Quicksort is a commonly used sorting algorithm that employs the idea of divide and conquer, and unlike merge sorting, quicksort is sorted in situ, i.e., no additional space is required to store intermediate results. In this article, we'll take a look at how quicksort works, how it works, and what it does when sorting subarrays.
The algorithm steps for quicksort are as follows:
Sentinel Division: First, we need to choose a benchmark number as the sentinel. Typically, we choose the leftmost element in the array as the base number. Next, we start traversing the left and right ends of the array, placing elements smaller than the base number to the left of the base number, and elements larger than the base number to the right of the base number. This process is known as sentinel division.
In the process of sentry division, we use two pointers, one to the start of the array and the other to the end of the array. We keep moving the pointer towards the middle until the two pointers meet. In the process of moving the pointer, if we find that the left pointer points to an element greater than the datum number, and the right pointer points to an element that is smaller than the datum number, we swap the positions of the two elements. In this way, you can ensure that the left side of the datum number is an element smaller than it, and the right side is an element that is larger than it.
Sort subarrays: After completing the sentry division, we use the index of the sentry division as the demarcation of the left and right subarrays. Then, we sentinel and sort the left and right subarrays separately, i.e., recursively do the same for the subarrays.
When sorting subarrays, we use the same method for sentinel division and sorting. By continuously dividing and sorting, the entire array is finally sorted.
The key to quick sorting is sentinel division. By constantly placing elements smaller than the datum to the left of the datum and elements larger than the datum to the right of the datum, we can guarantee that the datum is in the correct position. When sorting a subarray, we only need to do the same with the subarray to sort the entire array.
The time complexity of the quicksort is o(nlogn), where n is the length of the array. This is because after each sentinel division, we divide the array into two smaller sub-arrays, and then sentinel and sort the two sub-arrays separately. Therefore, the time complexity of quicksort can be calculated from the height of the recursive tree and the number of operations per layer.
It is important to note that quicksort is an unstable sorting algorithm. This is because in the process of sentinel division, we may change the relative order of the same elements. Therefore, in some cases, we may need additional operations to maintain the relative order of the same elements.
To sum up, quicksort is an efficient in-situ sorting algorithm that sorts the entire array by dividing and sorting subarrays by sentinels. The time complexity of quicksort is o(nlogn), and it doesn't require additional space to store intermediate results. However, it is important to note that quicksort is an unstable sorting algorithm. In practical applications, we can choose the appropriate sorting algorithm according to the specific situation to meet the needs of sorting.
Quick sort is an efficient sorting algorithm, and it is widely used in practical applications. Due to its in-place sort-in-place nature, Quick Sort does not require additional space to store intermediate results, which makes it advantageous when working with large-scale data. In addition, the time complexity of quicksort is o(nlogn), which gives it better performance than other sorting algorithms, such as bubbling sort and insert sorting.
To optimize the quicksort algorithm, you can skip the merge operation when the array is ordered. When we find that the array has been ordered in the process of sentry division, we can directly skip the sorting operation of the sub-array, so as to improve the efficiency of the algorithm. This optimization method can be achieved by adding judgment conditions to the sentinel division process.
In conclusion, quicksort is an efficient in-place sorting algorithm that sorts the entire array by dividing and sorting subarrays by sentinels. In practical applications, we can choose the appropriate sorting algorithm according to the specific situation to meet the needs of sorting. By optimizing the merge sort algorithm and skipping the merge operation when the array is ordered, we can further improve the performance of quick sort.