Implementing the Merge Sort Algorithm in C++
Merge sort is based on the divide-and-conquer principle, with the core being "divide-merge": first recursively split the array into individual elements (where subarrays are ordered), then merge two ordered subarrays into a larger ordered array. **Divide process**: Recursively split the array from the middle until each subarray contains only one element. **Merge process**: Compare elements from two ordered subarrays, take the smaller value and place it in the result array sequentially, then handle the remaining elements. The C++ implementation includes two core functions: `mergeSort` for recursively dividing the array, and `merge` for merging two ordered subarrays. The time complexity is O(n log n), and the space complexity is O(n) (due to the need for a temporary array). Merge sort is stable and efficient, making it suitable for sorting large-scale data. In the example, the array `[5,3,8,6,2,7,1,4]` is sorted into the ordered array `[1,2,3,4,5,6,7,8]` through division and merging, verifying the algorithm's correctness.
Read MoreImplementing the Merge Sort Algorithm with Python
Merge sort is based on the divide and conquer algorithm, with three core steps: divide (split the array into left and right subarrays until single elements), recursively sort (recursively sort each subarray), and merge (merge the ordered subarrays into a single ordered array). Taking the array [3, 1, 4, 2] as an example, after decomposition, each subarray is recursively sorted and then merged into [1, 2, 3, 4]. The Python implementation includes a merge function (to merge two ordered subarrays in sequence) and a recursive sorting function (to decompose and recursively call merge). Its characteristics: time complexity O(n log n), space complexity O(n) (requires additional storage for merge results), and it is a stable sort (the relative order of equal elements remains unchanged).
Read MoreImplementing the Merge Sort Algorithm in Java
Merge sort is an efficient sorting algorithm based on the divide-and-conquer paradigm, with three core steps: divide, conquer, and merge. It recursively splits the array into single-element subarrays, sorts these subarrays, and finally merges two ordered subarrays into a fully ordered array. In Java implementation, the `mergeSort` method recursively divides the array into left and right halves, sorts each half, and then calls the `merge` method to combine them. The `merge` method uses three pointers to traverse the left and right subarrays, compares elements, and fills the result array, while directly copying remaining elements. Algorithm complexity: Time complexity is O(n log n) (each merge operation takes O(n) time, with log n recursive levels), space complexity is O(n) (requires extra space for storing merged results), and it is a stable sort (relative order of equal elements is preserved). Merge sort has a clear logic and is suitable for large-scale data sorting. It serves as a classic example of divide-and-conquer algorithms, efficiently sorting by recursively splitting and merging ordered subarrays.
Read MoreFrom Insertion Sort to Quick Sort: A Beginner's Comparison of Sorting Algorithms
Sorting algorithms are methods to convert unordered data into ordered sequences. They are fundamental core algorithms in computer science, enabling optimization of subsequent operations such as searching and statistics. This article introduces four typical sorting algorithms: Insertion sort is similar to sorting playing cards, gradually building an ordered sequence. It has a time complexity of O(n²), space complexity of O(1), is stable, and is suitable for small-scale or nearly ordered data. Bubble sort involves comparing and swapping adjacent elements, allowing larger elements to "bubble up". It also has O(n²) time complexity, is stable but inefficient, and is only suitable for extremely small-scale data or educational purposes. Merge sort is based on the divide-and-conquer principle, decomposing arrays and merging ordered subarrays. It has O(n log n) time complexity, O(n) space complexity, is stable, and is suitable for large-scale data or scenarios requiring high stability. Quick sort combines divide-and-conquer with pivot partitioning. It has an average time complexity of O(n log n), O(log n) space complexity, is unstable, and is the most commonly used efficient algorithm in engineering, suitable for large-scale data. The article compares and summarizes the time complexity, space complexity, stability, and applicable scenarios of these algorithms. It suggests that beginners first understand the core ideas, learn from simple to complex cases gradually, and deepen their understanding through hands-on simulation.
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