Chapter 4 Trees and Graphs - 4.3

Problem 4.3 Given a sorted (increasing) array, write an algorithm to create a binary tree with minimal height.

Seems that we should construct a complete binary tree.

from queue import *class binary_tree_node:    def __init__(self, value = None):        self.value = value        self.left = None        self.right = Nonedef construct_min_btree(array):    # Keep track of current element in the array    i = 0    # Construct while doing BFS    q = queue()    root = binary_tree_node(array[i])    i += 1    q.enqueue(root)    while not q.is_empty():        n = q.dequeue()        # Construct left child        n.left = binary_tree_node(array[i])        i += 1        if i == len(array):            break        q.enqueue(n.left)        # Construct right child        n.right = binary_tree_node(array[i])        i += 1        if i ==  len(array):            break        q.enqueue(n.right)    return root# Test caseif __name__ == "__main__":    array = [i for i in range(0, 80)]    root = construct_min_btree(array)    # Print the binary tree in level-order    q = queue()    q.enqueue(root)    current_level = 0    num_in_current_level = 2**current_level    while not q.is_empty():        n = q.dequeue()        print n.value,        if n.left != None:            q.enqueue(n.left)        if n.right != None:            q.enqueue(n.right)        num_in_current_level -= 1        # End of a level        if num_in_current_level == 0:            current_level += 1            num_in_current_level = 2**current_level            print "\n"

The solution on the answer page constructs a binary search tree with recursion.

from queue import *class binary_tree_node:    def __init__(self, value = None):        self.value = value        self.left = None        self.right = Nonedef construct_min_btree(array, start, end):    if start > end:        return    mid = (start + end)/2    n = binary_tree_node(array[mid])    n.left = construct_min_btree(array, start, mid - 1)    n.right = construct_min_btree(array, mid + 1, end)    return n# Test caseif __name__ == "__main__":    array = [i for i in range(0, 8)]    root = construct_min_btree(array, 0, 7)    # Print the binary tree in level-order    q = queue()    q.enqueue(root)    current_level = 0    num_in_current_level = 2**current_level    while not q.is_empty():        n = q.dequeue()        print n.value,        if n.left != None:            q.enqueue(n.left)        if n.right != None:            q.enqueue(n.right)        num_in_current_level -= 1        # End of a level        if num_in_current_level == 0:            current_level += 1            num_in_current_level = 2**current_level            print "\n"