is an L-shaped tile formed by 1-by-1 adjacent squares. Given an 2^n × 2^n board (n ≥ 1) with one missing square, it is always possible to cover the board by triominos without overlapping tiles (you may assume this fact, or consider your solution to this question as a constructive proof) Given an 2^n×2^n board with one missing square, design a divide-and-conquer algorithm to determine how to cover the board with triominos

The travel time function of an algorithm has the form: f(n) = 3n^2 + 4n + 8  Prove that Big Oh is n^2 which is denoted by f(n) = O(n^2);

Suppose a 2D bounding box is given by (≤ is "less than or equal to"): -1 ≤ x ≤ 1-10 ≤ y ≤ 10 Compute the new Bounding Box for the transformation given by the following matrix: (see section 9.4.4) 0.866    -0.5  0.5    0.866 Now enter the xmax for the new Bounding Box (round it to 3 decimal places, if needed).

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.

Problem 2. Suppose we have an array A[1 : n] which consists of numbers {1,...,n} written in some arbitrary order (this means that A is a permutation of the set {1,...,n}). Our goal in this problem is to design a very fast randomized algorithm that can find an index i in this array such that A[i] mod 8 € {1,2}, i.e., the reminder of dividing A[i] by 8 is either 1 or 2. For simplicity, in the following, we assume that n itself is a multiple of 8 and is at least 8 (so a correct answer always exist). For instance, if n = 8 and the array is A = [8,7, 2,5, 4, 6,3, 1], we want to output either of indices 3 or 8. (a) Suppose we sample an index i from {1,...,n} uniformly at random. What is the probability that i is a correct answer, i.e., A[i] mod 8 E {1,2}? (b) Suppose we sample m indices from {1,...,n} uniformly at random and with repetition. What is the probability that none of these indices is a correct answer? Now, consider the following simple algorithm for this problem: Find-Index-1(A[1:…

PLEASE USE PYTHONGiven a jungle matrix NxM:jungle = [ [1, 0, 0, 0], [1, 1, 0, 1], [0, 1, 0, 0], [1, 1, 1, 1,]]Where 0 means the block is dead end and 1 means the block can be used in the path fromsource to destination.Task:Starting at position (0, 0), the goal is to reach position (N-1, M-1).Your program needs to build and output the solution matrix – a 4x4 matrix with 1’s inpositions used to get from the starting position (0,0) to the ending position (N-1,M-1)with the following constraints:You can only move one space at a timeYou can only in two directions: forward and down.You can only pass thru spaces on the jungle matrix marked ‘1’If you cannot reach the ending position – print a message that you’re trapped in thejungleAlgorithm:If destination is reachedprint the solution matrixElseMark current cell in the solution matrixMove forward horizontally and recursively check if this leads to a solution If there is no solution, move down and recursively check if this leads to a solution If…