Facebook Careers Puzzle—gattaca

This is a solution to a Facebook Job Puzzle.

Gattaca is a straightforward interval scheduling problem disguised as… I don’t know, some kind of maximum overlap problem. Anyways, I used a dynamic programming approach with a binary search to make it a little faster.

The following solution in Ruby passed the Facebook puzzle robot:

(gattaca.rb) download
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#!/usr/bin/env ruby
# DNA?
# Kanwei Li, 2009

# Make sure input file exists and read from it
filename = ARGV[0]
unless filename && File.exist?(filename)
  puts "error: must specify a valid input file"
  exit
end
input = File.open(filename)

dna_size = input.gets.to_i
input.pos += dna_size + (dna_size / 80) + (dna_size % 80 == 0 ? 0 : 1)

dots = []

input.gets.to_i.times { |idx|
  dots << input.gets.split(/\W+/).collect { |i| i.to_i }
}

s_by_finish = dots.sort_by { |b| b[1] }

p_i = {}

def search(container, start, high)
  # puts "Searching end < #{start}"
  low = 0
  best = nil
  while low <= high
    mid = (low + high) / 2
    finish = container[mid][1] # finish
    if finish >= start
      # went too far, go down
      high = mid - 1
    else
      # good so far, try going higher
      # puts "#{finish} (#{mid}) < #{start}"
      best = mid
      low = mid + 1
    end
  end
  # puts "Best: #{best}"
  return best
end

s_by_finish.each_with_index { |s, i|
  # puts i if i % 10000 == 0
  p = search(s_by_finish, s[0], i-1)
  p_i[i] = p if p
}

def max(a,b)
  return (a > b ? a : b)
end

mem = [0]
s_by_finish.each_with_index { |t, i|
  pi = p_i[i] ? mem[ p_i[i] ] : 0
  mem[i] = max(t[2] + pi, mem[i-1])
}
puts mem[-1]
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