1. Consider an array of n distinct values in which the first n − 1 values are sorted, and the las...
1. Consider an array of n distinct values in which the first n − 1 values are sorted, and the last element is not. (It could be smaller than the first element, larger than element n − 1, or anywhere in between.) Give the worst-case number of comparisons that Insertion Sort will perform in this scenario. You can give your answer in terms of big-Theta if you wish to ignore low-order terms and constants.
Homework Answers
The subarrays from [1,i] for 
The last insertion may take 1 comparison or n-1 comparisons depending on how large the last element is
In any case, the number of comparisons is
Add Answer to:
1. Consider an array of n distinct values in which the first n − 1 values are sorted, and the las...
4) [15 points total (5 points each)] Assume you are given a sorted array A of n numbers, where A is indexed from 1 up t...
4) [15 points total (5 points each)] Assume you are given a sorted array A of n numbers, where A is indexed from 1 up to n, anda number num which we wish to insert into A, in the proper sorted position. The function Search finds the minimum index i such that num should be inserted into Ali]. It searches the array sequentially until it finds the location i. Another function MakeRoom moves A[i], .., AIn] to Ali+1]...AIn+1] same sort...
6. Let T(1..n] be a sorted array of distinct integers, some of which may be negative....
6. Let T(1..n] be a sorted array of distinct integers, some of which may be negative. Give an algorithm that can find an index i such that 1 <i<n and T[i] = i, provided such an index exists. Your algorithm should take a time in O(lg n) in the worst case. Answers must be proven (or at least well justified)
Given two arrays A and B of n integers both of which are sorted in ascending...
Given two arrays A and B of n integers both of which are sorted in ascending order. Write an algorithm to check whether or not A and B have an element in common. Find the worst case number of array element comparisons done by this algorithm as a function of n and its Big-O complexity
1. (16 pts.) Sorted Array Given a sorted array A of n (possibly negative) distinct integers,...
1. (16 pts.) Sorted Array Given a sorted array A of n (possibly negative) distinct integers, you want to find out whether there is an index i for which Al = i. Give a divide-and-conquer algorithm that runs in time O(log n). Provide only the main idea and the runtime analysis.
Please answer by mathematical language: An array of n elements is almost sorted if and only...
Please answer by mathematical language: An array of n elements is almost sorted if and only if every element is at most k spots away from its actual location. Assuming that you can only perform pairwise comparisons, formally prove that any algorithm which can sort almost sorted arrays must have running time Ω(n log k), You may assume that n is a multiple of k.
1. Please write a Divide-and-Conquer Java algorithm solving the following problem: Given an "almost sorted" array...
1. Please write a Divide-and-Conquer Java algorithm solving the following problem: Given an "almost sorted" array of distinct integers, and an integer x, return the index of x in the array. If the element x is not present in the array, return -1. "Almost sorted" means the following. Assume you had a sorted array A[0…N], and then split it into two pieces A[0…M] and A[M+1…N], and move the second piece upfront to get the following: A[M+1]…A[N]A[0]…A[M]. Thus, the "almost sorted"...
Consider an array A[1...n] which is originally unsorted. One method to sort the array is as...
Consider an array A[1...n] which is originally unsorted. One method to sort the array is as follows: First find the largest key in the unsorted portion of the array (initially the entire array s unsorted) and swap this with the last position in the unsorted section. This last position is now considered part of the sorted portion. The procedure is repeated until the entire array is sorted. (a) Write an algorithm to sort A as outlined above (in pseudo-code, no...
3. Modify the insertion sort algorithm discussed in class so that it can sort strings. That...
3. Modify the insertion sort algorithm discussed in class so
that it can sort strings. That is, its input will be an array, the
type of which is string. The insertion sort algorithm will sort the
elements in this array. Finally, its output will be a sorted
array.
As the solution of this problem, you need to submit the
following answer(s): (1). The implementation of your algorithm in
C# (20points).
Algorithm: At each array-position, it checks the value there against...
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct...
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct integers which is already sorted into ascending order, will find if there is some i such that Ali] in worst-case 0(log n) time.
4. (7 pts) Let A be an array of 5 integers, whose contents are as follows:...
4. (7 pts) Let A be an array of 5 integers, whose contents are as follows: 3, 2, 1, 5, 4. We will apply insertion sort to sort this array. Show all of the element-wise comparisons made by the algorithm in the correct order. Here an element-wise comparison means the comparison of one element of the array with another element of the array or the key set in a particular step of the algorithm. Since the algorithm may move the...
4) [15 points total (5 points each)] Assume you are given a sorted array A of n numbers, where A is indexed from 1 up to n, anda number num which we wish to insert into A, in the proper sorted position. The function Search finds the minimum index i such that num should be inserted into Ali]. It searches the array sequentially until it finds the location i. Another function MakeRoom moves A[i], .., AIn] to Ali+1]...AIn+1] same sort...
6. Let T(1..n] be a sorted array of distinct integers, some of which may be negative. Give an algorithm that can find an index i such that 1 <i<n and T[i] = i, provided such an index exists. Your algorithm should take a time in O(lg n) in the worst case. Answers must be proven (or at least well justified)
1. (16 pts.) Sorted Array Given a sorted array A of n (possibly negative) distinct integers, you want to find out whether there is an index i for which Al = i. Give a divide-and-conquer algorithm that runs in time O(log n). Provide only the main idea and the runtime analysis.
Consider an array A[1...n] which is originally unsorted. One method to sort the array is as follows: First find the largest key in the unsorted portion of the array (initially the entire array s unsorted) and swap this with the last position in the unsorted section. This last position is now considered part of the sorted portion. The procedure is repeated until the entire array is sorted. (a) Write an algorithm to sort A as outlined above (in pseudo-code, no...
3. Modify the insertion sort algorithm discussed in class so
that it can sort strings. That is, its input will be an array, the
type of which is string. The insertion sort algorithm will sort the
elements in this array. Finally, its output will be a sorted
array.
As the solution of this problem, you need to submit the
following answer(s): (1). The implementation of your algorithm in
C# (20points).
Algorithm: At each array-position, it checks the value there against...
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct integers which is already sorted into ascending order, will find if there is some i such that Ali] in worst-case 0(log n) time.
4. (7 pts) Let A be an array of 5 integers, whose contents are as follows: 3, 2, 1, 5, 4. We will apply insertion sort to sort this array. Show all of the element-wise comparisons made by the algorithm in the correct order. Here an element-wise comparison means the comparison of one element of the array with another element of the array or the key set in a particular step of the algorithm. Since the algorithm may move the...
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