How many comparisons in insertion sort

Nearly always we want to sort more complex records that each have a key value. In such cases we must have a way to associate a key value with a record. The sorting algorithms will simply assume that the records are comparable.

This continues on with each record in turn. Insertion Sort will move it to the left so long as its value is less than that of the record immediately preceding it. However, there are situations where we can expect the input to be in sorted or nearly sorted order. One example is when an already sorted list is slightly disordered by a small number of additions to the list; restoring sorted order using Insertion Sort might be a good idea if we know that the disordering is slight.

Counting comparisons or swaps yields similar results. Each time through the inner for loop yields both a comparison and a swap, except the last i. Thus for larger arrays, Insertion Sort will not be so good a performer as other algorithms.

Insertion sort is the procedure that most people use to arrange a hand of cards. To begin to understand the algorithm, think of an unordered input list as two separate lists.

The first item of the input list is considered to be a sorted list one item long, with the rest of the input items 2 through N forming an unsorted list.

While this way of thinking about the input list may seem a bit odd at first, it really makes quite a bit of sense, since a list that is one item long certainly cannot be out of order and is thus sorted. Insertion sort removes the first item from the unsorted list and marks it as the item to be inserted. It then works its way from the back to the front of the sorted list, at each step comparing the item to be inserted with the current item.

As long as the current item is larger than the item to be inserted, the algorithm continues moving backward through the sorted list. Eventually it will either reach the beginning of the list or encounter an item that is less than or equal to the item to be inserted. When that happens the algorithm inserts the item at the current insertion point.

The entire process of selecting the first item from the unsorted list and scanning backwards through the sorted list for the insertion point is then repeated. Eventually, the unsorted list will be empty since all of the items will have been inserted into the sorted list. When this occurs, the sort is complete. The insertion sort procedure is illustrated on an eight item list in.

Notice that this is exactly the same list that was used to illustrate the behavior of selection sort in. A careful examination of will reveal that 19 comparison operations are required to sort these values using the insertion method.

This is approximately one half of the 36 comparisons needed by selection sort. A more formal version of the insertion sort algorithm is presented in. While this version of the algorithm may appear somewhat more complex than the English version presented above, it is really just a more detailed description of the same process. Most of the action occurs in Step 3. Step 3. When either the beginning of the sorted list is reached 3.

Problem Show all the steps used by the binary insertion s…. View Full Video Already have an account? Bryan L. Answer n-1 View Answer. Topics No Related Subtopics. Discrete Mathematics and its Applications math, calculus Chapter 3 Algorithms. Section 1 Algorithms. Discussion You must be signed in to discuss. Top Educators. Recommended Videos Problem 2. Problem 3. Problem 4. This can happen in only 2 cases: You are inserting elements in from a reverse sorted list and you compare the new element with the first element of the target list.

Improve this answer. Insertion sort does N - 1 comparisons if the input is already sorted. Salvador Dali Salvador Dali k gold badges silver badges bronze badges. Sign up or log in Sign up using Google.

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