binary-tree | 易学教程

Generating all possible topologies in a full binary tree having n nodes

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I want to create all possible topologies of a full binary tree which must have exactly n+1 leaf nodes and n internal nodes. I want to create it using recursion and tree must be simple binary tree not a binary search tree or BST. Kindly suggest algorithm to achieve this task. example: with 4 leaf nodes and 3 internal nodes. N N N / \ / \ /\ N N N N N N /\ /\ /\ /\ N N N N N N N N / \ /\ N N N N PS: There is a simlar thread .It will be helpful If anybody can elaborate the tree generation algorithm suggested by coproc in this thread . Thanks in advance. Here is the code for generating all

How do you save a tree data structure to binary file in Haskell

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问题 I'm trying to save a simple (but quite big) Tree structure into a binary file using Haskell. The structure looks something like this: -- For simplicity assume each Node has only 4 childs data Tree = Node [Tree] | Leaf [Int] And here is how I need the data look on disk: Each node starts with four 32-bit offsets to it's children, then follow the childs. I don't care much about the leafs, let's say it's just n consecutive 32-bit numbers. For practival purposes I would need some node labels or

making binary search tree

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问题 How do I make a BST when I have an array list of 100 elements like {3,2,6,7,...,99} ? 回答1: I believe TreeSet is an implementation of a binary search tree. Since integers have a natural ordering you could simply loop through your array of integers and add them all to a TreeSet<Integer> . Note also, that there is a method Arrays.binarySearch that does a binary search in a sorted array. int[] someInts = {3,2,6,7, /*...,*/ 99}; // use a TreeSet TreeSet<Integer> ints = new TreeSet<Integer>(); for

How to split a rope tree?

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I came across a rope tree as an alternative data structure for a string. http://en.wikipedia.org/wiki/Rope_(data_structure) To concat is easy, but I am stuck on the split operation. The wikipedia article states: For example, to split the 22-character rope pictured in Figure 2.3 into two equal component ropes of length 11, query the 12th character to locate the node K at the bottom level. Remove the link between K and the right child of G. Go to the parent G and subtract the weight of K from the weight of G. Travel up the tree and remove any right links, subtracting the weight of K from these

Trying to implement path record for Haskell binary tree search

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问题 I've been playing around with binary trees in Haskell, and I am attempting to implement a dfs variant that returns the path (composed of left and rights) from the root node to the node containing the value searched for. I think it would be best to return a Maybe Directions type. Here is what has been implemented so far. data Tree a = Empty | Node a (Tree a) (Tree a) deriving (Show, Eq) data Direction = L | R deriving (Show) type Directions = [Direction] inTree :: (Eq a) => a -> Tree a ->

What is the average asymptotic depth of a simple unbalanced search tree?

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For a balanced search tree, it is O(log(N)) for all cases. For unbalanced search trees, the worst case is O(N), e.g., insert 1, 2, 3, 4,.. and best case complexity is when it is balanced, e.g., insert 6, 4, 8, 3, 5 7. How do we define the average case complexity for unbalanced search tree? The average height of Binary Trees is Theta(sqrt(n)). This has been shown (or referenced, not very sure) in the following paper: http://www.dtc.umn.edu/~odlyzko/doc/arch/extreme.heights.pdf . But perhaps you are more interested in the average depth of a random node and this is Theta(log n), as can be seen

Binary tree that stores partial sums: Name and existing implementations

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问题 Consider a sequence of n positive real numbers, ( a i ), and its partial sum sequence, ( s i ). Given a number x ∊ (0, s n ], we have to find i such that s i −1 < x ≤ s i . Also we want to be able to change one of the a i ’s without having to update all partial sums. Both can be done in O(log n ) time by using a binary tree with the a i ’s as leaf node values, and the values of the non-leaf nodes being the sum of the values of the respective children. If n is known and fixed, the tree doesn’t

Simple numerical expression solver

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First of all, sorry for my bad English. For my last project on my Algorithms and Data Structures class, I need to create a simple numerical expression solver in C++. It needs to solve simple expressions like 3*12+(4-6) . I managed to split the expression and separate the operators from the numbers, but I can't go any further. The trick is putting the operators on a binary tree, but I haven't managed to do that. The program needs to use only the default C++ libs. Maybe there is some basic implementation I can build on? Thanks in advance. Forget binary trees for a moment. You need to convert the

Binary Tree Using PHP + MySQL

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问题 I am implementing an MLM tree for a website using PHP (CodeIgniter) and MySQL. I need a binary tree implementation in the database. The followings things are to be considered: For each node , Minimum of the number of children/nodes in left subtree and the number of children/nodes in right subtree is called a pair. For each pair one nodes gets 1 point - which should be stored in database (nodes represent users) When a new node is created (wherever), it is possible that many of the nodes' pair

Binary Process Tree with fork()

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My first project for my OS class is to create a process tree using fork() that has a depth that the user specifies at the command line. Each leaf level node needs to sort data and pass it back to its parent using named-pipes (FIFOs). I can create an N-depth tree with fork() , each process having 2 children. What I can’t figure out is how to pass a FIFO to each child all the way down the tree and then have this process perform a sort on certain data in the FIFO and then also pass it back up the tree to the top. Here is the pseudo-code of what I have so far for building the tree: void CreateTree