Given an array A = [10, 7, 4, 2, 1], and target = 7, return the index of the target if found, else return -1. 1. Can this problem be solved in O(logN)? 2. If so, write the implementation. Mention time and space complexity 3. If this problem cannot be solved using O(logN), what is the solution that you suggest - write the code and also mention time and space complexity.
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Given an array A = [10, 7, 4, 2, 1], and target = 7, return the index of the target if found, else return -1.
1. Can this problem be solved in O(logN)?
2. If so, write the implementation. Mention time and space complexity
3. If this problem cannot be solved using O(logN), what is the solution that you suggest - write the code and also mention time and space complexity.
Step by step
Solved in 3 steps
- Modify the ArrayDeque implementation so that it does not require the modulus (%) operator. The modulus operator is "expensive" on some systems. Instead, the implementation should make use of the fact that if a.length is a power of 2, then k % a.length = k & (a.length - 1). Here, & is the bitwise and operator. (p 61) Open Data Structures in Java, section 2.7The insertion sort was discussed and the implementation was demonstrated in the sorting lecture. In this assignment, you are asked to re-implement the insertion sort (InsertionSort.java),with additional requirements. Particularly, you need to show:1. For each iteration, how a number from a unsorted region is placed in the correctionposion in the sorted region;2. How to make the whole array be sorted based on the previous step, and count the totalnumber of shifts during the whole insertion sort process.2 Details of the ProgramTo complete the whole implementation, you should write at least the following importantmethods:2.1 Part1: insertLast/**A method to make an almost sorted array into fully sorted.@param arr: an array of integers, with all the numbers are sortedexcepted the last one@param size: the number of elements in an array*/public static void insertLast(int[] arr, int size){// your work}To make it concrete, let’s use the example shown in Figure 1. In this example, the…Now let's examine a Dynamic Program algorithm to solve this problem. 3.3 Let's say we have an array of length X+1. How would we define array[x]? or What is array[x] defined for?
- I just need the method they are asking for Write a recursive function that takes a start index, array of integers, and a target sum. Your goal is to find whether a subset of the array of integers adds up to the target sum. The start index is initially 0.A target sum of 0 is true for any array. Examples: subsetSum(0, {2, 4, 8}, 10) -> true public boolean subsetSum(int start, int[] nums, int target) { }Please help. How to solve this on Java language by using only Dynamic Programming? Thank you. We are given a set A of integers. Check whether we can partition A into three subsets with equal sums. It is important to note that all elements should be included in the equally divided subsets; no element should be left out, and none of the elements should be repeated in the subsets.For example: A={4,7,6,2,10,7,10,2} has such a partition: {4,2,10}, {7,7,2},{6,10}Input: A set, A, of integersOutput: if we can partition A into three subsets with equal sums, print subsets otherwise present a suitable message.Imagine a collection of nuts and bolts that are all together in one pile on a table. Describe, in pseudocode, how you would find all matching pairs of nuts and bolts. You need to find one solution for each of the problem-solving approaches given below. For each of your solutions, determine how many comparisons of pairs of nuts and bolts you might have to make in the best- and worst-case scenario. You can assume that there are complete pairs, no single nuts or bolts and that for each bolt, there is exactly one nut that fits. Describe a solution to the nuts and bolts problem (in pseudocode) using a Divide and Conquer Approach.
- In this programming assignment, you are expected to design an experimental study for thecomparison between Hoare’s partitioning and Lomuto’s partitioning in Quicksort algorithm.You must implement the recursive Quicksort algorithm using two partitioning algorithms inJava. You must design the experiments for the comparison of two algorithms both theoreticallyand empirically. You must write a detailed report including the pseudo-code of the algorithms,the time complexity of the algorithms, the experimental design, and your results. You canprovide some plots (scatter, line etc.) to illustrate your results.A graph is a collection of vertices and edges G(V, E). A weighted graph has weights (numbers, etc.) on every edge. A multigraph can have more than one edges between any vertices. Explain why a person should use a weighted graph instead of a multigraph. Give examples. An adjacency matrix might be a better choice for speeding up a program, however, it consumes huge memory for large graphs. How this situation can be improved? What programming constructs better suit graph representation? Explain with exampleYou are given an array of positive integers S[1, . . . , n]. You are initially positioned at the array’s first index 1, and each element S[i] represents your maximum length of jump at position i. For example, you can jump from position i to any position among i + 1, . . . , i + S[i]. Return true if you can reach the last index, or false otherwise. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.
- 1. Write a linear (0(n)) running time complexity program in Java to find all the dominant elements in the given array of n distinct integer elements. An element is a dominant element if it is greater than all the elements to its right side. The rightmost element in the array is always a dominant element. For example, in the array {16, 17, 4, 3, 5, 2}, dominant elements are 17, 5 and 2. 2. Prove that your algorithm takes (0(n)) running time to compute this task. Formulate the sum equation for this proof.II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 2. Let A be a sorted array of integers. You want to implement two functions: . update(i, x) - which takes as input an index i in A and sets A[i] = x. For example, calling update (3,10) will set A[3] = 10. Note that array A might not be completely sorted after an update. is Sorted(i) returns true if the subarray A[0... i] is sorted, otherwise it returns false. A straightforward implementation of the two operations using only the given array can be done as follows: update operation can directly change the value of A[i] to x. is Sorted will scan A[0] up to A[i] while checking if elements are non-decreasing. With the above implementations, update takes O(1) time but is Sorted takes O(n) time. b. Describe how to use a balanced BST to implement both operations in O(log n) time. Discuss why your implementation is correct, preferably using diagrams.Write an implementation of “func(A)” that returns a peak in 2 dimensions -as defined by an entry greater than or equal to its 4 neighbor values. Run it on the 'A' and assess the complexity in terms of n (in theory, not using doubling experiments). "A" = np.array([1,4,6,7], [3,5,12,23],[25,9,7,14],[17,16,14,5]) explanaiont and code please