Sorting in Linear Time in Analysis & Design of Algorithm
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The document discusses three linear time sorting algorithms: bucket sort, radix sort, and counting sort. Bucket sort divides elements into buckets and sorts each bucket individually before joining them, while radix sort sorts numbers from the least significant to the most significant digit. Counting sort organizes elements based on numeric keys without direct comparisons and is often used as a subroutine in other algorithms.
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Sorting in Linear Time in Analysis & Design of Algorithm
- 2. Contents • Introduction • Bucket Sort • Radix Sort • Counting Sort • References
- 3. Sorting in Linear Time • There are sorting algorithms that run faster than O(n lg n) time but they require special assumptions about the input sequence to be sort. • Ex: Bucket sort Radix sort Counting sort
- 4. Bucket Sort • In this algorithm, we create bucket and put elements into them • Then we apply some sorting algorithms (Insertion Sort) to sort the elements in each bucket • Finally we take elements out and join them to get the sorted result.
- 5. Example of Bucket Sort
- 6. Radix Sort • It is a sorting algorithm which is used to sort the numbers • We sort the numbers from least significant digit to the most significant digit • Ex: If we are dealing with unsorted numbers then we know that there are 10 digits from 0 to 9 that are used to form any number. So, we need 10 buckets in order to sort them.
- 7. Example of Radix Sort
- 8. Counting Sort • It is a sorting algorithm in which we sort a collection of elements based on numeric keys • In this algorithm, we don’t compare elements while sorting • It is also used as a subroutine in other sorting algorithm
- 9. Example of Counting Sort
- 10. References • Introduction to Algorithms 2e by Thomas H Cormen