DFS_pre - - def DFS_postorder(self, node): - if node is not None: - self.DFS_postorder(node.left) - self.DFS_postorder(node.right) - self.nodes_DFS_post.append(node.value) - return self.nodes_DFS_post - -def main(): - tree = BSTTraversal() - l1 = [10, 5, 15, 1, 6, 11, 50] - for i in l1: tree.insert(i) - - print('Breadth-First Traversal: ', tree.BFS()) - print('Inorder Traversal: ', tree.DFS_inorder(tree.root)) - print('Preorder Traversal: ', tree.DFS_preorder(tree.root)) - print('Postorder Traversal: ', tree.DFS_postorder(tree.root)) - -if __name__ == '__main__': - main() diff --git a/src/trees/traversals/BST_with_extra_methods.py b/src/trees/traversals/BST_with_extra_methods.py deleted file mode 100644 index fd6a424..0000000 --- a/src/trees/traversals/BST_with_extra_methods.py +++ /dev/null @@ -1,95 +0,0 @@ -#!/usr/bin/python3 -# mari von steinkirch @2013 -# steinkirch at gmail - -from BST_traversal import TranversalBST -from BST import BST - -class BSTwithExtra(TranversalBST): - def __init__(self): - self.bst = BST(None) - self.nodes = [] - - def get_inorder(self, k): - for i, value in enumerate(self.inorder()): - if value == k: - return i - - def get_preorder(self, k): - for i, value in enumerate(self.preorder()): - if value == k: - return i - - - def is_balanced(self, threshold=1): - maxd = self.get_max_depth() - mind = self.get_min_depth() - print('Max depth: ' + str(maxd)) - print('Min depth: ' + str(mind)) - return maxd -mind - - def get_min_depth(self, node=None, initial=1): - if node is None and initial == 1: - node = self.bst - if node.left and node.right: - return 1 + min(self.get_min_depth(node.left, 0), - self.get_min_depth(node.right, 0)) - else: - if node.left: - return 1 + self.get_max_depth(node.left, 0) - elif node.right: - return 1 + self.get_max_depth(node.right, 0) - else: - return 0 - - def get_max_depth(self, node=None, initial=1): - if node is None and initial == 1: - node = self.bst - if node.left and node.right: - return 1 + max(self.get_max_depth(node.left, 0), - self.get_max_depth(node.right, 0)) - else: - if node.left: - return 1 + self.get_max_depth(node.left, 0) - elif node.right: - return 1 + self.get_max_depth(node.right, 0) - else: - return 0 - -def main(): - """ - 10 - 5 15 - 1 6 11 50 - 60 - 70 - 80 - """ - t = BSTwithExtra() - l1 = [10, 5, 15, 1, 6, 11, 50, 60, 70, 80] - for i in l1: t.insert(i) - print(t.inorder()) - print(t.preorder()) - assert(t.get_max_depth() == 5) - assert(t.get_min_depth() == 2) - assert(t.is_balanced() == 3) - assert(t.get_inorder(10) == 3) - assert(t.get_preorder(10) == 0) - - - """ - 1 - 2 3 - 4 5 6 7 - """ - t2 = BSTwithExtra() - l2 = [1, 2, 3, 4, 5, 6, 7, 8] - for i in l2: t2.insert(i) - print(t2.inorder()) - print(t2.preorder()) - assert(t2.is_balanced() == 0) - - print("Tests Passed!") - -if __name__ == '__main__': - main() diff --git a/src/trees/traversals/__init__.py b/src/trees/traversals/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/src/trees/traversals/binary_tree.py b/src/trees/traversals/binary_tree.py deleted file mode 100644 index 253482c..0000000 --- a/src/trees/traversals/binary_tree.py +++ /dev/null @@ -1,464 +0,0 @@ -#!/usr/bin/python - -__author__ = "Mari Wahl" -__email__ = "marina.w4hl@gmail.com" - - - -''' Implementation of a binary tree and its properties. For example, the following bt: - - 1 ---> level 0 - 2 3 ---> level 1 - 4 5 ---> level 2 - 6 7 ---> level 3 - 8 9 ---> level 4 - - has the following properties: - - - SIZE OR NUMBER OF NODES: n = 9 - - NUMBER OF BRANCHES OR INTERNAL NODES: b = n-1 = 8 - - VALUE OF ROOT = 1 - - MAX_DEPTH OR HEIGHT: h = 4 - - IS BALANCED? NO - - IS BST? NO - - INORDER DFT: 8, 6, 9, 4, 7, 2, 5, 1, 3 - - POSTORDER DFT: 8, 9, 6, 7, 4, 5, 2, 3, 1 - - PREORDER DFT: 