Learning Insertion Sort: Principles and Code, Just Like Organizing Your Desktop
This article analogizes "sorting the desktop" to insertion sort, with the core idea being inserting elements one by one into their correct positions within the already sorted portion. The basic steps are: initializing the first element as sorted, starting from the second element, comparing it backward with the sorted portion to find the insertion position, shifting elements, and then inserting the current element. Taking the array `[5,3,8,2,4]` as an example: initially sorted as `[5]`, inserting 3 (after shifting 5) results in `[3,5]`; inserting 8 (directly appending) gives `[3,5,8]`; inserting 2 (shifting 8, 5, and 3 sequentially, then inserting at the beginning) yields `[2,3,5,8]`; inserting 4 (shifting 8 and 5, then inserting after 3) completes the sorting. The Python code implementation uses a double loop: the outer loop iterates over elements to be inserted, and the inner loop compares backward and shifts elements. It has a time complexity of O(n²), space complexity of O(1), and is suitable for small-scale data or nearly sorted data. It is an in-place sorting algorithm with no additional space required. This sorting analogy intuitively reflects the essence of "inserting one by one" and aids in understanding the sorting logic.
Read MoreWhat is Time Complexity O(n)? A Must-Learn Efficiency Concept for Data Structure Beginners
The article explains the necessity of time complexity: due to differences in hardware and compilers, direct timing is impractical, and an abstract description of the algorithm's efficiency trend is required. The core is linear time complexity O(n), which indicates that the number of operations is proportional to the input size n (such as the length of an array). Scenarios like traversing an array to find a target or printing all elements require n operations. Big O notation ignores constants and lower-order terms, focusing only on the growth trend (e.g., O(2n+5) is still O(n)). Comparing common complexities (O(1) constant, O(n) linear, O(n²) quadratic, O(log n) logarithmic), O(n) is more efficient than O(n²) but less efficient than O(1) or O(log n). Understanding O(n) is fundamental to algorithms, helping optimize code and avoid timeout issues caused by "brute-force solutions."
Read MoreDrawing Binary Trees Step by Step: The First Lesson in Data Structure Fundamentals
A binary tree is a fundamental data structure where each node has at most two child nodes (left and right), and nodes with no descendants are called leaves. Core terms include: root node (the topmost starting point), leaf node (node with no children), child node (a node on the next level below its parent), and left/right subtrees (the left/right children and their descendants of a node). Construction starts from the root node, with child nodes added incrementally. Each node can have at most two children, and child positions are ordered (left vs. right). A binary tree must satisfy: each node has ≤2 children, and child positions are clearly defined (left or right). Traversal methods include pre-order (root → left → right), in-order (left → root → right), and post-order (left → right → root). Drawing the tree is crucial for understanding core relationships, as it intuitively visualizes node connections and forms the foundation for complex structures (e.g., heaps, red-black trees) and algorithms (sorting, searching).
Read MoreStacks in Daily Life: Why Are Stacks the First Choice for Data Structure Beginners?
The article introduces "stack" through daily scenarios such as stacking plates and browser backtracking, with its core feature being "Last-In-First-Out" (LIFO). A stack is a container that can only be operated on from the top, with core operations being "Push" (pushing onto the stack) and "Pop" (popping from the stack). As a first choice for data structure introduction, the stack has a simple logic (only the LIFO rule), clear operations (only two basic operations), extensive applications (scenarios like bracket matching, browser backtracking, recursion, etc.), and can be easily implemented using arrays or linked lists. It serves as a foundation for learning subsequent structures like queues and trees, helps establish clear programming thinking, and is a "stepping stone" for understanding data structures.
Read MoreLinked List vs Array: Key Differences for Beginners in Data Structures
Arrays and linked lists are among the most fundamental data structures in programming. Understanding their differences and applicable scenarios is crucial for writing efficient code. **Array Features**: - Stores elements in contiguous memory locations, allowing random access via index (O(1) time complexity). - Requires a fixed initial size; inserting/deleting elements in the middle demands shifting elements (O(n) time complexity). - Ideal for scenarios with known fixed sizes and high-frequency random access (e.g., grade sheets, map coordinates). **Linked List Features**: - Elements are scattered in memory, with each node containing data and a pointer/reference. - No random access (requires traversing from the head, O(n) time complexity). - Offers flexible dynamic expansion; inserting/deleting elements in the middle only requires modifying pointers (O(1) time complexity). - Suitable for dynamic data and high-frequency insertion/deletion scenarios (e.g., queues, linked hash tables). **Core Differences**: - Arrays rely on contiguous memory but have restricted operations. - Linked lists use scattered storage but suffer from slower access speeds. - Key distinctions lie in storage method, access speed, and insertion/deletion efficiency. Selection should be based on specific requirements. Mastering their underlying logic enables more efficient code implementation.
Read MoreLearning Data Structures from Scratch: What Exactly Is an Array?
An array is an ordered collection of data elements of the same type, accessed via indices (starting from 0), with elements stored contiguously. It is used to efficiently manage a large amount of homogeneous data. For example, class scores can be represented by the array `scores = [90, 85, 95, 78, 92]` instead of multiple individual variables, facilitating overall operations. In Python, array declaration and initialization can be done with `scores = [90, 85, 95, 78, 92]` or `[0] * 5` (declaring an array of length 5). Elements are accessed using `scores[index]`, and it's important to note the index range (0 to length-1), as out-of-bounds indices will cause errors. Basic operations include traversal with loops (`for score in scores: print(score)`), while insertion and deletion require shifting subsequent elements (with a time complexity of O(n)). Core characteristics of arrays are: same element type, 0-based indexing, and contiguous storage. Their advantages include fast access speed (O(1)), but disadvantages are lower efficiency for insertions/deletions and fixed size. As a foundational data structure, understanding the core idea of arrays—"indexed access and contiguous storage"—is crucial for learning more complex structures like linked lists and hash tables, making arrays a fundamental tool for data management.
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