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Showing posts from November, 2009

Project Euler problem 220 - Heighway Dragon

This document goes through a Java solution for Project Euler problem 220 . If you want to achieve the pleasure of solving the unfamiliarity and you don't have a solution yet, PLEASE STOP READING UNTIL YOU FIND A SOLUTION. Problem 220 is to tell the coordinate after a given large number of steps in a Dragon Curve . The first thing came to my mind, is to DFS traverse a 50 level tree by 10^12 steps, during which it keeps track of a direction and a coordinate. Roughly estimate, this solution takes a 50 level recursion, which isn't horrible, and 10^12 switch/case calls. Written by a lazy and irresponsible Java engineer, this solution vaguely looks like: Traveler traveler = new Traveler(new Coordinate(0, 0), Direction.UP); void main() { try { traverse("Fa", 0); } catch (TerminationSignal signal) { print signal; } } void traverse(String plan, int level) { foreach(char c:plan) { switch(c) { case 'F': traveler.stepForward(); break; ca