编程语言中的数据结构详解---Here is the extracted content from the image:
**1. Array**
* **Type:** Linear data structure (Array)
* **Main Elements:**
* **Nodes/Elements:** Five blue rectangular cells arranged horizontally.
* **Content:** The cells contain numerical values: 6, 3, 8, 12, 11.
* **Indexing:** Below each cell, there is an index number: 0, 1, 2, 3, 4, corresponding to the element above it.
**2. Queue**
* **Type:** Linear data structure (Queue)
* **Main Elements:**
* **Nodes/Elements:** Three blue rectangular cells arranged horizontally.
* **Content:** The cells contain numerical values: 6, 3, 8.
* **Direction/Labels:**
* An arrow labeled "rear" points from left to right, indicating the insertion end.
* An arrow labeled "front" points from right to left, indicating the removal end.
**3. Matrix**
* **Type:** 2D data structure (Matrix)
* **Main Elements:**
* **Grid:** A 5x5 grid composed of 25 empty blue square cells.
* **Indexing:**
* Column indices: 0, 1, 2, 3, 4 are labeled horizontally above the grid.
* Row indices: 0, 1, 2, 3, 4 are labeled vertically along the left side of the grid.
**4. Stack**
* **Type:** Linear data structure (Stack)
* **Main Elements:**
* **Nodes/Elements:** Five blue rectangular cells stacked vertically.
* **Operations/Labels:**
* "push": A curved arrow points downwards into the top of the stack from the left.
* "pop": A curved arrow points upwards and out from the top of the stack to the right.
* "top": A label indicating the top of the stack.
**5. Tree**
* **Type:** Hierarchical data structure (Tree)
* **Main Elements:**
* **Nodes:** Seven blue circular nodes.
* **Connections:** Lines connect nodes in a hierarchical manner.
* **Label:** The topmost node is labeled "root". The tree has a root node, two children, and then each of those children has two children, forming three levels.
**6. Linked List**
* **Type:** Linear data structure (Linked List)
* **Main Elements:**
* **Nodes/Elements:** Five blue rectangular cells (nodes) arranged horizontally.
* **Content:** The cells contain numerical values: 6, 3, 8, 12, 11.
* **Connections:** Right-pointing arrows connect each node to the next in sequence.
* **Labels:**
* "head" points to the first node (6).
* "tail" points to the last node (11).
* **Annotation:** "@visualcoders" is displayed below the linked list diagram.
**7. HashMap**
* **Type:** Associative array (HashMap)
* **Main Elements:**
* **Keys:** Three blue rectangular cells labeled K1, K2, K3 on the left.
* **Hash Function:** A central element labeled "h(k)".
* **Values/Buckets:** On the right, a vertical list of indices (0, 1, 2, 3) representing buckets.
* **Connections:**
* Dashed lines connect K1, K2, K3 to "h(k)".
* Dashed lines connect "h(k)" to indices 0, 1, 2, 3.
* Small blue rectangles containing values V2, V1, V3 are associated with specific indices: V2 with 0, V1 with 1, V3 with 3. Index 2 appears empty.
**8. BST (Binary Search Tree)**
* **Type:** Hierarchical data structure (Binary Search Tree)
* **Main Elements:**
* **Nodes:** Seven blue circular nodes.
* **Content:** Nodes contain numerical values: 4 (root), 2, 6, 1, 3, 5, 7.
* **Connections:** Lines connect parent nodes to their child nodes, showing a binary tree structure.
* **Structure:** Node 4 is the root. Its left child is 2, and its right child is 6. Node 2 has left child 1 and right child 3. Node 6 has left child 5 and right child 7. The values respect the BST property (left child < parent < right child).
**9. Heap**
* **Type:** Hierarchical data structure (Heap)
* **Main Elements:**
* **Nodes:** Six blue circular nodes with numerical values, and one additional circular node that is empty/unlabeled in the diagram.
* **Content:** Nodes contain numerical values: 9 (root), 5, 8, 2, 3, 6.
* **Connections:** Lines connect parent nodes to their child nodes, forming a complete binary tree structure up to the last level.
