Implementing the Selection Sort Algorithm in Java
Selection sort is a simple and intuitive sorting algorithm. Its core idea is to repeatedly select the smallest (or largest) element from the unsorted portion and place it at the end of the sorted portion until the entire array is sorted. The basic approach involves an outer loop to determine the end position of the sorted portion, and an inner loop to find the minimum value in the unsorted portion, followed by swapping this minimum value with the element at the current position of the outer loop. In Java implementation, the `selectionSort` method is implemented with two nested loops: the outer loop iterates through the array (with `i` ranging from 0 to `n-2`), and the inner loop (with `j` ranging from `i+1` to `n-1`) finds the index `minIndex` of the minimum value in the unsorted portion. Finally, the element at position `i` is swapped with the element at `minIndex`. Taking the array `{64, 25, 12, 22, 11}` as an example, the sorted array `[11, 12, 22, 25, 64]` is gradually constructed through each round of swaps. The time complexity is O(n²), making it suitable for small-scale data. This algorithm has a simple logic and easy-to-implement code, serving as a typical example for understanding the basic sorting concepts.
Read MoreInspiration from Poker Sorting: A Life Analogy and Implementation of Insertion Sort
This article introduces the insertion sort algorithm. Its core idea is to gradually build an ordered sequence: the first element is defaulted as sorted, and starting from the second element, each element (the element to be inserted) is inserted into the correct position in the previously sorted sequence (where larger elements need to be moved to make space). Taking the array `[5, 3, 8, 4, 2]` as an example, the process of comparing and moving elements from back to front is demonstrated. The key steps are: traversing the array, temporarily storing the element to be inserted, moving the sorted elements, and inserting at the correct position. Algorithm characteristics: Advantages include simplicity and intuitiveness, in-place sorting (space complexity O(1)), stability, and suitability for small-scale or nearly ordered data; disadvantages include the worst-case time complexity of O(n²) and a relatively large number of move operations. In summary, insertion sort is a foundation for understanding sorting algorithms. It is explained through a life analogy (e.g., sorting playing cards) to aid comprehension and is applicable to simple scenarios or sorting small-scale data.
Read MoreThe 'Speed Code' of Sorting Algorithms: Time Complexity and Bubble Sort
This article focuses on the "speed code" of sorting algorithms, with a core emphasis on time complexity and bubble sort. Time complexity is measured using the Big O notation, with common types including O(n) (linear, growing proportionally with data size), O(n²) (quadratic, extremely inefficient for large datasets), and O(log n) (logarithmic, extremely fast). It serves as a key indicator for judging the efficiency of algorithms. Bubble sort, a fundamental algorithm, works by comparing and swapping adjacent elements to "float" smaller elements upward and "sink" larger elements downward. Using the array [5, 3, 8, 4, 2] as an example, it repeatedly traverses and compares adjacent elements until the array is sorted. Its time complexity is O(n²), with a space complexity of O(1) (in-place sorting). Its advantages include simplicity, intuitive logic, while its main drawback is low efficiency, making it extremely time-consuming for large datasets. In summary, despite its slowness (O(n²)), bubble sort is a valuable introductory tool that helps understand sorting principles and time complexity, laying the foundation for learning more efficient algorithms like quicksort (optimized to O(n log n)).
Read MoreBinary Search: How Much Faster Than Linear Search? Search Techniques in Data Structures
This article introduces search algorithms in computers, focusing on linear search and binary search. Linear search (sequential search) is a basic method that checks data one by one from the beginning to the end. It has a time complexity of O(n) and is suitable for scenarios with small data volumes or unordered data. In the worst case, it needs to traverse all data. Binary search, on the other hand, requires an ordered array. Its core is to eliminate half of the data each time, with a time complexity of O(log n). When the data volume is large, it is far more efficient than linear search (e.g., for n=1 million, binary search only needs 20 times, while linear search needs 1 million times). The two have different applicable scenarios: binary search is suitable for ordered, large - data - volume, and frequently searched scenarios; linear search is suitable for unordered, small - data - volume, or dynamically changing data. In summary, binary search significantly improves efficiency through "half - by - half elimination" and is an efficient choice for large - volume ordered data. Linear search is more flexible in scenarios with small data volumes or unordered data.
Read MoreHow Does a Hash Table Store Data? Hash Functions Simplify Lookup
The article uses the analogy of searching for a book to introduce the problem: sequential search of data (such as arrays) is inefficient, while a hash table is an efficient storage tool. The core of a hash table is the hash function, which maps data to "buckets" (array positions) to enable fast access and storage. The hash function converts data into a hash value (bucket number), for example, taking the last two digits of a student ID to get the hash value. When storing, the hash value is first calculated to locate the bucket. If multiple data items have the same hash value (collision), it can be resolved using the linked list method (chaining within the bucket) or open addressing (finding the next empty bucket). When searching, the hash value is directly calculated to locate the bucket, and then the search is performed within the bucket, eliminating the need to traverse all data, resulting in extremely fast speed. Hash tables are widely used (such as in address books and caches), with their core being the use of a hash function to transform the search from "scanning through everything" to "direct access".
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