xinyin025/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2026-07-23 03:46:05 +00:00
Code Issues Packages Projects Releases Wiki Activity

deploy

Browse Source
This commit is contained in:
krahets
2025-03-14 17:51:07 +08:00
parent 1b1e1e354a
commit 3b08169043
39 changed files with 956 additions and 958 deletions
Download Patch File Download Diff File Expand all files Collapse all files
en/chapter_sorting/insertion_sort/index.html
+10 -10
View File
@@ -3603,18 +3603,18 @@
<!-- Page content -->
<h1 id="114-insertion-sort">11.4 &nbsp; Insertion sort<a class="headerlink" href="#114-insertion-sort" title="Permanent link">&para;</a></h1>
<p><u>Insertion sort</u> is a simple sorting algorithm that works very much like the process of manually sorting a deck of cards.</p>
<p>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.</p>
<p>Figure 11-6 shows the process of inserting an element into an array. Assuming the pivot element is <code>base</code>, we need to move all elements between the target index and <code>base</code> one position to the right, then assign <code>base</code> to the target index.</p>
<p>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.</p>
<p>Figure 11-6 illustrates how an element is inserted into the array. Assuming the base element is <code>base</code>, we need to shift all elements from the target index up to <code>base</code> one position to the right, then assign <code>base</code> to the target index.</p>
<p><a class="glightbox" href="../insertion_sort.assets/insertion_operation.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Single insertion operation" class="animation-figure" src="../insertion_sort.assets/insertion_operation.png" /></a></p>
<p align="center"> Figure 11-6 &nbsp; Single insertion operation </p>
<h2 id="1141-algorithm-process">11.4.1 &nbsp; Algorithm process<a class="headerlink" href="#1141-algorithm-process" title="Permanent link">&para;</a></h2>
<p>The overall process of insertion sort is shown in Figure 11-7.</p>
<ol>
<li>Initially, the first element of the array is sorted.</li>
<li>The second element of the array is taken as <code>base</code>, and after inserting it into the correct position, <strong>the first two elements of the array are sorted</strong>.</li>
<li>The third element is taken as <code>base</code>, and after inserting it into the correct position, <strong>the first three elements of the array are sorted</strong>.</li>
<li>And so on, in the last round, the last element is taken as <code>base</code>, and after inserting it into the correct position, <strong>all elements are sorted</strong>.</li>
<li>Consider the first element of the array as sorted.</li>
<li>Select the second element as <code>base</code>, insert it into its correct position, <strong>leaving the first two elements sorted</strong>.</li>
<li>Select the third element as <code>base</code>, insert it into its correct position, <strong>leaving the first three elements sorted</strong>.</li>
<li>Continuing in this manner, in the final iteration, the last element is taken as <code>base</code>, and after inserting it into the correct position, <strong>all elements are sorted</strong>.</li>
</ol>
<p><a class="glightbox" href="../insertion_sort.assets/insertion_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Insertion sort process" class="animation-figure" src="../insertion_sort.assets/insertion_sort_overview.png" /></a></p>
<p align="center"> Figure 11-7 &nbsp; Insertion sort process </p>
@@ -3721,10 +3721,10 @@
<li><strong>Stable sorting</strong>: During the insertion operation, we insert elements to the right of equal elements, not changing their order.</li>
</ul>
<h2 id="1143-advantages-of-insertion-sort">11.4.3 &nbsp; Advantages of insertion sort<a class="headerlink" href="#1143-advantages-of-insertion-sort" title="Permanent link">&para;</a></h2>
<p>The time complexity of insertion sort is <span class="arithmatex">\(O(n^2)\)</span>, while the time complexity of quicksort, which we will study next, is <span class="arithmatex">\(O(n \log n)\)</span>. Although insertion sort has a higher time complexity, <strong>it is usually faster in cases of small data volumes</strong>.</p>
<p>This conclusion is similar to that for linear and binary search. Algorithms like quicksort that have a time complexity of <span class="arithmatex">\(O(n \log n)\)</span> and are based on the divide-and-conquer strategy often involve more unit operations. In cases of small data volumes, the numerical values of <span class="arithmatex">\(n^2\)</span> and <span class="arithmatex">\(n \log n\)</span> are close, and complexity does not dominate, with the number of unit operations per round playing a decisive role.</p>
<p>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.</p>
<p>Although bubble sort, selection sort, and insertion sort all have a time complexity of <span class="arithmatex">\(O(n^2)\)</span>, in practice, <strong>insertion sort is used significantly more frequently than bubble sort and selection sort</strong>, mainly for the following reasons.</p>
<p>The time complexity of insertion sort is <span class="arithmatex">\(O(n^2)\)</span>, while the time complexity of quicksort, which we will study next, is <span class="arithmatex">\(O(n \log n)\)</span>. Although insertion sort has a higher time complexity, <strong>it is usually faster in small input sizes</strong>.</p>
<p>This conclusion is similar to that for linear and binary search. Algorithms like quicksort that have a time complexity of <span class="arithmatex">\(O(n \log n)\)</span> and are based on the divide-and-conquer strategy often involve more unit operations. For small input sizes, the numerical values of <span class="arithmatex">\(n^2\)</span> and <span class="arithmatex">\(n \log n\)</span> are close, and complexity does not dominate, with the number of unit operations per round playing a decisive role.</p>
<p>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.</p>
<p>Although bubble sort, selection sort, and insertion sort all have a time complexity of <span class="arithmatex">\(O(n^2)\)</span>, in practice, <strong>insertion sort is commonly used than bubble sort and selection sort</strong>, mainly for the following reasons.</p>
<ul>
<li>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, <strong>the computational overhead of bubble sort is generally higher than that of insertion sort</strong>.</li>
<li>The time complexity of selection sort is always <span class="arithmatex">\(O(n^2)\)</span>. <strong>Given a set of partially ordered data, insertion sort is usually more efficient than selection sort</strong>.</li>