You have to sort a sequence of N elements. The N elements have N/K subsequences of...
Let S be a sequence of n distinct integers stored in an array as array elements S[1], S[2], · · · , S[n]. Use the technique of dynamic programming to find the length of a longest ascending subsequence of entries in S. For example, if the entries of S are 11, 17, 5, 8, 6, 4, 7, 12, 3, then one longest ascending subsequence is 5, 6, 7, 12. Specifically: (a) define a proper function and find the recurrence for...
You are given a sequence of integer values. Describe an algorithm requiring no worse than O(n2) time for finding the length of a longest rising subsequence in that array. A subsequence is rising when each element is less than or equal to the one following it. For example, in the sequence [23, -15, 10, 25, 7, 32], the length of a longest rising sequence is 4, found in the subsequence [-15, 10, 25, 32].
Use the following sequence as the list to sort: [ T, H, A, N, K, F, U, L ] You need to display the contents of the list during the execution of the algorithm. a) Sort the list using selection sort. b) Sort the list using heap sort. You do not need to draw the heap diagram unless you find it helpful, but you must still show the contents on the list during execution. c) What is the worst-case runtime...
6) Assume that we are using quick sort algorithm to sort the following elements in the array 26, 15,30,11,8,17 22, 40, 4, 10. Use the first element in the array as pivot. (20 pts.) 1- How total iterations it would take to complete the sorting process? 2- Simulate the entire sorting process. (If you need additional space, complete it at the other side of the paper) public static void quick_sort(intl] a, int left, int right) if (left < right) (...
9. [10 points) Consider the following algorithm: procedure Algorithm(n: positive integer; ddd: distinet integers) for k:=1 to n-1 for 1-1 to n-k print(k, I, di,da...-1,dn) if ds dti then interchange dy and d (a) Assume that this algorithm receives as input the integer n 6 and the input sequence 하하하하하하, Miss ^-ruteae rehen i12|3141516 Fill out the table below: ds ds (b) Assume that the algorithm receives the same input values as in part a). Once the algorithm finishes, what...
(20 points) You are given an array A of distinct integers of size n. The sequence A[1], A[2], ..., A[n] is unimodal if for some index k between 1 and n the values increase up to position k and then decrease the reminder of the way until position n. (example 1, 4, 5, 7, 9, 10, 13, 14, 8, 6, 4, 3, 2 where the values increase until 14 and then decrease until 1). (a) Propose a recursive algorithm to...
1. Show the steps in order to sort {11,5,6,3,8,1,9,2} using Mergesort algorithm. 2. Show the element sequences of running Shellsort on the input {15,2,8,1,10,7,4,3,9,11,12,6} at the increments {7, 3, 1}, respectively. 3. Show the steps in details of sorting {15, 2, 8, 1, 10, 7, 4, 3, 9, 11, 12, 6} using quicksort with median-of-three partitioning and a cutoff 3 (if the elements are less than 3, using insertion sort).
An m×n array A of real numbers is a Monge array if for all i,j,k, and l such that 1≤i<k≤m and 1≤j<l≤n , we have >A[i,j]+a[k,l]≤A[i,l]+A[k,j]> In other words, whenever we pick two rows and two columns of a Monge array and consider the four elements at the intersections of the rows and columns, the sum of the upper-left and lower-right elements is less than or equal to the sum of the lower-left and upper-right elements. For example, the following...
17. Consider the following algorithm: procedure Algorithm(n: positive integer; di,d2.. ,dn: distinct integers) for 1 to n-1 for 1 to n-k if ddi+ then interchange di and di+ print(k, I, d,ddn-1, dn) (a) |3 points Assume that this algorithm receives as input the integer-6 and the corresponding input sequence 41 36 27 31 17 20 Fill out the table below ds (b) 1 point Assume that the algorithm receives the same input values as in part a). Once the algo-...
4. (10 points) Suppose we are given a sequence S of n elements, each of which is colored red or blue. Assuming S is represented by an array, give a linear-time in-place algorithm for ordering S so that all the blue elements are listed before all the red elements. What is the running time of your method?