Problem 3. Consider the following recurrence, defined for n a power of 4 (for the time of some algorithm): T(n) = 3 if n = 1 2T(n/4) + 4n + 1 otherwise (a) Calculate T(16) by hand. Show your work. (b) Use the tree method to solve the recurrence exactly, assuming n is a power of 4. (c) Use the formula to calculate T(1). Show your work. (d) Use the formula to calculate T(4). Show your work. (e) Use the formula to calculate T(16). Show your work. (f) Use Mathematical Induction to prove that your formula is correct in general.

You will be given two character arrays of the same size, one will contain a number of ships. ships will move around the character array based on which way they are facing and the route they are on. routes are given in the other array. the route consists of '-' and '|' for straight paths, '\' and '/' for curves, and '+' for intersections. there are ships on these routes. ships always face a direction, '^' for up, '> ' for right, 'v' for down, and '< ' for left. any time the ships hit a '\' or a '/' it will turn as you would expect a ship to turn (e.g. a '^' that moves into a '/' will turn right). at an intersection, ships will always continue straight through. all ships move at the same speed, ships take turns moving and all ships move during one 'tick'. the one in the most top left goes first, followed by those to its right, then the ones in the next row. it iterates along the rows and then down the columns. each ship moves one space on its turn moving along the route. your function needs to return the position of the first collision between two ships and the number of ticks before the crash occurred.

By refraining from constructing a building until they are certain that it will not cause harm to the environment, an organization is adhering to the

Curriculum exam to process a resident's payment, you must click on onesite payments home page. from the a. reports b. my settings o c.transactions o d. rent tab