[ACE] Binary Search Tree


  • Tree Terminology
Root: node without parent
Internal node: node with at least one child
External node: node without children
Depth: number of ancestors(not counting itself)/ number of lines from the node to the root
Height: maximum depth of any node/ length of longest path from root to a leaf

  • Binary Search Tree and its implementation
Binary Search Tree(BST): A binary search tree is a rooted binary tree, whose internal nodes each store a key (and optionally, an associated value) and each have two distinguished sub-trees, commonly denoted left and right. The tree additionally satisfies the binary search tree property, which states that the key in each node must be greater than all keys stored in the left sub-tree, and not greater than all keys in the right sub-tree. 
Simply speaking, it is a binary tree and the left child is always smaller than the parent, the right child is always greater than the parent

 Implementation

Traversal: 
Preorder Traversal: 
  • In a preorder traversal, a node is visited before its descendants 

Inorder Traversal
  • In an inorder traversal a node is visited after its left subtree and before its right subtree 


Postorder Traversal
• In a postorder traversal, a node is visited after its descendants

  • Properties of perfect binary trees
At level d, the number of nodes on level d is 2d
The number of all nodes are 1+ 2d+1
For the perfect binary trees, the height(h) and size(n) has the following relationship:
  • h=log2 (n+1)-1
which can be proved by induction 
I won't give the prove process of this because it is really simple


评论

发表评论

此博客中的热门博文

[MLE] Linear Classification

图片
Linear Classification Discriminant functions Least squares for classification Fisher’s linear discriminant K-Nearest Neighbour(KNN) Classification What’s decision boundaries/linearly separable? The goal in classification is to take an input vector x and to assign it to one of K discrete classes \(C_k\) where k = 1,…,K. In the most common scenario, the classes are taken to be disjoint, so that each input is assigned to one and only one class. The input space is thereby divided into decision regions whose boundaries are called decision boundaries or decision surfaces. In this blog, we consider linear models for classification , by which we mean that the decision surfaces are linear functions of the input vector x and hence are defined by (D-1) -dimensional hyperplanes within the D-dimensional input space. For example: in 3D input space, the decision boundary will be a 2D surface What is Linear Separability Linearly separable data: Datasets whose classes can be separated by
阅读全文

[AIM] MetaHeuristics

图片
Day2 Outline Metaheuristics -definition Single point based search method(simple stochastic local search) Iterated local search Scheduling Tabu Search Metaheuristic what is a metaheuristic? A metaheuristic is a high-level problem independent algorithmic framework that provides a set of guidelines or strategies to develop heuristic optimization algorithms. what is the difference between heuristic and metaheuristic? Heuristic : Heuristics are problem-dependent techniques. As such, they usually are adapted to the problem at hand and they try to take full advantage of the particularities of this problem. However, because they are often too greedy, they usually get trapped in a local optimum and thus fail, in general, to obtain the global optimum solution. Metaheuristic : Meta-heuristics, on the other hand, are problem-independent techniques . As such, they do not take advantage of any specificity of the problem and, therefore, can be used as black boxes . In general, t
阅读全文

[CS231] Neural Networks

图片
Neural Network Table of Contents: Quick intro without brain analogies Modeling one neuron Biological motivation and connections Single neuron as a linear classifier Commonly used activation functions Neural Network architectures Layer-wise organization Summary Additional references Quick intro It is possible to introduce neural networks without appealing to brain analogies. In the section on linear classification we computed scores for different visual categories given the image using the formula \( s = W x \), where \(W\) was a matrix and \(x\) was an input column vector containing all pixel data of the image. In the case of CIFAR-10, \(x\) is a [3072x1] column vector, and \(W\) is a [10x3072] matrix, so that the output scores is a vector of 10 class scores. An example neural network would instead compute \( s = W_2 \max(0, W_1 x) \). Here, \(W_1\) could be, for example, a [100x3072] matrix transforming the image into a 100-dimensional intermediate vector. The funct
阅读全文