import random import queue # The program shows how a tree can be represented only by arrays of values. # each node is assigned a unique number (label) and by that number it is # recognized. The information related to a node, its key, the labels of # the children and parent etc, are stored in separate arrays. # The number (label) of the node serves as index to those arrays. # It is therefore unnecessary to store the number(label) of the node # anywhere in the memory. # Below, arrays K, L, R, P store Keys, Left child number, Right child # number, parent number, respectively, for all nodes in the tree. # ............................................................................ # N O D E # ............................................................................ class Node: def __init__(self, key): self.left = None self.right = None self.key = key self.xcoord = -1 self.tag = ' ' # one character self.num = 0 def print(self): print( "[" + str(self.key) + "]", end = "" ) print( str(self.xcoord)+", ", end = "") # ............................................................................ # B I N A R Y T R E E # ............................................................................ class BinaryTree: # ........................................................................ # C O N S T R U C T O R def __init__(self, key ): self.root = Node( key ) def rndTree(self, node, depth): node.key = 10+random.randrange(90) if depth <= 0: return node if random.randrange(0, 10) < 6: childNode = Node ( 0 ) # any key will do node.left = self.rndTree( childNode, depth-1 ) if random.randrange(0, 10) < 6: childNode = Node ( 0 ) # any key will do node.right = self.rndTree( childNode, depth-1 ) return node # ........................................................................ # S E R V I C E M E T H O D S (mainly printing) def countNodes(self, node): if node == None: return 0 return 1 + self.countNodes( node.left ) + self.countNodes( node.right ) # calculates x coord = node order of InOrder traversal def setXcoord(self, node, x_coord): if node == None: return x_coord node.xcoord = self.setXcoord(node.left, x_coord) + 1 #print(node.key, node.setXcoord) return self.setXcoord(node.right, node.xcoord) def display(self): self.setXcoord(self.root, 0) qu = queue.Queue() prevDepth = -1 prevEndX = -1 # in the queue store pairs(node, its depth) qu.put( (self. root, 0) ) while not qu.empty(): node, nodeDepth = qu.get() LbranchSize = RbranchSize = 0 if node.left != None: LbranchSize = (node.xcoord - node.left.xcoord) qu.put( (node.left, nodeDepth+1) ) if node.right != None: RbranchSize = (node.right.xcoord - node.xcoord) qu.put( (node.right, nodeDepth+1) ) LspacesSize = (node.xcoord - LbranchSize) - 1 # if first on a line if prevDepth == nodeDepth: # not first on line LspacesSize -= prevEndX # print the node, branches, leading spaces if prevDepth < nodeDepth and prevDepth > -1 : print() # next depth occupies new line nodelen = 5 print( " "*nodelen*LspacesSize, end = '' ) print( "_"*nodelen*LbranchSize, end = '' ) #print( "." + ("%2d"%node.key) + node.tag+".", end = '' ) print( ("%2d"%node.num) +"_" + ("%2d"%node.key), end = '' ) print( "_"*nodelen*RbranchSize, end = '' ) # used in the next run of the loop: prevEndX = node.xcoord + RbranchSize prevDepth = nodeDepth # end of queue processing N = self.countNodes( self.root ) print("\n"+ '-'*N*nodelen) # finish the last line of the tree # ........................................................................ # C U S T O M F U N C T I O N (S) # .............................................. # returns the number of the rightmost (last one) node # in the subtree rooted in "node" def NumberPreOrder_rec(self, node, currNum): if node == None: return currNum # no change # assign the number to the node currNum += 1 node.num = currNum # go left from this node # and update currrent number (currMun) currNum = self.NumberPreOrder_rec(node.left, currNum) # go right from this node and update currNum again currNum = self.NumberPreOrder_rec(node.right, currNum) return currNum def numberPreOrder(self): self.NumberPreOrder_rec(self.root, -1 ) # Setting the numbers of nodes in InOrder sequence, is a little bit more # tricky. In fact, it is used in the display method. # To assign to a node X a number which corresponds to the InOrder # position of the node, we must know how many nodes are there in total # to the left of X in the whole tree. The function setXcoord does it. # ..................................................................... def intoArrays_rec(self, node, currNum, K, L, R, P): if node == None: return currNum # no change # assign the number to the node currNum += 1 node.num = currNum #initialize node in arrays K[node.num] = node.key L[node.num] = -1 R[node.num] = -1 P[node.num] = -1 # go left from this node if node.left != None: currNum = self.intoArrays_rec(node.left, currNum, K, L, R, P) # register the link between node and its left child L[node.num] = node.left.num P[node.left.num] = node.num # go right from this node if node.right != None: currNum = self.intoArrays_rec(node.right, currNum, K, L, R, P) # register the link between node and its right child R[node.num] = node.right.num P[node.right.num] = node.num return currNum def intoArrays(self): countAll = self.countNodes(self.root) K = [-1] * countAll L = [-1] * countAll R = [-1] * countAll P = [-1] * countAll self.intoArrays_rec( self.root, -1, K, L, R, P) return K, L, R, P def print3(text, arr): print(text, end = '') for x in arr: print( ("%3d"%x), end = '') print() def inOrder(nodeNum): if nodeNum == -1: return # non-existent node inOrder( L[nodeNum] ) print( K[nodeNum], end = ' ') inOrder( R[nodeNum] ) # ............................................................................ # M A I N P R O G R A M # ............................................................................ # initialize the random number generator random.seed( 1038 ) # create a tree with a single node -- root. t = BinaryTree( 0 ) # create random tree with maximum depth 4 t.rndTree( t.root, 4 ) t.numberPreOrder() # display the created tree t.display() K, L, R, P = t.intoArrays() nums = list(range(len(K))) print3(" ", nums) print("---" + "---" * len(K)) print3("K: ", K) print3("L: ", L) print3("R: ", R) print3("P: ", P) print() inOrder(0) # ------------------------------ ''' Calling flipTree and using the random seed 1038, the output should be as follows: You may try other seed values as well. _______________ 24___ ____________ 42______ 89_________ ___ 25______ ___ 81___ ______ 32______ ___ 72 ___ 15___ 62 60___ 40___ ___ 12___ 68 87 44 18 10 70 78 --------------------------------------------------------- ___ 24_______________ _________ 89 ______ 42____________ ______ 32______ ___ 81___ ______ 25___ ___ 12___ ___ 40 ___ 60 62 ___ 15___ 72___ 78 70 10 18 44 87 68 --------------------------------------------------------- '''