project_euler_83.rb

# Path sum: four ways
# Problem 83
# NOTE: This problem is a significantly more challenging version of Problem 81.
#
# In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by moving left, right, up, and down, is indicated in bold red and is equal to 2297.
#
# 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 top left to the bottom right by moving left, right, up, and down.

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 = (i - content.size + 1).abs
          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 = [Node.new(start[0], start[1])]

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

      # puts
      # (0...matrix.size).each do |i|
      #   (0...matrix.size).each do |j|
      #     if closed_nodes.detect { |node| i == node.i && j == node.j }
      #       print "x"
      #     else
      #       print "-"
      #     end
      #   end
      #   puts
      # end

      open_nodes -= [current]
      closed_nodes << current

      # go left, 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 current.j - 1 >= 0 && closed_nodes_exclude?(current.i, current.j - 1)
        neighbors << Node.new(current.i, current.j - 1)
      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_83_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

klass = AStar.new
klass.find_path(m.content, [0, 0], [input.size - 1, input.size - 1]).print_trace