EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Write 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.
Write pseudocode of an insertion sort algorithm. Illustrate the execution of the algorithm on the array X = {2, 11, 98, 23, 48, 33, 97, 61, 3}, writing the intermediate values of X at each iteration of the algorithm.
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The ColumnChoice problem takes as input a two-dimensional array A[1..m, 1..n] of
Os and 1s with m rows and n columns along with a non-negative integer k < n. It asks
whether there exists a subset SC {1, ..., n} of k columns such that for each row i e {1,..., m}
there exists at least one column j e S where A[i, j] = 1. Prove that ColumnChoice is NP-
complete.
Chapter 9 Solutions
EBK DATA STRUCTURES AND ALGORITHMS IN C
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- In the data structure course Karim learned about a very interesting sorting algorithm known as “Bubble Sort". It was also mentioned during the course that this algorithm has more time complexity in the worst-case (0(n²)) in comparison to other sorting techniques. The course teacher then explained to the students that there is a way to reduce the number of iterations from the traditional algorithm if the array becomes sorted before n number of internal iterations. So teacher asked the students to introduce a variable named "CHECK" in order to check if swapping has taken place in a single iteration. If no swapping occurs for any single iteration then the iterations of the whole process can be terminated. The course teacher then asked Karim to write the pseudocode of the optimized version of "Bubble sort" on the black board. a) Write the pseudocode that Karim needs to write according to the above explained phenomena.arrow_forwardWrite a psuedo algorithm that solves the coin-row problem with dynamic programming, as a result, returns the maximum value of money that can be collected from the table under the specified conditions, but did not tell which coins should be taken from the table to reach this value (i.e. which elements of the array that comes as input to the algorithm). . Make the necessary changes in the algorithm that solves the Sequential Money problem with dynamic programming, make the algorithm return the values of the coins included in the maximum solution it finds in a series or a list. What are the time and space complexities of your algorithm, specify them separately.arrow_forwarddevelop an implementation TwoSumFaster that uses a linear algorithm to count the pairs that sum to zero after the array is sorted (instead of the binary-search-based linearithmic algorithm). Then apply a similar idea to develop a quadratic algorithm for the 3-sum problem.arrow_forward
- Consider a hybrid sorting algorithm that combines Mergesort with Insertion Sort.It uses Mergesort until the number of elements in the input becomes smaller than or equal to 8, after which it switches to Insertion Sort. What is the number of key comparisons performed by this hybrid sorting algorithm in the best case when running on an input array of size n? Briefly justify your answer. You could assume n = 2k, k is more than 3arrow_forwardAnswer the following question for basic sorting algorithms. Here is an array of 7 integers: (1) 8 3 2 0 1 9 7 Draw this array after the FIRST iteration of the large loop in a selection sort (sorting from smallest to largest, and always pick the smallest element in each iteration). Here is an array of 7 integers: (1) 8 3 2 0 1 9 7 Draw this array after the FIRST iteration of the large loop in a bubble sort (sorting from smallest to largest).arrow_forwardQuestion 2: Implement sequential search and binary search algorithms on your computer. Note down run time for each algorithm on arrays of size (1, 250, 500, 750, 1000, 1250, 1500, 5000). For both algorithms, store the values 0 throughn 1 in order in the array, and use a variety of random search values in the range 0 to n 1 on each size n. Graph the resulting times. When is sequential search faster than binary search for a sorted array? Solution: Execution Time for Input Size(N) Search Element Execution Time for Sequential Search(n) Binary Search(logn)arrow_forward
- Write an efficient algorithm for the following problem, and describe your reasoning. Determine the Time complexity and if you cannot find any polynomial time algorithm, then give a backtracking algorithm. Problem: Binary Array Core Input: Two integers p and q and a binary array A[1...n], i.e., each entry contains either a 0 or 1. Output: Print Yes - if there exists a subarray A[i...k], where 1<= i < k <= n, with exactly p zeros in A[1...i-1] (there may be 1s) and exactly q ones in A[k+1...n] (there may be 0s). Print No - otherwise. Outputs with examples Input: A = [0,1,1,0,1], p = 2, q =1, Output: No. Input: A = [0, 1,1,0, 0,1,0,1], p = 1, q =1, Output: Yes because we can have A[1...i-1] = [0] and A[k+1 ... n] = [0,1,0,1]arrow_forwardGiven two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)). Example 1: Input: nums1 = [1,3], nums2 = [2] Output: 2.00000 Explanation: merged array = [1,2,3] and median is 2. Example 2: Input: nums1 = [1,2], nums2 = [3,4] Output: 2.50000 Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5. Constraints: nums1.length == m nums2.length == n 0 <= m <= 1000 0 <= n <= 1000 1 <= m + n <= 2000 -106 <= nums1[i], nums2[i] <= 106 Write the whole code in python language Attach the code outputs also and explain the implementation.arrow_forwardUsing C++ or Java, compare the bubble sort, inclusion sort, and margesort algorithms. Make a large array (as large as 1 million) . After adding random numbers to it, record the time and all of the algorithms, record the time once again, and calculate the effective time. For each method, perform this at least 100 times, then calculate the average execution time.arrow_forward
- For a Given array of Size 100, do the following implementations - 1. Write a program to implement the Modified version of the bubble sort algorithm so that it terminates the outer loop when it detects that the array is sorted. Compare the running time of the modified algorithm with Original Bubble sort. 2. Implement Quick sort ( both iterative and recursive). Calculate the run time complexity of both the implementation and compare their performance in terms of best, average and worst time complexity.arrow_forwardConsider the following algorithm S, in which A represents a sorted array of n integers, andx is an integer in the array A, and l and r are indices l ≤ r between which the element x is located in A.The algorithm S returns the index (location) of the element x in the array A. H(A, x, l, r):if l == r:return lelse:m = (l+r)//2 # // returns integer component upon division: 7//2=3if x <= A[m]:return H(A, x, l, m)else:return H(A, x, m+1, r) Derive formally the running time of this algorithm and formally prove the correctness of the runningtime bound for the worst case, ie. O()arrow_forwardQuestion 2: Implement sequential search and binary search algorithms on your computer. Note down run time for each algorithm on arrays of size (1, 250, 500, 750, 1000, 1250, 1500, 5000). For both algorithms, store the values 0 through n - 1 in order in the array, and use a variety of random search values in the range 0 to n - 1 on each size n. Graph the resulting times. When is sequential search faster than binary search for a sorted array? Solution: Input Size(N) Search Element Execution Time for Execution Time for Sequential Search(n) Binary Search(logn)arrow_forward
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