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Chapter 9: Problem 17

Why is selection sort more efficient than bubble sort on large arrays?

Short Answer

Expert verified
Answer: Selection sort is more efficient for large arrays due to the minimized number of element swaps, resulting in a reduced frequency of element migrations compared to bubble sort. Although both algorithms have a time complexity of O(n^2) in the worst and average cases, selection sort is faster in practice when dealing with larger data sets.

Step by step solution

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1. Understanding Selection Sort algorithm

Selection sort is a comparison-based sorting algorithm that works by selecting the minimum/maximum element in the unsorted part of the array and swapping it with the first unsorted element, effectively sorting one element at a time. After each iteration, the next unsorted element gets sorted until the entire array is sorted. The algorithm can work in ascending or descending order.
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2. Understand Bubble Sort algorithm

Bubble sort is also a comparison-based sorting algorithm. It repeatedly steps through the array, compares adjacent elements, and swaps them if they are in the wrong order. This process is repeated until no swaps are needed, meaning the array is sorted. Like selection sort, bubble sort can work in ascending and descending order.
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3. Analyzing Time Complexity of Selection Sort

The time complexity of an algorithm is a measure of the number of operations required to perform the task. For selection sort, in the worst and average cases, it has a time complexity of O(n^2), where n is the number of elements in the array. This is because, for every element in the array, it must compare it with all remaining unsorted elements to find the minimum/maximum value. However, the number of element swaps is minimized, making it faster in practice than bubble sort when dealing with larger data sets.
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4. Analyzing Time Complexity of Bubble Sort

For bubble sort, the worst-case and average-case time complexity is also O(n^2), where n is the number of elements in the array. However, bubble sort tends to perform a larger number of unnecessary swaps compared to selection sort, making it slower in practice for larger data sets.
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5. Comparison and Conclusion

In summary, both selection sort and bubble sort have time complexities of O(n^2) in the worst and average cases. However, selection sort minimizes the number of element swaps and, as a result, tends to be more efficient than bubble sort when working with large arrays due to the reduced frequency of element migrations.

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Most popular questions from this chapter

Complete the following table by calculating the average and maximum number of comparisons the linear search will perform, and the maximum number of comparisons the binary search will perform. $$\begin{array}{l|lllll} & 50 & 500 & 10,000 & 100,000 & 10,000,000 \\ \text { Array Size } \rightarrow & \text { Elements } & \text { Elements } & \text { Elements } & \text { Elements } & \text { Elements } \\ \hline \begin{array}{l} \text { Linear Search } \\ \text { (Average Comparisons) } \end{array} & & & & & \\ \hline \begin{array}{l} \text { Linear Search } \\ ( \text { Maximum Comparisons) } \end{array} & & & & & \\ \hline \begin{array}{l} \text { Binary Search } \\ ( \text { Maximum Comparisons) } \end{array} & & & & & \\ \hline \end{array}$$

The average number of comparisons performed by linear search to find an item in an array of \(\mathrm{N}\) elements is ___________.

The _________ search algorithm requires that the array's contents be sorted.

The maximum number of comparisons performed by linear search to find an item in an array of N elements is ___________.

Team up with two to three other students and jointly decide how you would organize, order, and locate the data used in the following application. Be prepared to present your group's design to the rest of the class. The program to be developed is a menu-driven program that will keep track of parking tickets issued by the village that is hiring you. When a ticket is issued the program must be able to accept and store the following information: ticket number, officer number, vehicle license plate state and number, location, violation code (this indicates which parking law was violated), and date and time written. The program must store information on the amount of the fine associated with each violation code. When a ticket is paid the program must be able to accept and store the information that it has been paid, the amount of the payment, and the date the payment was received. The program must be able to accept inquiries such as displaying the entire ticket record when a ticket number is entered. The program must also be able to produce the following reports: A list of all tickets issued on a specific date, ordered by ticket number A list of all tickets for which payment was received on a specific date and the total amount of money collected that day A report of all tickets issued in a one-month period, ordered by officer number, with a count of how many tickets each officer wrote A report of all tickets that have not yet been paid, or for which payment received was less than payment due, ordered by vehicle license number
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