#127

Love Triangle

 

Everyone loves triangles, and it's easy to understand why—they're so wonderfully symmetric (except scalenes, they suck).

Your passion for triangles has led you to become a miner (and part-time Clojure programmer) where you work all day to chip out isosceles-shaped minerals from rocks gathered in a nearby open-pit mine. There are too many rocks coming from the mine to harvest them all so you've been tasked with writing a program to analyze the mineral patterns of each rock, and determine which rocks have the biggest minerals.

Someone has already written a computer-vision system for the mine. It images each rock as it comes into the processing centre and creates a cross-sectional bitmap of mineral (1) and rock (0) concentrations for each one.

You must now create a function which accepts a collection of integers, each integer when read in base-2 gives the bit-representation of the rock (again, 1s are mineral and 0s are worthless scalene-like rock). You must return the cross-sectional area of the largest harvestable mineral from the input rock, as follows:

• The minerals only have smooth faces when sheared vertically or horizontally from the rock's cross-section
• The mine is only concerned with harvesting isosceles triangles (such that one or two sides can be sheared)
• If only one face of the mineral is sheared, its opposing vertex must be a point (ie. the smooth face must be of odd length), and its two equal-length sides must intersect the shear face at 45° (ie. those sides must cut even-diagonally)
• The harvested mineral may not contain any traces of rock
• The mineral may lie in any orientation in the plane
• Area should be calculated as the sum of 1s that comprise the mineral
• Minerals must have a minimum of three measures of area to be harvested
• If no minerals can be harvested from the rock, your function should return nil

	(= 10 (__ [15 15 15 15 15])) ; 1111 1111 ; 1111 *111 ; 1111 -> **11 ; 1111 ***1 ; 1111 ****
	(= 15 (__ [1 3 7 15 31])) ; 00001 0000* ; 00011 000** ; 00111 -> 00*** ; 01111 0**** ; 11111 *****
	(= 3 (__ [3 3])) ; 11 *1 ; 11 -> **
	(= 4 (__ [7 3])) ; 111 *** ; 011 -> 0*1
	(= 6 (__ [17 22 6 14 22])) ; 10001 10001 ; 10110 101*0 ; 00110 -> 00**0 ; 01110 0***0 ; 10110 10110
	(= 9 (__ [18 7 14 14 6 3])) ; 10010 10010 ; 00111 001*0 ; 01110 01**0 ; 01110 -> 0***0 ; 00110 00**0 ; 00011 000*1
	(= nil (__ [21 10 21 10])) ; 10101 10101 ; 01010 01010 ; 10101 -> 10101 ; 01010 01010
	(= nil (__ [0 31 0 31 0])) ; 00000 00000 ; 11111 11111 ; 00000 -> 00000 ; 11111 11111 ; 00000 00000