From 16fbc4979f0ebd73a8f87c1c51306c3d44bbaf6c Mon Sep 17 00:00:00 2001 From: SamJin98 Date: Mon, 24 Feb 2025 15:38:19 -0500 Subject: [PATCH] translation: update insertion_sort.md (#1630) * translation: update insertion_sort.md * fix: revise insertion_sort.md translation * fix: revert title name * fix: updating `key` to `base` --- en/docs/chapter_sorting/insertion_sort.md | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/en/docs/chapter_sorting/insertion_sort.md b/en/docs/chapter_sorting/insertion_sort.md index d0be09533..aca1f8af1 100644 --- a/en/docs/chapter_sorting/insertion_sort.md +++ b/en/docs/chapter_sorting/insertion_sort.md @@ -2,9 +2,9 @@ Insertion sort is a simple sorting algorithm that works very much like the process of manually sorting a deck of cards. -Specifically, we select a pivot element from the unsorted interval, compare it with the elements in the sorted interval to its left, and insert the element into the correct position. +Specifically, we select a base element from the unsorted interval, compare it with the elements in the sorted interval to its left, and insert the element into the correct position. -The figure below shows the process of inserting an element into an array. Assuming the pivot element is `base`, we need to move all elements between the target index and `base` one position to the right, then assign `base` to the target index. +The figure below illustrates how an element is inserted into the array. Assuming the base element is `base`, we need to shift all elements from the target index up to `base` one position to the right, then assign `base` to the target index. ![Single insertion operation](insertion_sort.assets/insertion_operation.png) @@ -12,10 +12,10 @@ The figure below shows the process of inserting an element into an array. Assumi The overall process of insertion sort is shown in the figure below. -1. Initially, the first element of the array is sorted. -2. The second element of the array is taken as `base`, and after inserting it into the correct position, **the first two elements of the array are sorted**. -3. The third element is taken as `base`, and after inserting it into the correct position, **the first three elements of the array are sorted**. -4. And so on, in the last round, the last element is taken as `base`, and after inserting it into the correct position, **all elements are sorted**. +1. Consider the first element of the array as sorted. +2. Select the second element as `base`, insert it into its correct position, **leaving the first two elements sorted**. +3. Select the third element as `base`, insert it into its correct position, **leaving the first three elements sorted**. +4. Continuing in this manner, in the final iteration, the last element is taken as `base`, and after inserting it into the correct position, **all elements are sorted**. ![Insertion sort process](insertion_sort.assets/insertion_sort_overview.png) @@ -33,13 +33,13 @@ Example code is as follows: ## Advantages of insertion sort -The time complexity of insertion sort is $O(n^2)$, while the time complexity of quicksort, which we will study next, is $O(n \log n)$. Although insertion sort has a higher time complexity, **it is usually faster in cases of small data volumes**. +The time complexity of insertion sort is $O(n^2)$, while the time complexity of quicksort, which we will study next, is $O(n \log n)$. Although insertion sort has a higher time complexity, **it is usually faster in small input sizes**. -This conclusion is similar to that for linear and binary search. Algorithms like quicksort that have a time complexity of $O(n \log n)$ and are based on the divide-and-conquer strategy often involve more unit operations. In cases of small data volumes, the numerical values of $n^2$ and $n \log n$ are close, and complexity does not dominate, with the number of unit operations per round playing a decisive role. +This conclusion is similar to that for linear and binary search. Algorithms like quicksort that have a time complexity of $O(n \log n)$ and are based on the divide-and-conquer strategy often involve more unit operations. For small input sizes, the numerical values of $n^2$ and $n \log n$ are close, and complexity does not dominate, with the number of unit operations per round playing a decisive role. -In fact, many programming languages (such as Java) use insertion sort in their built-in sorting functions. The general approach is: for long arrays, use sorting algorithms based on divide-and-conquer strategies, such as quicksort; for short arrays, use insertion sort directly. +In fact, many programming languages (such as Java) use insertion sort within their built-in sorting functions. The general approach is: for long arrays, use sorting algorithms based on divide-and-conquer strategies, such as quicksort; for short arrays, use insertion sort directly. -Although bubble sort, selection sort, and insertion sort all have a time complexity of $O(n^2)$, in practice, **insertion sort is used significantly more frequently than bubble sort and selection sort**, mainly for the following reasons. +Although bubble sort, selection sort, and insertion sort all have a time complexity of $O(n^2)$, in practice, **insertion sort is commonly used than bubble sort and selection sort**, mainly for the following reasons. - Bubble sort is based on element swapping, which requires the use of a temporary variable, involving 3 unit operations; insertion sort is based on element assignment, requiring only 1 unit operation. Therefore, **the computational overhead of bubble sort is generally higher than that of insertion sort**. - The time complexity of selection sort is always $O(n^2)$. **Given a set of partially ordered data, insertion sort is usually more efficient than selection sort**.