binary-tree

问题 What is the benefit of a binary search tree over a sorted array with binary search? Just with mathematical analysis I do not see a difference, so I assume there must be a difference in the low-level implementation overhead. Analysis of average case run time is shown below. Sorted array with binary search search: O(log(n)) insertion: O(log(n)) (we run binary search to find where to insert the element) deletion: O(log(n)) (we run binary search to find the element to delete) Binary search tree

问题 What is the benefit of a binary search tree over a sorted array with binary search? Just with mathematical analysis I do not see a difference, so I assume there must be a difference in the low-level implementation overhead. Analysis of average case run time is shown below. Sorted array with binary search search: O(log(n)) insertion: O(log(n)) (we run binary search to find where to insert the element) deletion: O(log(n)) (we run binary search to find the element to delete) Binary search tree

问题 I have some questions on binary trees: Wikipedia states that a binary tree is complete when "A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible." What does the last "as far left as possible" passage mean? A well-formed binary tree is said to be "height-balanced" if (1) it is empty, or (2) its left and right children are height-balanced and the height of the left tree is within 1 of the height

问题 I created a tuple from a binary tree and it looks like this: tuple = (1,(2,(4,5,6),(7,None,8)),(3,9,(10,11,12))) The tree structure becomes more clear by applying indentation: (1, (2, (4, 5, 6 ), (7, None, 8 ) ), (3, 9, (10, 11, 12 ) ) ) I know how to find the maximum depth of the binary tree using recursive method, but I am trying to find the maximum depth using the tuple I created. Can anyone help me with how to do it? 回答1: Recursive method: a = (1,(2,(4,5,6),(7,None,8)),(3,9,(10,11,12)));

问题 How can I get the tree form these pre/in order traversal: Pre: A,B,D,E,C,F,G,H in:E,D,B,A,G,F,H,C EDITED: MY Answer A / \ B C / \ D F / / \ E G H 回答1: EDIT: Correction, You don't have the correct answer, FGH is to the left of C. To verify just run the two algorithms against it: PreOrder(node) if node is null return Print(node) PreOrder(node.left) PreOrder(node.Right) InOrder(node) if node is null return InOrder(node.left) Print(node) InOrder(node.Right) You know that A is the root because it

问题 I am reading a book on data structures and it says that a left balanced binary tree is a tree in which the leaves only occupy the leftmost positions in the last level. This seemed a little vague to me. Does this mean that leaves are only on the left side of a root and are distributed throughout the whole level, or leave exists only on the left side of the entire tree. Exactly what constitute left balanced? I am not sure if my guess even covers any of the answer, so if anyone could help, it

问题 I am trying to perform an inorder traversal of a tree. The code itself feels right, except it is not working properly. I have a feeling it has to either do with the if condition, how append works in python, or something perhaps with return. This works correctly if I use print instead of return, I think, but I want to be able to use return and still get the correct answer. For example, for the tree [1,None,2,3], my code returns [1] which is clearly incorrect. Additionally is it possible to

问题 Calculate the longest path between two nodes. The path is in an arch. Signature of method is: public static int longestPath(Node n) In the example binary tree below, it is 4 (going thru 2-3-13-5-2). This is what I have right now and for the given tree it just returns 0. public static int longestPath(Node n) { if (n != null) { longestPath(n, 0); } return 0; } private static int longestPath(Node n, int prevNodePath) { if (n != null && n.getLeftSon() != null && n.getRightSon() != null) { int

问题 I want to implement an algorithm that inserts sorted arrays into binary search trees but I don't want ending up with a tree that only grows to one side. Do you have any ideas? Thanks. 回答1: This should give you a balanced tree (in O(n)): Construct a node for the middle element in the array and return it (this will be the root in the base case). Repeat from 1. on the left half of the array, assigning the return value to the left child of the root. Repeat from 1. on the right half of the array,

问题 What would be the efficient algorithm to find if two given binary trees are equal - in structure and content? 回答1: It's a minor issue, but I'd adapt the earlier solution as follows... eq(t1, t2) = t1.data=t2.data && eq(t1.left, t2.left) && eq(t1.right, t2.right) The reason is that mismatches are likely to be common, and it is better to detect (and stop comparing) early - before recursing further. Of course, I'm assuming a short-circuit && operator here. I'll also point out that this is