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
Program Plan Intro
To describe the operation of the insertion sort on the array A.
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there is array
[46,93,12,82,83,32,36,78,15]
Using quicksort to sort them, and visualize all steps and explain.
The privot must be 46
Python
Fit a cubic to the following data set:
x = array([ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])
y = array([ -23.01372758, -98.68128886, -193.98575465, -278.72527151, -323.22426954, -298.42667233, -172.78799319, 82.63979118, 497.75672707, 1101.55912648])
What is the best-fit value of the y-intercept of this curve (i.e., the constant term in the polynomial)? Give your answer to at least eight decimal places.
Pseudo 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)
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Introduction to Algorithms
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- Apply quick sort on array [5, 4, 3, 1, 6, 7, 11, 9, 2, 10, 8]. Assuming the pivot value selected on the first pass of the sort is 8, what is the content of the array after the first pass of "Partition" around pivot completes? [8, 4, 3, 1, 6, 7, 2, 5, 11, 10, 9] [3, 1, 2, 4, 5, 8, 6, 7, 11, 10, 9] [5, 4, 3, 1, 2, 7, 11, 9, 6, 10, 8] [5, 4, 3, 1, 6, 7, 2, 8, 11, 10, 9]arrow_forwardConsider the following unsorted array. [234, 634, 1234, 210, 123, 542, 1021, 909, 321, 552, 135, 432, 1943, 53] In each column below, we give the intermediate results for some sort that has not yet completed. The left most column a is the original array (as shown above), and the last column i is the sorted result. 0234 0909 1021 0053 0123 0123 0234 0123 0053 0634 0210 0909 0123 0135 0210 0634 0053 0123 1234 1021 0542 0135 0210 0234 0210 0135 0135 0210 0321 0634 0210 0234 0542 0123 0210 0210 0123 0123 0552 0234 0321 0634 0542 0234 0234 0542 0432 0432 0321 0432 1021 0909 0542 0321 1021 0234 0053 0432 0542 1234 0321 1021 0432 0909 0634 0210 0542 0552 0321 0552 0909 0542 0321 1234 0321 0552 0634 0552 0135 0321 0552 0552 0135 0123 0634 0909 0909 0432 0552 0634 0135 0542 0135 0909 1021 0053 0053 1234 0909 0432 1943 0234 1021 1234 0135 1234 0432 1021 1943 0552 1234 1943 1943 0432 1021 1943 1234 0053 0053 1943 1234 0053 1943 1943 0634 1943 a b с d e (1) ய f g h iarrow_forwardIllustrate (step by step) the operation of COUNTING-SORT on the array A = {6, 2, 0, 1, 3, 4, 6, 3, 2}.arrow_forward
- 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.arrow_forwardGiven array: (623, 47, -42, 9, -308, -4, -17) After initial sorting, but before the negative and non-negative buckets are built, what is the array? Ex: 1, 2, 3 After reversal, what integers are in the negative bucket?arrow_forwardFor the given array, simulate the working operation of Insertion Sort. Show your work at eachstep. Make sure to show the status of the array after every insertion.[ 28, 13, 22, 7, 34, 2, 15, 18 ]arrow_forward
- Given an infix expression 2*3/(2-1)+5*3. Your task is to covert the givenexpression into postfix notation. The final result should be 23*21-/53*+. (Note: Make use ofstack data structure only. However the underlying implementation should be an array). Evaluatethe resultant postfix notation and show the final result. The final result should be 21arrow_forwardWrite the code of the insertion-sort algorithm. Illustrate the execution of the algorithm on the array A = 3, 13, 89, 34, 21, 44, 99, 56, 9, writing the intermediate values of A at each iteration of the algorithm.arrow_forwardWrite a program to remove duplicate values in an array. e.g. ar[ ]={1,2,3,2,4,5,4,6,7,4,6,5,7} After the deletion of duplicate values the array becomes arr[ ={1,2,3,4,5,6,7}arrow_forward
- Develop an implementation of insertion sortthat moves larger elements to the right one position with one array access per entry,rather than using exch(). Use SortCompare to evaluate the effectiveness of doing so.Develop an implementation of insertion sortthat moves larger elements to the right one position with one array access per entry,rather than using exch(). Use SortCompare to evaluate the effectiveness of doing so.arrow_forwardSO You have been given two integer arrays/lists (ARR1 and ARR2) of size N and M, respectively. You need to print their intersection; An intersection for this problem can be defined when both the arrays/lists contain a particular value or to put it in other words, when there is a common value that exists in both the arrays/lists.Note :Input arrays/lists can contain duplicate elements.The intersection elements printed would be in the order they appear in the first sorted array/list (ARR1).Input format :The first line of input contains an integer 'N' representing the size of the first array/list.The second line contains 'N' single space separated integers representing the elements of the first the array/list.The third line contains an integer 'M' representing the size of the second array/list.The fourth line contains 'M' single space separated integers representing the elements of the second array/list.Output format :Print the intersection elements. Each element is printed in a separate…arrow_forwardH3. Let S = [x1, x2, x3, ...xn], where n ≥ 5. How many ways can you choose five of the values in the array S, given that x1 = x2 = x3 and all other xi are distinct? The order of the chosen elements does not matterarrow_forward
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