Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 8.2, Problem 1E
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To illustrate the operation of the counting sort on the array
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Introduction to Algorithms
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- (b) Explain in your own words why even the more efficient versions of bubble sort are considered to be slow algorithms. Illustrate your answer using the example data: {17, 15, 11, 13}arrow_forwardWe learned from mathematics that addition is commutative (i.e. a+b = b+a) and associative (i.e. (a + b) + c = a + (b + c)). Consider the expression in which the n elements of the array A is a numeric type. A[0] + A[1] + ... + A[n-1]; If A is an array of integers, is the result the same if the expression above is evaluated in any order (using properties of commutativity and associativity)?Why or why not?arrow_forwardCreate a bottom-up mergesort that takes advantage of array order by doing the following each time it has to identify two arrays to merge: locate a sorted subarray (by incrementing a pointer until it finds an entry in the array that is smaller than its predecessor), then locate the next, and finally merge them. Examine the algorithm's running time in terms of array size and the number of maximal rising sequences in the array.arrow_forward
- Explain step-by-step, showing all possible detail, how a binary search algorithm works on the array {1, 2, 3, 4, 5, 6, 7, 8} searching for the values of 5 and 12.arrow_forwardApply Selection Sort on the following list of elements: 16, 23, 19, 6, 20, 10, 34, 54arrow_forwardGiven an array arg[] below, use the incremental approach to sort it in assending order 11 42 35 38 22 45 18 39 3arrow_forward
- Given an array of integers arr, sort the array by performing a series of pancake flips. In one pancake flip we do the following steps: Choose an integer k where 1 <= k <= arr.length. Reverse the sub-array arr[0...k-1] (0-indexed). For example, if arr = [3,2,1,4] and we performed a pancake flip choosing k = 3, we reverse the sub-array [3,2,1], so arr = [1,2,3,4] after the pancake flip at k = 3. Print out the k-values corresponding to a sequence of pancake flips that sort arr. Example 1: Input: arr = [3,2,4,1] Output: 4, 2, 4, 3 Explanation: We perform 4 pancake flips, with k values 4, 2, 4, and 3. Starting state: arr = [3, 2, 4, 1]. After 1st flip (k = 4): arr = [1, 4, 2, 3] After 2nd flip (k = 2): arr = [4, 1, 2, 3] After 3rd flip (k = 4): arr = [3, 2, 1, 4] After 4th flip (k = 3): arr = [1, 2, 3, 4], which is sorted. Another potential solution is: Output = 3, 4, 2, 3, 1, 2, 1, 1 with a similar explanation. All potential solutions that solve the problem are…arrow_forwardConsider the array L = 387, 690, 234 435 567 123 441 as an example. The number of components in this case is 7, the number of numbers is 3, and the radix is 10. This suggests that radix sort would require 10 bins and 3 cycles to complete the sorting. shows how the radix order is followed by the list. Each key is probably thrown into the garbage bin facing down. Each bin is turned into a key when the output to the is to be attached to the phrase: at the end of the bin.arrow_forwardImplement the following algorithms in Java: A) A variant of QUICKSORT which returns without sorting subarrays with fewer than k elements and then uses INSERTION-SORT to sort the entire nearly-sorted array (slide 24).B) A variant of QUICKSORT using the median-of-three partitioning scheme.Slide 24:•Cutoff to INSERTION-SORT (as in MERGE-SORT). Alternatively: −When calling QUICKSORT on a subarray with fewer than k elements, return without sorting the subarray −After the top-level call to QUICKSORT returns, run INSERTION-SORT on the entire array to finish the sorting process −Taking advantage of the fast running time of INSERTION-SORT when its input is “nearly” sorted •Tail call optimisation convert the code so that it makes only one recursive call −Usually good compilers do that for us • Iterative version with the help of an auxiliary stackarrow_forward
- Q: Explain in your own words the Analysis of each Array list operation (add, remove and find)?arrow_forwardShow the steps for sorting 2, 6, 4, 1, 2, 4, 1, 4 using counting sort (first version) with additional arrays B and C. A 2 6 4 1 2 4 1 4 1 2 3 4 5 6 7 8arrow_forwardDevelop a merge implementation that reduces the extra space requirement to max(M, N/M), based on the following idea: Divide the array into N/M blocks of size M (for simplicity in this description, assume that N is a multiple of M). Then, (i) considering the blocks as items with their first key as the sort key, sort them using selection sort; and (ii) run through the array merging the first block with the second, then the second block with the third, and so forth.arrow_forward
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