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Pizza Delivery

Part 1

Maria is delivering pizzas to an infinite two-dimensional grid of houses. She begins by delivering a pizza to the house at her starting location; a dispatcher then calls via radio and tells her where to move next. Moves are always exactly one house to the north (^), south (v), east (>), or west (<). After each move, Maria delivers a pizza to the house at her new location. The dispatcher has been a little spacey lately, so Maria sometimes ends up delivering more than one pizza to the same house.

Here are some examples:

  • > delivers pizzas to two houses: one to the house at the starting location, and one to the house directly east of the starting location.

  • ^>v< delivers pizzas to four houses in a square; the house at the starting/ending location ends up with two pizzas.

  • ^v^v^v^v^v delivers a bunch of pizzas to some very lucky people at only two houses.

Given the string of dispatcher inputs attached to this gist, how many houses receive at least one pizza?

Part 2

The next day, to speed up the process, Maria rents a pizza-delivering goat named Clovis. Maria and Clovis begin at the same starting location, and they both deliver a pizza to this starting house. Maria and Clovis then take turns moving based on the dispatcher's instructions.

Here are some examples:

  • ^v now delivers pizzas to three houses; Maria goes north and Clovis goes south.

  • ^>v< now delivers pizzas to three houses; Maria and Clovis both end up back where they started.

  • ^v^v^v^v^v now delivers pizzas to 11 houses; Maria treks north and Clovis treks south.

Given the same string of dispatcher inputs as in Part One, how many houses receive at least one pizza?

Guidelines for your solution

Please provide a solution to Part 1 and Part 2 in JavaScript (any flavor is acceptable) or CoffeeScript.

By design, this is a fairly simple exercise. We want to get a quick baseline on your coding proficiency, and we'll use your solution as the basis for discussion in a technical interview.

We'd like to see code that you consider production-quality. The best solutions will be elegant, as well as correct. Feel free to pull in any libraries you like. Extra points for a functional style.