Create Binary_Search_Tree.py

Author: ashwek

Data_Structure/src/Binary_Search_Tree.py

@@ -0,0 +1,173 @@
+"""
+A binary search tree is a rooted binary tree, whose internal nodes each
+store a key (and optionally, an associated value) and each have two
+distinguished sub-trees, commonly denoted left and right.
+
+The tree additionally satisfies the binary search property, which states that
+the key in each node must be greater than or equal to any key stored in the
+left sub-tree, and less than or equal to any key stored in the right sub-tree.
+
+https://en.wikipedia.org/wiki/Binary_search_tree
+
+"""
+
+from random import randint
+
+class Node:         # class to create nodes
+    def __init__(self, Parent = None, Value = None, Left = None, Right = None):
+        self.parent = Parent        # points to parent of Node
+        self.value = Value          # value in Node
+        self.left = Left            # points to left child
+        self.right = Right          # points to right child
+
+    def __str__(self):
+        return str(self.value)
+
+class BST:
+
+    def __init__(self):
+        self.__root = None      # initially root = None
+
+    def is_empty(self):
+        return self.__root == None
+
+    def insert(self, val):
+        if( self.is_empty() ):          # if root = None (no nodes added to tree)
+            self.__root = Node(Value = val)     # create new node & assign to root
+        else:
+            current = self.__root           # current node = root (initially)
+            while( current != None ):
+                parent = current
+                current = current.left if( val <= current.value ) else current.right    # if val < current.value, goto left child, else goto right child
+
+            if( val <= parent.value ):          # if val < parent.value
+                parent.left = Node(parent, val)     # assign new node as Left child
+            else:
+                parent.right = Node(parent, val)    # assign new node as Right child
+
+    def preorder(self, current = -1):
+        if (current == -1 ): current = self.__root      # if current == -1 (no argument passed), current = root
+
+        # Pre-Order = (Root, Left, Right)
+        Ret = []
+        if(current != None):
+            Ret.append(current.value)   # Root (value)
+            Ret.extend(self.preorder(current.left))     # Left (subtree)
+            Ret.extend(self.preorder(current.right))    # Right (subtree)
+        return Ret
+
+    def inorder(self, current = -1):
+        if (current == -1 ): current = self.__root      # if current == -1 (no argument passed), set current = root
+
+        # In-Order = (Left, Root, Right)
+        Ret = []
+        if(current != None):
+            Ret.extend(self.inorder(current.left))     # Left (subtree)
+            Ret.append(current.value)   # Root (value)
+            Ret.extend(self.inorder(current.right))    # Right (subtree)
+        return Ret
+
+    def postorder(self, current = -1):
+        if (current == -1 ): current = self.__root      # if current == -1 (no argument passed), set current = root
+
+        # Post-Order = (Left, Right, Root)
+        Ret = []
+        if(current != None):
+            Ret.extend(self.postorder(current.left))     # Left (subtree)
+            Ret.extend(self.postorder(current.right))    # Right (subtree)
+            Ret.append(current.value)   # Root (value)
+        return Ret
+
+    def levelorder(self, current = -1):
+
+        Ret = []
+
+        if( self.is_empty() ): return Ret       # if tree is empty, return empty list
+
+        if( current == -1 ):
+            current = [self.__root]      # if current == -1 (no argument passed), set current = [root]
+            Ret.append(self.__root.value)       # append root.value to Ret
+
+        next_level = []     # list of all nodes on Next Level
+
+        for each in current:    # current -> list of all nodes on any particular level
+
+            if( each.left != None ):    # if node on current level has left child
+                Ret.append(each.left.value)     # insert its value to Ret
+                next_level.append(each.left)    # add left child to next_level
+
+            if( each.right != None ):   # if node on current level has right child
+                Ret.append(each.right.value)    # insert its value to Ret
+                next_level.append(each.right)   # add right child to next_level
+
+        if( next_level ):       # if there are any nodes in the next_level
+            Ret.extend(self.levelorder(next_level))     # process nodes in next_level
+
+        return Ret
+
+    def search(self, find):
+        current = self.__root
+
+        while current and current.value != find :       # while current (current != None) and value is not found
+            current = current.right if(current.value < find) else current.left      # if "find" is larger than current.value, traverse Right sub-tree, else left sub-tree
+
+        return current      # return Node (None if value not found)
+
+    def maximum(self, current = -1):
+        if current == -1:           # find maximum of current sub tree, if argument is not passed, use root
+            current = self.__root
+
+        while current and current.right != None :       # while current != None & current has a right child
+            current = current.right
+        return current
+
+    def minimum(self, current = -1):
+        if current == -1:           # find minimum of current sub tree, if argument is not passed, use root
+            current = self.__root
+
+        while current and current.left != None :       # while current != None & current has a left child
+            current = current.left
+        return current
+
+    def successor(self, node):
+
+        if node.right == None:          # if node does not have right child
+            while node.parent != None and node.parent.right == node :   # traverse to parent while Parent != None & node is right child of parent
+                node = node.parent
+            return node.parent
+        else:
+            return self.minimum(node.right)     # return Minimum from right subtree
+
+    def predecessor(self, node):
+
+        if node.left == None:
+            while node.parent != None and node.parent.left == node :
+                node = node.parent
+            return node.parent
+        else:
+            return self.maximum(node.left)      # return Maximum from left subtree
+
+if __name__ == "__main__":
+
+    T1 = BST()
+
+    # insert random 10 numbers in the tree
+    for i in range(10):
+        T1.insert(randint(1, 50))
+
+    print("Level-Order = ", T1.levelorder())
+    print("  Pre-Order = ", T1.preorder())
+    print(" Post-Order = ", T1.postorder())
+    print("   In-Order = ", T1.inorder())
+
+    find = 10
+    Found_Node = T1.search(find)
+    if(Found_Node):
+        print("Successor of", find, " = ", T1.successor(Found_Node))
+        print("Predecessor of", find, " = ", T1.predecessor(Found_Node))
+        print("\nValue Found, Parent = ", Found_Node.parent, "left = ", Found_Node.left, "right = ", Found_Node.right)
+    else:
+        print("\n", find, "not found in tree")
+
+    print("\nMaximum = ", T1.maximum())
+    print("Minimum = ", T1.minimum())