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 5.3, Problem 3E
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To decide whether the code PERMUTE-WITH_ALL
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Given an unsorted array A of size N that contains only positive integers, find a continuous sub-array that adds to a given number S and return the left and right index(1-based indexing) of that subarray.
In case of multiple subarrays, return the subarray indexes which come first on moving from left to right.
Note:- You have to return an ArrayList consisting of two elements left and right. In case no such subarray exists return an array consisting of element -1.code.
Given an integer n and an array a of length n, your task is to apply the following mutation to a:
Array a mutates into a new array b of length n. For each i from 0 to n - 1, b[i] = a[i - 1] + a[i] + a[i + 1]. If some element in the sum a[i - 1] + a[i] + a[i + 1] does not exist, it should be set to 0. For example, b[0] should be equal to 0 + a[0] + a[1].
Let's say that B is an array with a size of n > 6 that has integers from 1 to n-5, inclusive, in it. There are exactly five repeats in B. Explain how to find the five numbers in B that are the same.
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- Write a version of bottom-up mergesort that takes advantage of order in the array by proceeding as follows each time it needs to find two arrays to merge: find a sorted subarray (by incrementing a pointer until finding an entry thatis smaller than its predecessor in the array), then find the next, then merge them. Analyze the running time of this algorithm in terms of the array size and the number of maximal increasing sequences in the array.arrow_forwardWrite a program that reads an array A of N elements containing only 0's and 1's. Your program should find the position of a 0 and replace it with a 1 to get the longest continuous sequence of 1's. Let this position of 0 be called P. Print P if such a 0 exists and print -1 if the original array A contains only 1's. Assume the array indexing starts from 0.arrow_forwardWrite a version of bottom-up mergesort that takes advantage of order in the array by proceeding as follows each time it needs to find two arrays to merge: find a sorted subarray (by incrementing a pointer until finding an entry that is smaller than its predecessor in the array), then find the next, then merge them. Analyze the running time of this algorithm in terms of the array size and the number of maximal increasing sequences in the array.arrow_forward
- suppose we are maintaining a collection of C elements such that, each time we add a new element to the collection, we copy the contents of C into a new array list of just the right size. What is the running time of adding n elements to an initially empty collection C in this case?arrow_forwardWrite a program (in mars ) maxarray that computes the double of maximum of values of any given array of length L=7. The computation of the maximum is done in a procedure. For example : if the values in the array are : 14, 5, 85, 17, 9, 1, 47. The result is 170.arrow_forwardWrite a program that plots a histogram of the subarray sizes leftfor insertion sort when you run quicksort for an array of size N with a cutoff for subarrays of size less than M. Run your program for M=10, 20, and 50 and N = 105arrow_forward
- Consider an array A of N values (N entered by the user). Write a C program that creates a second array B such that the i-th element of B, i.e., B[i] is equal to A[0] *A[1] * A[2] * ... A[i]; In other words:- B[0] = A[0]- B[1] = A[0] * A[1];- B[2] = A[0] * A[1] * A[2];- B[3] = A[0] * A[1] * A[2] * A[3]- ....etc.For this exercise, we would like to implement two solutions and compare their complexity /performance in terms of computation time.Solution 1: Implement blindly the following algorithms: for each element B[i], compute A[0] *A[1] * A[2] * .... *A[i] and save the result in B[i];To test the solution, create an array A of 1000 elements and initialize each of its elements with arandom value (instead of asking the user to . To do that, use the function rand, which, every timecalled, returns a random number Questions:- How long does your program take to produce the solution?- Analyze the solution above and explain why it is taking long time. What are the mainfactors that affect how long…arrow_forwardGiven a large list of positive integers, count the number of k-subsequences. A k-subarray of an array is defined as follows: It is a subarray, i.e. made of contiguous elements in the array The sum of the subarray elements, s, is evenly divisible by _k, _i.e.: sum mod k = 0. Given an array of integers, determine the number of k-subarrays it contains. For example, k = 5 and the array nums = [5, 10, 11, 9, 5]. The 10 k-subarrays are: {5}, {5, 10}, {5, 10, 11, 9}, {5, 10, 11, 9, 5}, {10}, {10, 11, 9}, {10, 11, 9, 5}, {11, 9}, {11, 9, 5}, {5}. **Function Description ** Complete the function kSub in the editor below. The function must return a long integer that represents the number of k-subarrays in the array. kSub has the following parameter(s): k: the integer divisor of a k-subarray nums[nums[0],...nums[n-1]]: an array of integers Constraints 1 ≤ n ≤ 3 × 105 1 ≤ k ≤ 100 1 ≤ nums[i] ≤ 104 Input Format For Custom Testing Input from stdin will be processed as follows and…arrow_forwardCreate a programme that, when quicksort is run on an array of size N with a cutoff for subarrays less than M, produces a histogram of the subarray sizes still available for insertion sort. Run your programme with N = 105 and M = 10, 20, and 50.arrow_forward
- Implement the pikles array in Python with the value [self.important_data].For instance, if __setstate__ knew how to do the reverse, it could have returned anything picklable from __getstate__. A dictionary of all values, such as "important_data: self.important_data," is a suitable substitute.arrow_forwardUsing an unsorted array to implement a map would allow an O(log2N) get operation (where N is the number of elements in the map). Group of answer choices True False also explain why?arrow_forwardCodeGiven an unsorted array A of size N that contains only positive integers, find a continuous sub-array that adds to a given number S and return the left and right index(1-based indexing) of that subarray. In case of multiple subarrays, return the subarray indexes which come first on moving from left to right. Note:- You have to return an ArrayList consisting of two elements left and right. In case no such subarray exists return an array consisting of element -1.arrow_forward
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