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 33.4, Problem 6E
Program Plan Intro
To modify the closest pair
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Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
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- Show the steps of Counting Sort (second version that doesn’t use array B as given in the lectures) for the following array A of values with C for counting. A 3 2 5 1 0 7 8 index 1 2 3 4 5 6 7 C 0 0 0 0 0 0 0 0 index 1 2 3 4 5 6 7 8arrow_forwardModify the Partition function so that after running it, any input array A is partitioned into three parts: the left part consisting of all elements < pivot, the middle part consisting of all elements = pivot, and the right part consisting of the rest Write down the pseudo-code for this modified version of the Partition function. (must be an in-place algorithm with Θ(n) time complexity.) Hint: Define three indices: i as the end of the left part, k as the end of the middle part, and j denoting the current index which is used in the for-loop.arrow_forwardWhat is the best case complexity (in terms of the number of comparisons) for standard (non-early termination) bubble sort, sorting an array of n elements?arrow_forward
- Apply Selection Sort on the following list of elements: 16, 23, 19, 6, 20, 10, 34, 54arrow_forwardWhat is the asymptotic time (big Oh) of the following operation used in quicksort: Partition array A [1 .. n] into a left subarray with elements <= A[1] and a right subarray of elements >= A[1].arrow_forwardApply bubble sort algorithm to the following array, and contents of arr[] after each pass. arr[] 65 55 35 25 45 15 After pass 1: After pass 2: After pass 3: After pass 4: After pass 5:arrow_forward
- What is the running time of finding a single number from an unsorted array of p elements. (a) O(n)(b) O(p)(c) O(lgp)(d) O(p^2) What is the running time of finding your name from a sorted list of names.(a) O(n)(b) O(n^3)(c) O(lgn)(d) O(n^2)arrow_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_forwardRewrite this code, using modular programming style, and correcting any errors if necessary. 2. Optimize the algorithm by making the following modifications: (a) After the first pass, the largest number is guaranteed to be in the highest- numbered element in the array; after the second pass, the two highest numbers are "in place," and so on. Instead of comparing every pair on every pass, modify the algorithm to make as few comparisons as necessary on each pass. (b) Modify the algorithm to check at the end of each pass if any swaps have been made. If none have been made, the data must already be in the proper order, so the program should terminate. Observe the single-exit point rule when making this modification. 3. Insert appropriate statements in your code to output the state of the array after every pass. #include <iostream> #include <iomanip> using namespace std; using std::setw; using std::cout; using std::endl; using std::size_t; int main() { const short…arrow_forward
- Given two arrays A and B of equal size N, the task is to find if given arrays are equal or not. Two arrays are said to be equal if both of them contain same set of elements, arrangements (or permutation) of elements may be different though.Note : If there are repetitions, then counts of repeated elements must also be same for two array to be equal. Example 1: Input: N = 5 A[] = {1,2,5,4,0} B[] = {2,4,5,0,1} Output: 1.arrow_forwardYou are given an unsorted array A[1, ..., n].We know that the maximum (or minimum) element in the array can be found in (n-1) comparisons.Write an algorithm that finds both the maximum and the minimum element in the array in ~(3n/2) comparisons, i.e., (3n/2) + THETA(1) comparisons.arrow_forwardWrite a technique to locate the indices m and n in an array of integers such that sorting items m through n will sort the entire array. Find the smallest such sequence by minimising n - m. Example inputs: 1, 2, 4, 7, 10, 11, 7, 12, 6, 7, 16, and 19; outputs: 3 and 9.arrow_forward
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