1, 2, 4, 6, 8, 9, 7, 5, 3 - - BFT: 1, 2, 3, 4, 5, 6, 7, 8, 9 -''' - -from collections import deque -class NodeBT(object): - def __init__(self, item=None, level=0): - ''' Construtor for a Node in the Tree ''' - self.item = item - self.level = level - self.left = None - self.right = None - self.traversal = [] - #self.parent = None # not used here but can be necessary for some problems - - ''' - METHODS TO MODIFY NODES - ''' - - def _addNextNode(self, value, level_here=1): - ''' Aux for self.addNode(value)''' - self.traversal = [] - new_node = NodeBT(value, level_here) - if not self.item: - self.item = new_node - elif not self.left: - self.left = new_node - elif not self.right: - self.right = new_node - else: - self.left = self.left._addNextNode(value, level_here+1) - return self - - - - ''' - METHODS TO PRINT/SHOW NODES' ATTRIBUTES - ''' - - def __repr__(self): - ''' Private method for this class'string representation''' - return '{}'.format(self.item) - - def _getDFTpreOrder(self, node): - ''' Traversal Pre-Order, O(n)''' - if node: - if node.item: self.traversal.append(node.item) - self._getDFTpreOrder(node.left) - self._getDFTpreOrder(node.right) - return self - - def _printDFTpreOrder(self, noderoot): - ''' Fill the pre-order traversal array ''' - self.traversal = [] - self._getDFTpreOrder(noderoot) - return self.traversal - - def _getDFTinOrder(self, node): - ''' Traversal in-Order, O(n)''' - if node: - self._getDFTinOrder(node.left) - if node.item: self.traversal.append(node.item) - self._getDFTinOrder(node.right) - return self - - def _printDFTinOrder(self, noderoot): - ''' Fill the in-order traversal array ''' - self.traversal = [] - self._getDFTinOrder(noderoot) - return self.traversal - - def _getDFTpostOrder(self, node): - ''' Traversal post-Order, O(n)''' - if node: - self._getDFTpostOrder(node.left) - self._getDFTpostOrder(node.right) - if node.item: self.traversal.append(node.item) - return self - - def _getBFT(self, node): - ''' Traversal bft, O(n)''' - if node: - queue = deque() - queue.append(node) - while len(queue) > 0: - current = queue.popleft() - if current.item: self.traversal.append(current) - if current.left: queue.append(current.left) - if current.right: queue.append(current.right) - return self - - def _printBFT(self, noderoot): - ''' Fill the in-order traversal array ''' - self.traversal = [] - self._getBFT(noderoot) - return self.traversal - - - def _printDFTpostOrder(self, noderoot): - ''' Fill the post-order traversal array ''' - self.traversal = [] - self._getDFTpostOrder(noderoot) - return self.traversal - - def _searchForNode(self, value): - ''' Traverse the tree looking for the node''' - if self.item == value: return self - else: - found = None - if self.left: found = self.left._searchForNode(value) - if self.right: found = found or self.right._searchForNode(value) - return found - - def _findNode(self, value): - ''' Find whether a node is in the tree. - if the traversal was calculated, it is just a membership - checking, which is O(1), otherwise it is necessary to traverse - the binary tree, so best case is O(1) and worst is O(n). ''' - if self.traversal: return value in self.traversal - else: return self._searchForNode(value) - - def _isLeaf(self): - ''' Return True if the node is a leaf ''' - return not self.right and not self.left - - def _getMaxHeight(self): - ''' Get the max height at the node, O(n)''' - levelr, levell = 0, 0 - if self.right: - levelr = self.right._getMaxHeight() + 1 - if self.left: - levell = self.left._getMaxHeight() + 1 - return max(levelr, levell) - - def _getMinHeight(self, level=0): - ''' Get the min height at the node, O(n)''' - levelr, levell = -1, -1 - if self.right: - levelr = self.right._getMinHeight(level +1) - if