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 2.3, Problem 1E
Program Plan Intro
To describe the operation of the merge sort on the array
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Consider 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.
Merge sort algorithm is about to complete the sort and is at the point just before the last merge. At this point, elements in each half of the array are sorted amongst themselves.
Illustrate the above statement by looking at the array of the following ten integers: 5 3 8 9 1 7 0 2 6 4 and drawing the array before the final merge sort is completed (sorting from Smallest to largest)
2.Consider a polynomial that can be represented as a node which will be of fixed size having 3 fields which represent the coefficient and exponent of a term plus a pointer to the next term or to 0 if it’s the last term in the polynomial.
Then A = 11x4 -2x is represented by fig below
A
11
4
-2
1
0
Represent the following polynomials in linked list form
P = G – 3L +2F
Following is the function for interpolation search. This searching algorithm estimates the position (index) of a key in array based on the elements in the first position and last position in the array, and the length of array. The array must be sorted in ascending order.
Suppose array A contains the following 15 elements:
A = [1, 3, 3, 10, 17, 22, 22, 22, 24, 25, 26, 27, 27, 28, 28]
At first iteration, at which position (index) the element of 24 is estimated in array A?
In which part of array (starting index and ending index) the searching should continue?
How many iterations the searching are performed until the element of 24 is found?
int InterpolationSearch(int x[], int key, int n) {
int mid, min = 0, max = n-1;
while(x[min] < key && x[max] > key) {
mid = min + ((key-x[min])*(max-min)) / (x[max]-x[min]);
if(x[mid] < key)
min = mid + 1;
else if(x[mid] > key)
max = mid - 1;
else return mid;
}
if…
Chapter 2 Solutions
Introduction to Algorithms
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- 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_forwardApply Quick sort on a given sequence 7 11 14 6 9 4 3 12. What is the sequence after first phase, pivot is first element? 7 6 14 11 9 4 3 12 6 4 3 7 11 9 14 12 6 3 4 7 9 14 11 12 7 6 4 3 9 14 11 12 Quick sort follows Divide-and-Conquer strategy. True False Assume you have the array 7,9,6,10,3,5,8. What will the array look like after we call build-min-heap on the entire array? 3, 7, 5, 10, 9, 8, 6 3, 5, 6, 7, 8, 9, 10 3, 7, 5, 10, 9, 6, 8 10, 9, 8, 7, 6, 5, 3 3, 5, 7, 10, 9, 6, 8 Assume you have the following array: 30, 50, 20, 80, 10, 90, 100. Assume you were to select the quicksort pivot as the middle element of the array. What are the two sub-arrays to be sorted that result after one iteration of quicksort? 30, 50, 20, 10 | 90, 100 10, 20, 30, 50 | 90, 100 30, 50, 20, 10 | 100, 90 30, 20, 50, 10 | 100, 9arrow_forwardSolve the 6 number, 4 is the reference Topic: Searching and Sorting Please do it in python: 6.Search 42 in the sorted array of Q. No. 4 using ternary search algorithm. Show the values of low,mid1, mid2, high at each step. 4.Write the algorithm of Merge Sort in brief and show the steps of sorting this array of integersusing Merge Sort. [ 43, 65, 23, 19, 32, 39, 42, 26, 52, 28, 36, 58, 12, 15, 49 ]arrow_forward
- Given the following array: [7,8, 5, 2, 4, 6, 3, 99] Illustrate the sorting of the array using insertion sort. Illustrate the sorting of the array using merge sort.arrow_forwardWrite a bottom-up mergesort that makes use of the array's order by carrying out the following steps each time it needs to locate two arrays to merge: locate the first entry in an array that is smaller than its predecessor, then locate the next, and finally merge them to form a sorted subarray. Consider the array size and the number of maximal ascending sequences in the array while analysing the running time of this algorithm.arrow_forwarda. Show step-by-step application of the Selection sort algorithm for the array given below. What is the time complexity of this algorithm? 20 12 10 15 2 b. Consider the below array and show all steps for carrying out one partition of quick sort algorithm. Consider first element as the pivot element. 54 26 93 17 77 31 44 55 20arrow_forward
- A = [6, 5, 8, 7, 3, 4, 2, 1]. Perform the Merge Sort algorithm on this array, using a visual illustration of each step to generate the sorted array [1, 2, 3, 4, 5, 6, 7, 8]. Show that exactly 12 comparisons are needed to sort this input array A.arrow_forwardUnordered list: 33 42 35 50 20 16 45 26 5 72 18 Please answer the ff: 1. Merge sort uses the "divide and conquer" paradigm. If we divide the array, we have left and right items. After the last process in the right side, what are the items? 2. Merge sort uses the "divide and conquer" paradigm. If we divide the array, we have left and right items. After the last process in the left side, what are the items? 3. What is the 1st process using Insertion sort? 4. How many process using insertion sort? 5. How many process using bubble sort algorithm? 6. What is the 5th process using bubble sort algorithm? 7. What is the 8th process using Insertion sort? 8. How many process using Selection Sort? 9. What is the 2nd process using Selection Sort? 10. What is the 11th process using Selection Sort?arrow_forwardPseudo Code shown in Figure Q1(a) is an algorithm for binary searching for an array with n number of elements. By applying this algorithm, show step by step approach on how to find number 11 in an array as depicted in Figure Q1(b). low + 0 high e n-1 while (low s high) do ix + (low + high) /2 if (t = Alix)) then return ix else if (t < A[ix]) then high e ix - 1 else low + ix + 1 return -1 Figure Ql(a) 2 4 6 9 11 12 | 25 [0] [1) [2] [3] (4) [5) [6] Figure Q1(b)arrow_forward
- Consider an array A containing elements 12, 23, 18, 19, 2,7, 8 starting from index 0 to 6. What will be the sum of the middle three values after the second pass of the merge procedure in the merge sort algorithm?arrow_forwardDuring each iteration of Quick Sort algorithm, the first element of array is selected as a pivot. The algorithm for Quick Sort is given below. Modify it in such a way that last element of array should be selected as a pivot at each iteration. Also explain the advantages.arrow_forwardEvery time it has to identify two arrays to combine, perform the following to create a bottom-up mergesort that benefits from array order: Locate the first entry in a sorted subarray, then the second, and finally merge them (by increasing a pointer until it finds an element in the array that is smaller than its predecessor). Consider the array size and the number of maximal ascending sequences in the array when calculating the algorithm's execution time.arrow_forward
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