Sorting Algorithms: An Introduction to Bubble Sort, Step-by-Step Explanation + Code Examples
Bubble Sort is one of the simplest sorting algorithms in computer science. Its core idea is to repeatedly compare adjacent elements and swap their positions, allowing larger elements to gradually "bubble" up to the end of the array. The basic steps are: the outer loop controls n-1 rounds of comparisons (each round determines the position of one large element), and the inner loop starts from the first element, comparing adjacent elements in sequence; if the previous element is larger and the next is smaller, they are swapped. An optimization is that if no swaps occur in a round, it indicates the array is already sorted, and the process can terminate early. In terms of time complexity, the worst-case scenario (completely reverse ordered) is O(n²), while the best case (already sorted) is O(n). The space complexity is O(1) (only constant extra space is required). This algorithm is simple to implement and easy to understand, making it suitable for sorting small-scale data and serving as a foundational entry point for sorting algorithms.
Read MoreImplementing the Counting Sort Algorithm in Java
Counting sort is a simple and intuitive non-comparison sorting algorithm. It determines the position of elements by counting their occurrences and using prefix sums. It is suitable for scenarios where the element range is small (e.g., integers), there are many repeated elements, and stable sorting is required. The core idea is: first, determine the element range (find min and max), count the occurrences of each element, calculate the prefix sum to get the final position of the element, and then traverse the original array from the end to generate the sorted result. Implementation steps: handle edge cases (no sorting needed for empty/single-element arrays), determine min/max, create a count array to tally occurrences, compute prefix sums (accumulate to get the final position of elements), and traverse from the end to generate the result. The time complexity is O(n+k) (where n is the array length and k is the element range), and the space complexity is O(n+k). Applicable scenarios include small integer ranges (e.g., scores, ages), many repeated elements, and the need for stable sorting. This algorithm achieves sorting through counting and accumulation without comparisons, making it suitable for beginners to understand the basic ideas of sorting.
Read MoreImplementing QuickSort Algorithm in Java
QuickSort is based on the divide-and-conquer approach. Its core involves selecting a pivot element to partition the array into elements less than and greater than the pivot, followed by recursively sorting the subarrays. With an average time complexity of O(n log n), it is a commonly used and efficient sorting algorithm. **Basic Steps**: 1. Select a pivot (e.g., the rightmost element). 2. Partition the array based on the pivot. 3. Recursively sort the left and right subarrays. **Partition Logic**: Using the rightmost element as the pivot, define an index `i` to point to the end of the "less than pivot" region. Traverse the array, swapping elements smaller than the pivot into this region. Finally, move the pivot to its correct position. The Java code implements this logic. The time complexity is O(n log n) on average and O(n²) in the worst case, with an average space complexity of O(log n). A notable drawback is that QuickSort is an unstable sort, and its worst-case performance can be poor, so optimizing the pivot selection is crucial to improve performance.
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