self.left: - levell = self.left._getMinHeight(level +1) - return min(levelr, levell) + 1 - - def _isBalanced(self): - ''' Find whether the tree is balanced, by calculating heights first, O(n2) ''' - if self._getMaxHeight() - self._getMinHeight() < 2: - return False - else: - if self._isLeaf(): - return True - elif self.left and self.right: - return self.left._isBalanced() and self.right._isBalanced() - elif not self.left and self.right: - return self.right._isBalanced() - elif not self.right and self.left: - return self.right._isBalanced() - - - - def _isBalancedImproved(self): - ''' Find whehter the tree is balanced in each node, O(n) ''' - return 'To Be written' - - ''' There are two solutions to check whether a bt is a bst: - (1) Do an inorder, check if the inorder is sorted. However inorder - can't handle the difference between duplicate values on the left - or on the right (if it is in the right, the tree is not bst). - ''' - - - def _isBST(self): - ''' Find whether the tree is a BST, inorder ''' - if self.item: - if self._isLeaf(): return True - elif self.left: - if self.left.item < self.item: return self.left._isBST() - else: return False - elif self.right: - if self.right.item > self.item: return self.right._isBST() - else: return False - else: - raise Exception('Tree is empty') - - - def _getAncestorBST(self, n1, n2): - ''' Return the ancestor of two nodes if it is a bst. - we are supposing the values in the tree are unique.''' - if n1 == self.item or n2 == self.item : return self.item - elif self.item < n1 and self.item < n2: - self.right.getAncestorBST(n1, n2) - elif self.item > n1 and self.item > n2: - self.left.getAncestorBST(n1, n2) - else: - return self.item - - - - -class BinaryTree(object): - ''' - >>> bt = BinaryTree() - >>> for i in range(1, 10): bt.addNode(i) - >>> bt.hasNode(7) - True - >>> bt.hasNode(12) - False - >>> bt.printTree() - [1, 2, 4, 6, 8, 9, 7, 5, 3] - >>> bt.printTree('pre') - [1, 2, 4, 6, 8, 9, 7, 5, 3] - >>> bt.printTree('bft') - [1, 2, 3, 4, 5, 6, 7, 8, 9] - >>> bt.printTree('post') - [8, 9, 6, 7, 4, 5, 2, 3, 1] - >>> bt.printTree('in') - [8, 6, 9, 4, 7, 2, 5, 1, 3] - >>> bt.hasNode(9) - True - >>> bt.hasNode(11) - False - >>> bt.isLeaf(8) - True - >>> bt.getNodeLevel(1) - 0 - >>> bt.getNodeLevel(8) - 4 - >>> bt.getSizeTree() - 9 - >>> bt.isRoot(10) - False - >>> bt.isRoot(1) - True - >>> bt.getHeight() - 4 - >>> bt.isBST(1) - False - >>> bt.isBalanced() - False - >>> bt.isBalanced(2) - False - >>> bt.getAncestor(8, 5) - 2 - >>> bt.getAncestor(8, 5, 'pre-post') - 2 - >>> bt.getAncestor(8, 5, 'post-in') - 2 - ''' - - - - def __init__(self): - ''' Constructor for the Binary Tree, which is a container of Nodes''' - self.root = None - - - ''' - METHODS TO MODIFY THE TREE - ''' - - def addNode(self, value): - ''' Add new node to the tree, by the left first, O(n) ''' - if not self.root: self.root = NodeBT(value) - else: self.root._addNextNode(value) - - ''' - METHODS TO PRINT/SHOW TREES' ATTRIBUTES - ''' - - def __repr__(self): - ''' Private method for this class'string representation''' - return '{}'.format(self.item) - - def printTree(self, order = 'pre'): - ''' Print Tree in the chosen order ''' - if self.root: - if order == 'pre': return self.root._printDFTpreOrder(self.root) - elif order == 'in': return self.root._printDFTinOrder(self.root) - elif order == 'post': return self.root._printDFTpostOrder(self.root) - elif order == 'bft': return self.root._printBFT(self.root) - else: raise Exception('Tree is empty') - - def hasNode(self, value): - ''' Verify whether the node is in the Tree ''' - return bool(self.root._findNode(value)) - - def isLeaf(self, value): - ''' Return True if the node is a Leaf ''' - node = self.root._searchForNode(value) - return