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Chapter 8: Problem 6

Why is the bubble sort inefficient for large arrays?

Short Answer

Expert verified
Answer: Bubble sort is inefficient for large arrays due to its worst-case and average-case time complexity of O(n^2). This is because the algorithm requires a large number of comparisons and swaps, which leads to a slow and impractical sorting process for large datasets. Other algorithms with better time complexity, such as Merge sort and Quicksort, are more efficient for sorting large arrays.

Step by step solution

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1. Understanding Bubble Sort Algorithm

Bubble sort compares adjacent elements in an array and swaps them if they are in the wrong order. It continues to iterate through the array until no more swaps are needed. In the worst-case scenario, the algorithm must perform one pass for every element in the array. This results in a quadratic time complexity of O(n^2), where n represents the number of elements in the array.
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2. Number of Comparisons

The number of comparisons made in bubble sort directly influences the time it takes to complete the sorting process. For an array of n elements, there are n-1 pairs of adjacent elements to compare, and this process must be repeated for each element in the array. As a result, there are approximately (n-1) * n/2 comparisons made in total, which again leads to the time complexity of O(n^2).
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3. Number of Swaps

In addition to the number of comparisons, the number of swaps also contributes to the inefficiency of bubble sort. In the worst case, when the array is in reverse order, the algorithm needs n-1 swaps in the first pass, n-2 swaps in the second pass, and so on, resulting in (n-1) * n/2 total swaps. This leads to a worst-case time complexity of O(n^2).
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4. Time Complexity

Bubble sort has a worst-case and average-case time complexity of O(n^2), which makes it inefficient for large arrays. As the size of the array increases, the time it takes bubble sort to sort the array increases quadratically, making it impractical for large datasets. Other sorting algorithms, such as Merge sort and Quicksort, have better average-case and worst-case time complexity (O(n log n)), which makes them much more efficient for sorting large arrays.
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5. Conclusion

The bubble sort algorithm is inefficient for large arrays due to the time complexity of O(n^2) in both worst-case and average-case scenarios. This is because the algorithm demands a high number of comparisons and swaps, which leads to a slow and impractical sorting process for large datasets. This is why other algorithms with better time complexity, such as Merge sort and Quicksort, are preferable for large arrays.

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Most popular questions from this chapter

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

T F The average number of comparisons performed by the linear search on an array of N elements is N/2 (assuming the search values are consistently found).

The _________ search algorithm steps sequentially through an array, comparing each item with the search value.

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

What is the maximum number of comparisons that a binary search function will make when searching for a value in a 1,000-element array?
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