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Maximize Array Value Given an array arr of n positive integers, the following operation can be performed any number of times. Use a 1-based index for the array. Choose any i such that 2 ≤ i ≤ n. Choose any x such that 1 ≤ x ≤ arr[i]. Set arr[i-1] to arr[i-1] + x. Set arr[i] to arr[i] - x. Minimize the maximum value of arr using the operation and return the value. Example: n = 4, arr = [1, 5, 7, 6] Assuming 1-based indexing, one optimal sequence is: Operation 1: choose i = 3, x = 4 (note that x ≤ arr[3], i.e. 4 < 7) - Replace arr[i-1] with arr[i-1] + x = 5 + 4 = 9 - Replace arr[i] with arr[i] - x = 7 - 4 = 3 - The array is now [1, 9, 3, 6], maximum = 9 Operation 2: i = 2, x = 4 - Replace arr[2-1] with 1 + 4 = 5 - Replace arr[2] with 9 - 4 = 5 - The array is now [5, 5, 3, 6], maximum = 6 Operation 3: i = 4, x = 1 - The resulting array is [5, 5, 4, 5], maximum = 5 The minimum possible value of max(arr) is 5 after operation 3. Function Description: Complete the function getMaximum in the editor below. getMaximum has the following parameter: - int arr[n]: an array of integers Returns: - int: the minimum maximum value possible Constraints: - 1 ≤ n ≤ 10^5 - 1 ≤ arr[i] ≤ 10^9
Breanna O.
Write a function: class Solution { public int solution(int[] A); } that, given an array A consisting of N integers, returns the beginning of any ascending slice of A of maximal size. For instance, in the above example, the function may return 4, 6, or 8 as explained above. For the following array A consisting of N = 3 elements: A[0] = 30 A[1] = 20 A[2] = 10 the function may return 0, 1, or 2 because all ascending slices of this array have size 1. Write an efficient algorithm for the following assumptions: - N is an integer within the range [1..150,000]; - each element of array A is an integer within the range [-2,147,483,648..2,147,483,647]. A non-empty array A consisting of N integers is given; a slice of that array is a pair of integers (P, Q) such that 0 < P < Q < N. Integer P is called the beginning of the slice; Integer Q is called the end of the slice. The number Q - P + 1 is called the size of the slice. A slice (P, Q) of array A is called ascending if the corresponding items form a strictly increasing sequence: A[P] < A[P+1] < ... < A[Q-1] < A[Q]. Note that we consider a slice (P, P) consisting of one element to be ascending. For example, consider array A such that: A[0] < A[1] < A[2] < A[3] < A[4] < A[5] < A[6] < A[7] < A[8] < A[9]. Pair (0, 3) is a slice of array A of size 4 that is not ascending. Pair (2, 2) is a slice of size 1 that is ascending. Pair (4, 5) is a slice of...
Akash M.
In this assignment, you will code the Quick Sort to find the elements that appear the maximum number of times in an array. In addition, the same problem should be coded by implementing a new algorithm that starts by dividing the given array into three sub-arrays. You must code the two algorithms in Python, compute the complexity of the new algorithm, and compare the performance of the new algorithm with the Quick Sort. You must write your solutions on your own. Any copying of solutions will result in a zero grade. Problem: 1. Write a Python code that implements the Quick Sort Algorithm to find the elements that appear the maximum number of times in an array. 2. Write a Python code that implements a new algorithm of Quick Sort to find the elements that appear the maximum number of times in an array. The new algorithm chooses a random pivot from the input array and divides the array into three parts: (a) An array with the elements that are less than the chosen pivot (b) An array with the elements that are equal to the chosen pivot (c) An array with the elements that are greater than the chosen pivot. Note: The codes should include checking the validity of the outputs. The outputs should be sorted ascendingly. 3. Compute the complexity of the new algorithm. 4. Compare the performance of the new algorithm with the regular Quick Sort Algorithm. 5. Explain how to check the validity of the outputs. Constraint: The number that has appeared the maximum number of times should be checked if it is a prime number. If it is a prime number, then you should exclude it. The output should be the number which appeared the maximum number of times AND is not a prime number. Input: Your two codes should generate arrays of random numbers as test inputs in the following ranges: Test input 1: Array size [10³] with random numbers in the range [0-10³] Test input 2: Array size [10⁶] with random numbers in the range (0-10⁹] Test input 3: Array size [10⁹] with random numbers in the range [0-10⁹] Output: Your code should print the output to a file. Deliverables: You should submit the following: 1. .py file that includes the new algorithm code. 2. .py file that includes the regular Quick Sort algorithm code. 3. 6 sample output files (All 3 input cases should be included for both algorithms). 4. Complexities and performance of both codes should be explained in a separate word file.
Madhur L.
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