There’s a length n (n ≥ 3) array and we’d like to fill in each element of the array with an integer. The integers should be in {1, 2, . . . , k} and any 3 adjacency entries cannot have the same number. Given n and k , design a polynomial time algorithm to compute the number of ways to fill this array. Please also justify the correctness and the time complexity of your answers.

I am just needing pseudo code, and an explanation for this. I do not need any actual code. Thank you. Assume that algorithm X, which is an algorithm that can iterate through an array A, has been solved. Let Y be some new algorithm that can find the minimum element in the array. Use reduction to prove that Y is possible.

I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(n^2).

Get the time complexity function from the pseudocode for the addition of the 2 matrices below, and prove whether the big-oh is O(n^2) so that it satisfies the rule f(n) <= c g(n) for(i = 0 ; i < rows; i++){for(j = 0; j < columns; j++)matrix2[i][j] = matrix1[i][j] + matrix2[i][j];} for(i = 0 ; i < rows; i++){for(j = 0; j < columns; j++){printf("%d ", matrix2[i][j]);}printf("\n");}

In Python: Let n be a (large) positive integer of your choice. We want to know which of the two Quicksort algorithms methods (he Lomuto method and the Hoare method) is superior when sorting arrays containing n elements. To answer this question, you will run Quicksort on 10000 random permutations of [1,2,3, . . . , n], on each of your two Quicksort algorithms.

Given an unsorted array of integers, write a function in Python to find the length of the longest increasing subsequence (LIS) in the array. For example, given the array [10, 9, 2, 5, 3, 7, 101, 18], the LIS is [2, 3, 7, 101], which has a length of 4. Your solution should have a time complexity of O(n log n), where n is the length of the input array. Here's some code to get you started: def longest increasing_subsequence(arr): # TODO: implement function pass # example usage arr = [10, 9, 2, 5, 3, 7, 101, 18] print(longest_increasing_subsequence(arr)) # should print 4

What is the best case scenario? What is the exact number of operations for the best case scenario in terms of n and m? What is the big-oh for the best case scenario? What is the worst case scenario? What is the exact number of operations for the worst case scenario in terms of n and m? What is the big-oh for the worst case scenario? Consider the following algorithm tha finds a row where every entry is x in a 2-D array. Assume that (a) the array has n rows and m columns, and that (b) the comparison on line 3 counts towards the running time.