* **Structure:** Node 9 is the root. Its left child is 5, and its right child is 8. Node 5 has left child 2 and right child 3. Node 8 has left child 6. (The diagram illustrates a max-heap where parent values are greater than or equal to child values).
**10. Trie**
* **Type:** Tree-like data structure (Trie / Prefix Tree)
* **Main Elements:**
* **Nodes:** Blue circular nodes, including a root node and subsequent nodes.
* **Connections/Labels:** Lines connect nodes, and characters (c, a, n, p, t, e, n, t, s, e) are labeled along these connecting lines, representing path segments (e.g., characters of a word).
* **Structure:** Represents a set of strings, where common prefixes share the same path from the root.
**11. Graph**
* **Type:** Non-linear data structure (Directed Graph)
* **Main Elements:**
* **Nodes:** Six blue circular nodes.
* **Connections:** Lines with arrows (directed edges) connect nodes, indicating relationships with a specific direction.
* **Structure:** Shows a general directed graph with various nodes and directed connections between them.
**12. Union Find**
* **Type:** Data structure for maintaining disjoint sets (Union Find)
* **Main Elements:**
* **Nodes:** Four blue circular nodes.
* **Connections:** Three lines connect the nodes:
* Top-left node is connected to the bottom-left node.
* Bottom-left node is connected to the bottom-right node.
* Top-right node is connected to the bottom-right node.
* **Structure:** The diagram illustrates a single connected component of four nodes, forming a shape resembling a 'U' with an additional vertical segment on its right arm.
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Data structures are fundamental concepts in computer science that define how we organize and store data efficiently. They provide different methods for accessing, inserting, and managing information based on specific programming requirements. We can categorize data structures into three main types: Linear structures like arrays and stacks arrange data sequentially, non-linear structures like trees and graphs model complex relationships, and specialized structures like hash maps provide optimized solutions for specific problems.
Linear data structures organize elements in a sequential manner, where each element has a unique predecessor and successor. Arrays provide random access to elements using indices, making them efficient for direct element retrieval. Stacks follow the Last In First Out principle, where elements are added and removed from the top, like a stack of plates. Queues implement First In First Out behavior, where elements enter from the rear and exit from the front, similar to a waiting line. Linked lists use dynamic memory allocation, connecting elements through pointers, allowing flexible insertion and deletion operations.
Tree structures organize data hierarchically using parent-child relationships. A basic tree starts with a root node at the top, which has no parent, and branches down to child nodes. Leaf nodes are those with no children. The Binary Search Tree is a specialized tree where each node's left child is smaller and right child is larger than the parent, enabling efficient searching. In our example, the root is 4, with left subtree containing 1, 2, 3 and right subtree containing 5, 6, 7. The Heap is a complete binary tree with ordering properties - in a max heap, each parent is greater than or equal to its children, making it perfect for priority queues and sorting algorithms.
The Trie, also known as a Prefix Tree, is a specialized tree structure designed for efficient string storage and retrieval. It works by sharing common prefixes among stored strings, which makes it extremely memory efficient for large dictionaries. In our example, we can see how the words 'can', 'cap', and 'tent' are stored. The words 'can' and 'cap' share the common prefix 'ca', so they follow the same path from the root through 'c' and 'a' nodes before branching at 'n' and 'p'. The word 'tent' follows a separate path starting with 't'. This structure enables fast string searches, insertions, and prefix matching operations, making it ideal for applications like auto-complete systems, spell checkers, and IP routing tables.
Hash-based structures and matrices represent two important categories of data organization. HashMap uses hash functions to convert keys into array indices, providing average O(1) lookup time. In our example, keys K1, K2, and K3 are processed through hash function h(k) to map to specific buckets numbered 0 through 3. Values V2, V1, and V3 are stored in buckets 0, 1, and 3 respectively, while bucket 2 remains empty. When collisions occur, various strategies like chaining or open addressing handle multiple keys mapping to the same bucket. Matrix structures organize data in a two-dimensional grid with row and column indexing, making them essential for mathematical operations, graphics processing, and algorithm implementations that require spatial data representation.