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 2.1, Problem 1E
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To describe the operation of the insertion sort on the array A.
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Create and implement a mergesort variant that returns an int[] array perm with perm[i] being the index of the i th smallest entry instead of rearranging the array.
Create 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.
Create and implement a mergesort variant that yields an int[] array perm instead of rearranging the array's entries, with perm[i] being the index of the array's i th smallest element.
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Introduction to Algorithms
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- Make and implement a mergesort variation that gives an int[] array perm, where perm[i] is the index of the array's i th smallest element, rather than rearranges the array's elements.arrow_forwardUsing heapsort to sort [10,5,10,5] and [5,10,5,10], on which of the two arrays, the relative order of all the elements of the same values will be preserved? Can you show a working behind your answer? Options are: 1. only [10,5,10,5] 2. only [5,10,5,10] 3. none 4. botharrow_forwardAny could help me the following question From the original array of [8 12 14 1 3 5 11 10 9 7 4 2 6 13 16 15], show what the entire array looks like after each time the partition function is called within the Quicksort algorithm. Indicate each time what the selected pivot value is for that partition.arrow_forward
- Consider the array that is given below. Provide step by step process to show how the merge sort would sort the array. 13 11 34 20 17 9 32arrow_forwardUsing HeapSort, find the total number of swaps in a 100 element array when the array is: - strictly increasing - strictly decreasing - randomarrow_forwardWrite a program to compute the exact value of the number of array accesses usedby top-down mergesort and by bottom-up mergesort. Use your program to plot the values for N from 1 to 512, and to compare the exact values with the upper bound 6N lg Narrow_forward
- Create a programme that generates the best-case array for sort() (with no duplicates). an array of N items with different keys with the characteristic that each partition produces subarrays that differ in size by no more than one (the same subarray sizes as would occur for an array of N equal keys). (Ignore the first shuffle for the sake of this exercise.)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_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_forward
- Using an unsorted array to implement a map would allow an O(log2N) get operation (where N is the number of elements in the map). Group of answer choices True False also explain why?arrow_forwardDevelop and implement a version of mergesort that does not rearrange the array, but returns an int[] array perm such that perm[i] is the index of the i th smallest entry in the array.arrow_forwardWrite a version of bottom-up mergesort that takes advantage of order in the array by proceeding as follows each time it needs to find two arrays to merge: find a sorted subarray (by incrementing a pointer until finding an entry that is smaller than its predecessor in the array), then find the next, then merge them. Analyze the running time of this algorithm in terms of the array size and the number of maximal increasing sequences in the array.arrow_forward
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