I love the game Roller Coaster Tycoon: it is a simulation game where you have to

Question

I love the game Roller Coaster Tycoon: it is a simulation game where you have to build an amusement park to achieve some goal, like have at least 10 roller coasters constructed, or have a monthly income of tickets at least a certain value. An image of gameplay is below. The game is composed of a grid (say, n times m in size), and a single path tile can be placed on each cell of the grid. Adjacent cells automatically connect. Also, a path can, within a single cell, increase in altitude by 1. Paths can only cross each other iff their heights differ by at least 2. Suppose that we are midway through building a park, and we have run low on cash! We cannot delete any of the existing rides/paths to get some more money. Moreover, the park we are building is very large, and our pathways were very sloppy: the guests cannot reach the roller coasters and other rides! Guests are not allowed to walk on surfaces that are not pathways. However, we were lucky in that the paths are almost connected. We want to determine if we can connect as few paths as possible (say, at most k of them) so that there is a path from the entrance to the roller coasters. Formally, let the language L = {{R, k): R is a Roller Coaster Tycoon game in progress, and without deleting any objects from R, there can be a path constructed from the entrance to the roller coasters in R with at most k placements of path tiles}. Show that L is NP-complete.

Explanation / Answer

ANSWER::

RollerCoaster Tycoon® Classic™ is a new RCT experience, combining the best features from two of the most successful and beloved RCT games in the series’ history – RollerCoaster Tycoon® and RollerCoaster Tycoon® 2. Create and run amazing parks complete with the most outrageous rides imaginable. RCT Classic includes a mixture of authentic playability, depth of gameplay and unique graphical style of Chris Sawyer’s original best-selling RollerCoaster Tycoon® PC Games, now enhanced for handheld devices. Packed with content, players can enjoy designing and building roller coasters and rides, landscaping parks and managing the staff and finances to keep their guests happy and the money flowing in. Can you become the next RollerCoaster Tycoon?

FEATURES

SYSTEM REQUIREMENTS

iOS – Requires iOS 7.0 or later. Compatible with iPhone, iPad, and iPod touch.

Android – Minimum OS 4.0.3, resolution 960×640.

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