node._isLeaf() - - def getNodeLevel(self, item): - ''' Return the level of the node, best O(1), worst O(n) ''' - node = self.root._searchForNode(item) - if node: return node.level - else: raise Exception('Node not found') - - def getSizeTree(self): - ''' Return how many nodes in the tree, O(n) ''' - return len(self.root._printDFTpreOrder(self.root)) - - def isRoot(self, value): - '''Return the root of the tree ''' - return self.root.item == value - - def getHeight(self): - ''' Returns the height/depth of the tree, best/worst O(n) ''' - return self.root._getMaxHeight() - - def isBalanced(self, method=1): - ''' Return True if the tree is balanced''' - if method == 1: - ''' O(n2)''' - return self.root._isBalanced() - else: - ''' O(n)''' - return self.root._isBalancedImproved() - - - - ''' The following methods are for searching the lowest common ancestor - in a BT. Since a simple BT does not have ordering, it can be O(n). If - we have a link for the ancestors, the steps are: - (1) search both trees in order to find the nodes separately - (2) list all ancestors - (3) find first that mach - obs: if we do this too many times we can do a pre and use the methods here''' - - def isBST(self, method=1): - ''' Return True if the tree is BST''' - if method == 1: - inorder = self.root._printDFTinOrder(self.root) - return inorder == sorted(inorder) - elif method == 2: - return self.root._isBST() - - - def _getAncestorPreIn(self, preorder, inorder, value1, value2): - ''' Return the ancestor of two nodes with pre and in''' - root = preorder[0] - preorder = preorder[1:] - i = 0 - item = inorder[0] - value1left, value2left = False, False - while item != root and i < len(inorder): - if item == value1: value1left = True - elif item == value2: value2left = True - i += 1 - item = inorder[i] - if (value1left and not value2left) or (value2left and not value1left): - return root - else: - return self._getAncestorPreIn(preorder, inorder[:i] + inorder[i+1:], value1, value2) - - def _getAncestorPrePost(self, preorder, postorder, value1, value2): - ''' Return the ancestor of two nodes with pre and post''' - root = preorder[0] - preorder = preorder[1:] - postorder = postorder[:-1] - value1right, value2right = False, False - i = len(postorder)-1 - itempre = preorder[0] - itempos = postorder[i] - while itempre != itempos and i > 0: - if itempos == value1: value1right = True - elif itempos == value2: value2right = True - i -= 1 - itempos = postorder[i] - - if (value1right and not value2right) or (value2right and not value1right): - return root - else: - return self._getAncestorPrePost(preorder, postorder[:i] + postorder[i+1:], value1, value2) - - def _getAncestorInPost(self, inorder, postorder, value1, value2): - ''' Return the ancestor of two nodes with in and post''' - root = postorder[-1] - postorder = postorder[:-1] - value1left, value2left = False, False - i = 0 - item = inorder[i] - while item != root and i < len(inorder): - if item == value1: value1left = True - elif item == value2: value2left = True - i += 1 - item = inorder[i] - - if (value1left and not value2left) or (value2left and not value1left): - return root - else: - return self._getAncestorInPost(postorder, inorder[:i] + inorder[i+1:], value1, value2) - - - - - - def _getAncestorBST2(self, preorder, value1, value2): - ''' Return the ancestor of two nodes if it is a bst, using traversal''' - while preorder: - current = preorder[0] - if current < value1: - try: preorder = preorder[2:] - except: return current - elif current > value2: - try: preorder = preorder[1:] - except: return current - elif value1 <= current <= value2: - return current - return None - - def getAncestor(self, value1, value2, method='pre-in'): - ''' Return the commom ancestor for two