Day 13 - Puzzle 2

lib/solutions/day_13.rb

@@ -1,51 +1,72 @@
 class Day13
   def part_one(input)
+    run(input, 100)
+  end
+
+  def part_two(input)
+    run(input, nil)
+  end
+
+  def run(input, max_presses = nil)
     input.split(/(?:^\r?\n)+/).map do |block|
       lines = block.split("\n")
       a_match = lines[0].match(/^Button A:\s+X\+(\d+),\s+Y\+(\d+)$/)
       b_match = lines[1].match(/^Button B:\s+X\+(\d+),\s+Y\+(\d+)$/)
       prize_match = lines[2].match(/^Prize:\s+X=(\d+),\s+Y=(\d+)$/)
 
+      prize_x = prize_match[1].to_i
+      prize_y = prize_match[2].to_i
+
+      if max_presses.nil?
+        prize_x += 10_000_000_000_000
+        prize_y += 10_000_000_000_000
+      end
+
       ClawMachine.new(
         a_match[1].to_i,
         a_match[2].to_i,
         b_match[1].to_i,
         b_match[2].to_i,
-        prize_match[1].to_i,
-        prize_match[2].to_i
+        prize_x,
+        prize_y,
+        max_presses
       )
     end.map(&:solve!)
        .compact
        .map(&:first)
        .sum
   end
-
-  def part_two(input)
-    0
-  end
 end
 
 class ClawMachine
-  attr_accessor :ax, :ay, :bx, :by, :prize_x, :prize_y
+  attr_accessor :ax, :ay, :bx, :by, :prize_x, :prize_y, :max_presses
 
-  MAX_PRESSES = 100
   COST_A = 3
   COST_B = 1
 
-  def initialize(ax, ay, bx, by, prize_x, prize_y)
+  def initialize(ax, ay, bx, by, prize_x, prize_y, max_presses = nil)
     @ax = ax
     @ay = ay
     @bx = bx
     @by = by
     @prize_x = prize_x
     @prize_y = prize_y
+    @max_presses = max_presses
   end
 
   def solve!
+    if max_presses.nil?
+      advanced_math_solution!
+    else
+      brute_force!
+    end
+  end
+
+  def brute_force!
     cheapest = nil
 
-    (0..MAX_PRESSES).each do |a|
-      (0..MAX_PRESSES).each do |b|
+    (0..max_presses).each do |a|
+      (0..max_presses).each do |b|
         # Check if this combination hits the prize location
         if a * ax + b * bx == prize_x && a * ay + b * by == prize_y
           cost = COST_A * a + COST_B * b
@@ -56,4 +77,34 @@ def solve!
 
     cheapest
   end
+
+  def advanced_math_solution!
+    # SEe https://en.wikipedia.org/wiki/Cramer%27s_rule
+    # Applications -> Small systems
+
+    # WE need to solve
+    # A.ax + B.bx = prize_x
+    # A.ay + B.by = prize_y
+
+    # Enter the matrix
+    # [ ax bx ] [ A ] = [ prize_x]
+    # [ ay by ] [ B ] = [ prize_y]
+
+    # compute Determinatn
+    det = ax * by - ay * bx
+    return nil if det == 0
+
+    # Check if there is an int solution
+    _a = (prize_x * by - prize_y * bx)
+    _b = (ax * prize_y - ay * prize_x)
+    return nil unless _a % det == 0 && _b % det == 0
+
+    # Verify we have positive solutions
+    push_a = _a / det
+    push_b = _b / det
+    return nil if push_a < 0 || push_b < 0
+
+    # Done ;-)
+    [COST_A * push_a + COST_B * push_b, push_a, push_b]
+  end
 end

spec/solutions/day_13_spec.rb

@@ -6,22 +6,22 @@
 
   describe '#part_one' do
     it 'calculates machine 1' do
-      m = ClawMachine.new(94, 34, 22, 67, 8400, 5400)
+      m = ClawMachine.new(94, 34, 22, 67, 8400, 5400, 100)
       expect(m.solve!).to eq([280, 80, 40])
     end
 
     it 'calculates machine 2' do
-      m = ClawMachine.new(26, 66, 67, 21, 12_748, 12_176)
+      m = ClawMachine.new(26, 66, 67, 21, 12_748, 12_176, 100)
       expect(m.solve!).to be_nil
     end
 
     it 'calculates machine 3' do
-      m = ClawMachine.new(17, 86, 84, 37, 7870, 6450)
+      m = ClawMachine.new(17, 86, 84, 37, 7870, 6450, 100)
       expect(m.solve!).to eq([200, 38, 86])
     end
 
     it 'calculates machine 2' do
-      m = ClawMachine.new(69, 23, 27, 71, 18_641, 10_279)
+      m = ClawMachine.new(69, 23, 27, 71, 18_641, 10_279, 100)
       expect(m.solve!).to be_nil
     end
 
@@ -31,8 +31,24 @@
   end
 
   describe '#part_two' do
-    it 'calculates the correct solutions for part two' do
-      expect(subject.part_two(input)).to eq(0)
+    it 'calculates machine 1' do
+      m = ClawMachine.new(94, 34, 22, 67, 10_000_000_008_400, 10_000_000_005_400)
+      expect(m.solve!).to be_nil
+    end
+
+    it 'calculates machine 2' do
+      m = ClawMachine.new(26, 66, 67, 21, 10_000_000_012_748, 10_000_000_012_176)
+      expect(m.solve!).not_to be_nil
+    end
+
+    it 'calculates machine 3' do
+      m = ClawMachine.new(17, 86, 84, 37, 10_000_000_007_870, 10_000_000_006_450)
+      expect(m.solve!).to be_nil
+    end
+
+    it 'calculates machine 2' do
+      m = ClawMachine.new(69, 23, 27, 71, 10_000_000_018_641, 10_000_000_010_279)
+      expect(m.solve!).not_to be_nil
     end
   end
 end