Learning data structure_3 _ string and tree (1)

Today, I went on to work as a part-time employee. After lunch, I went to the library to check the data structure. Oh, I was abused by the KMP algorithm for one afternoon, when I first took the data structure electives, why didn't I have a good time. The following are the study notes for today.

String)

1. Definition: a finite sequence consisting of 0 or more characters, that is, a string.

2. The comparison of strings is achieved by the character encoding size, including the ASCII code (7-bit and 8-bit binary) and Unicode code (16-bit); the strings are equal.

3. the string is not a linear table, because the string targets character sets and focuses on searching and replacing substrings. The linear table operates on a single element.

4. strings are also stored in a sequential and chained manner.

5. Simple pattern matching algorithm: A large loop is made on the Main string. Each character of the Main string starts with a small loop of the Child String Length t until the matching is successful or all traversal is performed. Time complexity O (n-m + 1) * m)

6. KMP pattern matching algorithm

Principle: Use completed matching results to save repeated matching operations. Time complexity O (N + M)

Difficulties: Solving next [J] and using next [] array for index operations

Next [J]: when the first J-1 matches, the first I of the Main string does not match the fourth J of the pattern, the next [J] character must be compared with the I character of the Main string (I does not move ).

Void get_next (string T, int * Next)

{

Int I, J;

I = 1, j = 0;

Next [1] = 0;

While (I <t [0])

{

If (j = 0 | T [I] = T [J])

{

I ++;

J ++;

Next [I] = J;

}

Else J = next [J];

}

}

7. Improved KMP Algorithm

Improvement on next []: when calculating next [], if the character is equal to the B character pointed to by next, the nextval of a points to the nextval of B. Otherwise, the nextval of A is equal to the next value of.

Tree)

1. Definition: it is a finite set of N nodes. There is only one root node, and the subtree does not overlap.

2. node classification: If the degree (number of sub-trees owned by the node) is 0, the leaf node (terminal node). The degree of the tree is the maximum degree of each node.

3. Forest: m> = a set of 0 trees that do not match each other.

4. Tree Storage Structure: parental notation; Child sibling notation. You can add a specific pointer field according to the needs of the algorithm to implement the functions in the above three kinds of notation.

5. Binary Tree: Therefore, the degree of the node <= 2; left and right Subtrees are ordered.

6. Special Binary Tree

Oblique tree: All nodes have only the left (right) subtree. A linear table is a special case of a tree.

Full Binary Tree: All branch nodes have left and right Subtrees, and all leaves are on the last layer.

Full Binary Tree: Binary Tree without blocks by sequence number.

7. The nature of Binary Trees

Layer I has a maximum of 2 ^ (I-1) nodes;

A binary tree with a depth of K can have at most (2 ^ K)-1 node;

Any Binary Tree meets the requirements: the number of knots with a leaf node tree = degree of 2 + 1;

If the Complete Binary Tree node is N, its depth is (log2 N) rounded up to + 1;

The parent node of the Complete Binary Tree node I is I/2 rounded up; the left child is 2I.

8. Binary Tree Storage Structure

A Complete Binary Tree can be represented by a simple sequence structure. A common binary tree needs to be represented by a binary linked list: lchild + Data + rchild. If yes, you can add a pointer to the parent tree, that is, the triple linked list.

9. binary tree traversal: each node is accessed only once.

Forward traversal: Root, left, and right subtree

Middle-order traversal: Left subtree, root, right subtree

Post-order traversal: First leaves and then nodes (from left subtree to right subtree), and then the root node