2014 soft test programmer-frequent test knowledge point review notes [Chapter 4]

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4. String

The following are the main bastion hosts that need to be cracked in the following chapters:

1. Basic concepts of strings: Relationships between strings and linear tables (strings are special linear tables whose elements are complex data), differences between empty strings and space strings, conditions where strings are equal;

2. Basic operations on strings and the use of these basic functions, including getting substrings, connecting strings, replacing strings, and obtaining string lengths. Using the basic operations of strings to complete specific algorithms is the focus of many schools on basic operations.

3. Differences and connections between sequential strings and blockchain strings and their implementation methods.

4. KMP algorithm IDEA. The method for finding the next array and nextval array in KMP. Identify the shortcomings of the traditional pattern matching algorithm, and clarify the need to improve the next array. The possible methods are as follows: Evaluate the values of the next and nextval arrays, and give the matching process using the KMP Algorithm Based on the obtained values of the next or nextval arrays.

5. Multi-dimensional array and generalized table

A matrix includes a symmetric matrix, a triangular matrix, and a sparse matrix with certain characteristics.

Three storage methods familiar with sparse matrices: triplet, binary groups with auxiliary row vectors, and cross-linked list storage.

Master the algorithm for converting the triplet or Binary Group of the sparse matrix to the cross linked list.

6. Tree and binary tree

Knowledge points in the tree Chapter include:

The concept, nature, and storage structure of Binary Trees, three algorithms for binary tree traversal (recursion and non-recursion), implement other algorithms for Binary Trees Based on the three basic Traversal Algorithms, the concept, structure, and application of the optimal binary tree, and the concept and storage form of the tree, tree-to-Forest Traversal Algorithms and Their Relationships with binary tree traversal algorithms. Tree-to-forest and binary tree conversion.

(1) concepts, properties, and storage structure of Binary Trees

Test methods include: directly examine the definition of a binary tree, let you explain the difference between a binary tree and a common double branch tree (left and right Subtrees unordered); examine the nature of a full binary tree and a full binary tree, five properties of a common Binary Tree:

A. Maximum number of knots at layer I,

B. the maximum number of knots of a binary tree with a depth of K,

C. N0 = properties of N2 + 1,

D. Depth of the Complete Binary Tree of N nodes,

E. The Conversion Relationship Between the child node and the parent node when the binary tree is stored sequentially (the root node starts from 1, the left is 2 * I, and the right is 2 * I + 1 ).

The advantages and disadvantages of Binary Tree sequential storage and binary linked list storage and their application scenarios are as follows.

(2) Three Traversal Algorithms of Binary Trees

The knowledge points are directly related to the understanding of algorithms in the tree chapter, and the success of algorithm design in the tree chapter. There are three types of binary tree traversal algorithms: first, middle, and last. The division is based on the access sequence of the root node data in each algorithm. Not only do you have to master three types of traversal recursive algorithms, understand the actual steps of execution, but you should also be familiar with the three types of traversal non-recursive algorithms. Because many algorithms in the chapter of binary tree can be directly transformed based on three recursive algorithms (for example, finding the number of leaves), after mastering the three non-Recursive Algorithms for traversal, we can deal with the following algorithms: the question "using non-recursive algorithms to calculate the number of leaf trees in a binary tree" is just as fascinating.

(3) Other Binary Tree algorithms that can be transformed based on the three Traversal Algorithms:

Calculate the number of leaves, the total number of Binary Tree nodes, the total number of nodes whose degree is 1 or the degree is 2, the binary tree is copied, the binary tree is established, and the left and right Subtrees are exchanged, find a specified node with a value of N, delete a specified node with a value of N, and so on. If you are familiar with the recursive and non-recursive Traversal Algorithms of Binary Trees, solving the above problems is just a piece of cake.

(4) clue Binary Tree:

The lead binary tree is derived to avoid recursive solutions such as binary tree traversal. As we all know, although recursion is easy to understand, it consumes a lot of memory resources. If there are more than one recursive hierarchy, it will inevitably lead to the risk of resource depletion. To avoid such situations, the clues of the Binary Tree appeared. For the clue binary tree, you should master the essence of the clue, three clue algorithms, the clue-based post-binary tree traversal algorithm, and other basic clue binary tree algorithm problems (such: finding the frontend or successor node of a specified node in a type of clue Binary Tree is a common question ).

(5) optimal binary tree ):

The optimal binary tree is a special binary tree structure to solve specific problems. The premise is that each edge of the binary tree is assigned a weight value, so that the sum of the weights of the binary tree is the smallest. In the optimal binary tree section, the source code of the algorithm is very small. Generally, you are given a set of data. You are required to create an optimal binary tree based on this set of data and find the sum of its minimum weights, this type of question is not difficult.

(6) trees and forests:

A binary tree is a special kind of tree. This kind of tree is not only because its branches are up to 2 and other features, but also the most important thing is that the binary tree is ordered! That is, the left and right children of Binary Trees cannot be exchanged. If they are exchanged, they become another binary tree. Tree and forest traversal are not as rich as binary trees. They only have two kinds of Traversal Algorithms: First root and last root (for forests, they are called first and last traversal ). The first root and the second root traversal correspond to the traversal algorithm in the binary tree: The first root traversal corresponds to the first sequential traversal of the binary tree, and then the root traversal corresponds to the middle-order traversal of the binary tree. Binary Tree, tree, and forest correspond to the above relationship, thanks to the binary linked list. The binary tree uses the binary linked list to store the left and right children respectively. The tree uses the binary linked list to store the children and their brothers (called the Child brother linked list), and the forest uses the binary linked list to store the children and their brothers.

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