Computers and Technology, 23.08.2021 16:30 luffybunny
Consider an array of distinct positive integers where the elements are sorted in ascending order. We want to find all the subsequences of the array consisting of exactly m elements. For example, given array a = [1, 2, 3, 4), the subsequences consisting of m = 3 elements are [1, 2, 3). [1, 2, 4), (1, 3, 4), and [2, 3, 4). Once we have all of the m-element subsequences, we find the value of globalMaximum using the following pseudocode: globalMaximum = 0 for each subsequence, s, consisting of m elements { currentMinimum 1018 for each (x, y) pair of elements in subsequence si absoluteDifference = abs(x - y) if absoluteDifference < currentMinimum currentMinimum = absoluteDifference } } if currentMinimum > globalMaximum { globalMaximum = currentMinimum } } For example, given the array a = [2,3,5,9) and a length m = 3, first find all subsequences of length m. [2,3,5) [2,3,9) [2,5,9] [3,5,9] Debugging output from the pseudocode is: globalMaximum: 0 Subsequence: [2, 3, 5] currentMinimum: 1000000000000000000 x: 3 y: 2 abs(x-y): 1 currentMinimum: 1 x: 5 y: 2 abs(x-y): 3 currentMinimum: 1 x: 5 y: 3 abs(x-y): 2 currentMinimum: 1 globalMaximum: max(globalMaximum, currentMinimum) max(1, 0) = 1 Subsequence: [2, 3, 9] currentMinimum: 1000000000000000000 X: 3 y: 2 abs(x-y): 1 currentMinimum: 1 X: 9 y: 2 abs(x-y): 7 currentMinimum: 1 X: 9 y: 3 abs(x-y): 6 currentMinimum: 1 globalMaximum: max(1, 1) = 1 Subsequence: [2, 5, 9] currentMinimum: 1000000000000000000 X: 5 y: 2 abs(x-y): 3 currentMinimum: 3 X: 9 y: 2 abs(x-y): 7 currentMinimum: 3 2. After the iteration on subsequence {1, 2, 4), the minimum difference between adjacent elements is 1. The value of globalMaximum is 1. 3. After the iteration on subsequence (1, 3, 4), the minimum difference between adjacent elements is 1. The value of globalMaximum is 1. 4. After the iteration on subsequence (2, 3, 4), the minimum difference between adjacent elements is 1. The value of globalMaximum is 1. Thus, the function returns 1 as the answer. Sample Case 1 Sample Input 1 STDIN Function 4 β arr[] size n = 4 [1, 2, 3, 4] 1 arr = 2 3 4 2 m = 2 Sample Output 1 3 Explanation 1 The subsequences of array arr = [1, 2, 3, 4] consisting of m = 2 elements are {1, 2}, {1,3}, {1, 4), (2, 3), (2, 4), and {3,4}. 1. After the iteration on the subsequence {1, 2}, the value of globalMaximum is 1. Explanation 1 The subsequences of array arr = [1, 2, 3, 4) consisting of m = 2 elements are {1, 2}, {1,3}, {1,4} {2, 3), (2, 4), and (3, 4). 1. After the iteration on the subsequence {1, 2}, the value of globalMaximum is 1. 2. After the iteration on the subsequence {1, 3}, the value of globalMaximum is 2. 3. After the iteration on the subsequence {1,4}, the value of globalMaximum is 3. 4. After the iteration on the subsequence (2, 3), the value of globalMaximum is 3. 5. After the iteration on the subsequence (2,4}, the value of globalMaximum is 3. 6. After the iteration on the subsequence (3, 4), the value of globalMaximum is 3. Thus, the function returns 3 as the answer. Sample Case 2 Sample Input 2 STDIN Function 5 1 arr[] size n = 5 arr = [1, 2, 4, 5, 8] 4 5 8 3 > m = 3 Sample Output 2 3 Explanation 2 The subsequences of array arr = [1, 2, 4, 5, 8] consisting of m = 3 elements are {1, 2, 4}, {1, 2, 5}, {1, 2,8}, {1, 4, 5}, {1, 4, 8}, {1, 5, 8}, {2, 4, 5), {2, 4, 8), (2, 5, 8), and {4, 5, 8). Language Java 8 Autocomplete Ready O 15 1 > import java. io.*; ** 14 class Result { 16 17 /* 18 * Complete the 'findMaximum' function below. 19 20 * The function is expected to return an INTEGER. 21 * The function accepts following parameters: 22 1. INTEGER_ARRAY arr 23 2. INTEGER m 24 */ * * * 25 26 27 public static int findMaximum(List arr, int m) { // write your code here 28 29 } 30 31 } 32 33 > public class Solution { ***
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