Shine Bright like a Sharknado

Prelude

After your amazing performance in your first week at Buzzfeed, they’ve moved you into something resembling an office- well it’s technically a bathroom, but at least there’s working lighting.

“We have such an exciting new opportunity for you!” your boss exclaims. She’s flushing with enthusiasm, echoing the toilets behind your small desk. But your cynicism fades in the face of her excitement- you can’t help but sit up straight- feeling tall- ready to finally make a meaningful contribution to the world through the art of programming.

“We’re desiging a online minigame to accompany the release of Sharknado 5, and we need you to set up the data types and functions. It’s such a fabulous opportunity! Oh, think of the children our work will inspire- we’ll create a new generation of passionate weather forecasters, waiting for their glimpse of a real sharknado!”

Your mouth begins to open in retaliation, but it’s too late. The boss disappears in a flash, leaving only a sticky note behind her… you almost fall off your stool in a rush to grab it, terrified it might make contact with the moist floor…

Since we are looking at a plane inside a sharknado, we will need to record the direction that the plane is facing. The directions that the plane can face are North, East, South and West. We will also need the location of the plane, this can be done by looking at location of the plane on a 2D grid (ignore altitude). We will keep track of this information through a record type called Plane.

  1. Define the data type Plane that includes all of the above specifications.

  2. The plane is caught in a sharknado! Write a function called changeDir which changes the direction of the plane by a quarter of a full rotation. For example: if the plane was originally facing North, changeDir would change the direction of the plane to East (since sharknadoes in the southern hemisphere spin clockwise).

  3. If the plane stays in the sharknado for a long time, then it will change its direction multiple times. Write a recursive function called changeDir_n that changes the direction of the plane n times, each time the direction changes by a quarter of a full circle.

The sharknado moves as time passes, causing the plane to also move with it. The movement of the sharkado also has a direction, North, East, South and West. Note that this is not the direction that the plane is facing! Assume that every time the sharknado moves it only moves in step sizes of 1.

  1. Write a function movePlane that will change the coordinate of the plane by 1 grid point, given an input direction of the sharknado. For example: movePlane called with the input North on a plane at location (1,0) will move the plane to location (1,1).

  2. Now write a function movePlane_n that will recursively change the direction and coordinate of the plane n times.

Extension: Further recursion questions

Write a recursive function which:

  1. Multiplies two numbers, without using the multiplies * function. e.g. multiply (4,5) = 20
  2. Adds up all the numbers before it down to 0. e.g. adder 5 = 4 + 3 + 2 + 1 + 0 = 10
  3. Finds the number of digits in a positive Integer e.g. digits 100 = 3
  4. Finds if a number is even or odd e.g. 5 = "odd", 6 = "even"
  5. Decides if a number is prime (formal definition: divisible by only 1 and itself)