This is a Python program to implement a binomial tree.

The program creates binomial trees and presents a menu to the user to perform operations on these trees.

1. Create a class BinomialTree with instance variables key, children and order. children is set to an empty list and order is set to 0 when an object is instantiated.

2. Define method add_at_end which takes a binomial tree of the same order as argument and adds it to the current tree, increasing its order by 1.

Here is the source code of a Python program to implement a binomial tree. The program output is shown below.

class BinomialTree: def __init__(self, key): self.key = key self.children = [] self.order = 0 def add_at_end(self, t): self.children.append(t) self.order = self.order + 1 trees = [] print('Menu') print('create <key>') print('combine <index1> <index2>') print('quit') while True: do = input('What would you like to do? ').split() operation = do[0].strip().lower() if operation == 'create': key = int(do[1]) btree = BinomialTree(key) trees.append(btree) print('Binomial tree created.') elif operation == 'combine': index1 = int(do[1]) index2 = int(do[2]) if trees[index1].order == trees[index2].order: trees[index1].add_at_end(trees[index2]) del trees[index2] print('Binomial trees combined.') else: print('Orders of the trees need to be the same.') elif operation == 'quit': break print('{:>8}{:>12}{:>8}'.format('Index', 'Root key', 'Order')) for index, t in enumerate(trees): print('{:8d}{:12d}{:8d}'.format(index, t.key, t.order))

1. An empty list is created to store the binomial trees.

2. The user is presented with a menu to create and combine two binomial trees.

3. Only trees of the same order k are allowed to combine to form a tree of order k + 1.

4. The corresponding methods are called to perform each operation.

Case 1: create <key> combine <index1> <index2> quit What would you like to do? create 7 Binomial tree created. Index Root key Order 0 7 0 What would you like to do? create 3 Binomial tree created. Index Root key Order 0 7 0 1 3 0 What would you like to do? create 4 Binomial tree created. Index Root key Order 0 7 0 1 3 0 2 4 0 What would you like to do? create 1 Binomial tree created. Index Root key Order 0 7 0 1 3 0 2 4 0 3 1 0 What would you like to do? combine 0 1 Binomial trees combined. Index Root key Order 0 7 1 1 4 0 2 1 0 What would you like to do? combine 1 2 Binomial trees combined. Index Root key Order 0 7 1 1 4 1 What would you like to do? combine 0 1 Binomial trees combined. Index Root key Order 0 7 2 What would you like to do? quit Case 2: Menu create <key> combine <index1> <index2> quit What would you like to do? create 2 Binomial tree created. Index Root key Order 0 2 0 What would you like to do? create 3 Binomial tree created. Index Root key Order 0 2 0 1 3 0 What would you like to do? create 1 Binomial tree created. Index Root key Order 0 2 0 1 3 0 2 1 0 What would you like to do? combine 2 0 Binomial trees combined. Index Root key Order 0 3 0 1 1 1 What would you like to do? quit

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