project_euler_82.rb

# Path sum: three ways
# Problem 82
# NOTE: This problem is a more challenging version of Problem 81.
#
# The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, and right, is indicated in red and bold; the sum is equal to 994.
#
# 131 673 234 103  18
# 201  96 342 965 150
# 630 803 756 422 111
# 537 699 497 121 956
# 805 732 524  37 331
#
# Find the minimal path sum, in matrix.txt (right click and "Save Link/Target As..."), a 31K text file containing a 80 by 80 matrix, from the left column to the right column.

require 'singleton'

class MatrixAnalyzer
  include Singleton
  attr_accessor :content
  attr_reader :d, :h

  def set_d
    if @d.nil?
      (0...content.size).each do |i|
        (0...content.size).each do |j|
          @d = content[i][j] if @d.nil? || @d > content[i][j]
        end
      end
    end
    @d
  end

  # Heuristic matrix(based on Manhattan distance)
  def set_h
    if @h.nil?
      @h = []
      (0...content.size).each do |i|
        @h[i] ||= []
        (0...content.size).each do |j|
          dx = 0
          dy = (j - content.size + 1).abs
          h[i][j] = d * (dx + dy)
        end
      end
    end
    @h
  end
end

class Node
  attr_reader :i, :j, :matrix, :prev, :g, :f

  def initialize(i, j, prev_node = nil)
    @matrix = MatrixAnalyzer.instance

    @i, @j = i, j
    @prev = prev

    set_g
    set_f
  end

  def prev=(prev)
    @prev = prev

    set_g
    set_f
  end

  # f = g + h
  def set_f
    @f = g.to_i + matrix.h[i][j]
  end

  def set_g
    @g =
      if prev.nil?
        matrix.content[i][j]
      else
        prev.g + matrix.content[i][j]
      end
  end

  def print_trace(sum = 0)
    # puts "i[#{ self.i }][#{ self.j }], val=#{ matrix.content[self.i][self.j] }" \
    #   " g=#{ self.g } f=#{ self.f }"
    if prev.nil?
      puts "sum = #{ sum + matrix.content[self.i][self.j] }"
      return
    end
    prev.print_trace(sum + matrix.content[self.i][self.j])
  end
end

class AStar
  def find_path(matrix, start, goal)
    open_nodes = start

    until open_nodes.empty?
      current = open_nodes.min_by { |node| node.f }
      goal.each do |goal_node|
        if current.i == goal_node[0] && current.j == goal_node[1]
          return current
        end
      end

      open_nodes -= [current]
      closed_nodes << current

      # go right, top or bottom
      neighbors = []
      if current.i - 1 >= 0 && closed_nodes_exclude?(current.i - 1, current.j)
        neighbors << Node.new(current.i - 1, current.j)
      end

      if matrix[current.i][current.j + 1] && closed_nodes_exclude?(current.i, current.j + 1)
        neighbors << Node.new(current.i, current.j + 1)
      end

      if matrix[current.i + 1] && closed_nodes_exclude?(current.i + 1, current.j)
        neighbors << Node.new(current.i + 1, current.j)
      end

      neighbors.each do |neighbor|
        neighbor.prev = current
        if open_nodes.detect { |node| node.i == neighbor.i && node.j == neighbor.j }.nil?
          open_nodes << neighbor
        end
      end
    end
    puts 'Unable to find path'
  end

  def closed_nodes_exclude?(i, j)
    closed_nodes.detect { |node| node.i == i && node.j == j }.nil?
  end

  def closed_nodes
    @closed_nodes ||= []
  end
end

# input = [
#   [131, 673, 234, 103,  18],
#   [201,  96, 342, 965, 150],
#   [630, 803, 746, 422, 111],
#   [537, 699, 497, 121, 956],
#   [805, 732, 524,  37, 331],
# ]

file  = File.read('project_euler_82_matrix.txt')
input = file.split("\n").map { |row| row.split(',').map(&:to_i) }

m = MatrixAnalyzer.instance
m.content = input
m.set_d
m.set_h

start_nodes = (0...input.size).inject([]) { |memo, i| memo << Node.new(i, 0) }
goal_nodes  = (0...input.size).inject([]) { |memo, i| memo << [i, input.size - 1] }

klass = AStar.new
klass.find_path(m.content, start_nodes, goal_nodes).print_trace