nodes''' - if method == 'pre-in': - ''' Using pre and inorder, best/worst O(n)''' - preorder = self.root._printDFTpreOrder(self.root) - inorder = self.root._printDFTinOrder(self.root) - return self._getAncestorPreIn(preorder, inorder, value1, value2) - if method == 'pre-post': - ''' Using pre and postorder, best/worst O(n)''' - preorder = self.root._printDFTpreOrder(self.root) - postorder = self.root._printDFTpostOrder(self.root) - return self._getAncestorPrePost(preorder, postorder, value1, value2) - if method == 'post-in': - ''' Using in and postorder, best/worst O(n)''' - inorder = self.root._printDFTinOrder(self.root) - postorder = self.root._printDFTpostOrder(self.root) - return self._getAncestorInPost(inorder, postorder, value1, value2) - if method == 'bst': - if self.isBST(): - return self.root._getAncestorBST(value1, value2) - - #preorder = self.root._printDFTpreOrder(self.root) - #return self._getAncestorBST2(preorder, value1, value2) - else: - return Exception('The tree is not a BST') - - -if __name__ == '__main__': - import doctest - doctest.testmod() diff --git a/src/trees/traversals/traversals.py b/src/trees/traversals/traversals.py deleted file mode 100644 index a962d46..0000000 --- a/src/trees/traversals/traversals.py +++ /dev/null @@ -1,131 +0,0 @@ -#!/usr/bin/python3 -# mari von steinkirch @2013 -# steinkirch at gmail - -from BST import BST - - -from collections import deque -class TranversalBST(object): - def __init__(self): - self.bst = BST(None) - self.nodes = [] - - def insert(self, value): - if not self.bst.value: - self.bst.value = value - else: - self.bst.insert(value) - - def contains(self, value): - return bool(self.bst.find(value)) - - def get(self, index): - for i, value in enumerate(self.inorder()): - if i == index: - return value - - def inorder(self): - current = self.bst - self.nodes = [] - stack = [] - while len(stack) > 0 or current is not None: - if current is not None: - stack.append(current) - current = current.left - else: - current = stack.pop() - self.nodes.append(current.value) - current = current.right - return self.nodes - - - def preorder(self): - self.nodes = [] - stack = [self.bst] - while len(stack) > 0: - curr = stack.pop() - if curr is not None: - self.nodes.append(curr.value) - stack.append(curr.right) - stack.append(curr.left) - return self.nodes - - - def preorder2(self): - self.nodes = [] - current = self.bst - stack = [] - while len(stack) > 0 or current is not None: - if current is not None: - self.nodes.append(current.value) - stack.append(current) - current = current.left - else: - current = stack.pop() - current = current.right - return self.nodes - - - - def preorder3(self): - self.nodes = [] - node = self.bst - if not node: return None - stack = [] - stack.append(node) - while stack: - node = stack.pop() - self.nodes.append(node.value) - if node.right: stack.append(node.right) # RIGHT FIRST! - if node.left: stack.append(node.left) - return self.nodes - - - - - def BFT(self): - self.nodes = [] - node = self.bst - if not node: return None - queue = deque() - queue.append(node) - while queue: - node = queue.popleft() - self.nodes.append(node.value) - if node.left: queue.append(node.left) # LEFT FIRST! - if node.right: queue.append(node.right) - - return self.nodes - - - - -def main(): - """ - 10 - 5 15 - 1 6 11 50 - """ - t = TranversalBST() - t.insert(10) - t.insert(5) - t.insert(15) - t.insert(1) - t.insert(6) - t.insert(11) - t.insert(50) - print(t.preorder()) - print(t.preorder2()) - print(t.preorder3()) - print(t.inorder()) - print(t.BFT()) - ''' - [10, 5, 1, 6, 15, 11, 50] - [10, 5, 1, 6, 15, 11, 50] - [10, 5, 1, 6, 15, 11, 50] - [1, 5, 6, 10, 11, 15, 50] - [10, 5, 15, 1, 6, 11, 50] - ''' -if __name__ == '__main__': - main()