common variants binary trees boot camp good way to get up to speed with binary trees is to implement the three basic traversals--inorderpreorderand postorder def tree_traversal (root)if rootpreorder processes the root before the traversals of left and right children print('preorder %droot datatree_traversal (root leftinorder processes the root after the traversal of left child and before the traversal of right child print('inorder %droot datatree_traversal (root right postorder processes the root after the traversals of left and right children print('postorder %droot datathe time complexity of each approach is ( )where is the number of nodes in the tree although no memory is explicitly allocatedthe function call stack reaches maximum depth of hthe height of the tree thereforethe space complexity is (hthe minimum value for is log (complete binary treeand the maximum value for is (skewed treerecursive algorithms are well-suited to problems on trees remember to include space implicitly allocated on the function call stack when doing space complexity analysis please read the introduction to if you need refresher on recursion some tree problems have simple brute-force solutions that use (nspace solutionbut subtler solutions that uses the existing tree nodes to reduce space complexity to ( consider leftand right-skewed trees when doing complexity analysis note that (hcomplexitywhere is the tree heighttranslates into (log ncomplexity for balanced treesbut (ncomplexity for skewed trees if each node has parent fielduse it to make your code simplerand to reduce time and space complexity it' easy to make the mistake of treating node that has single child as leaf table top tips for binary trees test if binary tree is height-balanced binary tree is said to be height-balanced if for each node in the treethe difference in the height of its left and right subtrees is at most one perfect binary tree is height-balancedas is complete binary tree height-balanced binary tree does not have to be perfect or complete--see figure on the next page for an example