Day 13
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day13.py
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day13.py
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#!/usr/bin/env python3
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from dataclasses import dataclass
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from typing import Tuple
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import re
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from ortools.linear_solver import pywraplp
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from ortools.math_opt.python import mathopt
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@dataclass
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class Claw:
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button_a: Tuple[int, int]
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button_b: Tuple[int, int]
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prize: Tuple[int, int]
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claws = []
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with open("day13") as f:
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l = f.readline()
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while l:
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if l == '\n':
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l = f.readline()
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continue
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button_a = re.match(r"Button A: X\+([0-9]+), Y\+([0-9]+).*", l).groups()
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button_b = re.match(r"Button B: X\+([0-9]+), Y\+([0-9]+).*", f.readline()).groups()
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prize = re.match(r"Prize: X=([0-9]+), Y=([0-9]+).*", f.readline()).groups()
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c = Claw(
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button_a=(int(button_a[0]), int(button_a[1])),
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button_b=(int(button_b[0]), int(button_b[1])),
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prize=(int(prize[0]), int(prize[1]))
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)
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claws.append(c)
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l = f.readline()
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def part1():
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# (k * b_a.x) + (j * b_b.x) - x = (k * b_a.y) + (j * b_b.y) - y
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# cost = k*3 + j
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def gensol(claw: Claw):
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for k in range(100):
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for j in range(100):
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left = (k*claw.button_a[0]) + (j*claw.button_b[0]) - claw.prize[0]
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right = (k*claw.button_a[1]) + (j*claw.button_b[1]) - claw.prize[1]
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if left == 0 and right == 0:
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yield (k,j)
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def cost(k,j):
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return k*3 + j
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res = 0
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for claw in claws:
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min_cost = 500*3
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for (k,j) in gensol(claw):
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sol_cost = cost(k,j)
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print(f"Found cost for claw {claw}. k={k}, j={j}, cost={sol_cost}")
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if sol_cost < min_cost:
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min_cost = sol_cost
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if min_cost != 500*3:
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res += min_cost
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print(res)
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def part2():
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# UPDATE: In fact all that below works perfectly fine if one understands
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# `add` as normal addition instead of concatenation. But for historical
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# reference:
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#
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# lots of math transformations later...
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#
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# I think this is correct. It works with part1 at least.
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#
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# It does not work with part2. I do think it could be "only" numerical errors
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# due to floating point math. Or this whole math is BS. That's very possible
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# too.
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#
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# - tried high precision math libs, didn't work
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# - tried searching around the proximity of the "exact" solution, didn't work
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# !!!!! THAT'S NOT WHAT IS MEANT WITH ADD !!!!!!!
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#
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# uncomment this to make it fail
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# for claw in claws:
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# prize_x = int("10000000000000" + str(claw.prize[0]))
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# prize_y = int("10000000000000" + str(claw.prize[1]))
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# claw.prize = (prize_x, prize_y)
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for claw in claws:
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prize_x = 10000000000000 + claw.prize[0]
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prize_y = 10000000000000 + claw.prize[1]
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claw.prize = (prize_x, prize_y)
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def gensol(claw: Claw):
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a_x = claw.button_a[0]
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a_y = claw.button_a[1]
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b_x = claw.button_b[0]
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b_y = claw.button_b[1]
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p_x = claw.prize[0]
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p_y = claw.prize[1]
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epsilon = 0.00001
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y = ((a_y*p_x)-(a_x*p_y))/((b_x*a_y)-(a_x*b_y))
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print(f"{y:.200f}")
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x = ((p_x - (y*b_x))/a_x)
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print(f"{x:.200f}")
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if x>0 and abs(y - round(y)) <= epsilon and y>0 and abs(x - round(x)) <= epsilon:
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return (x, y)
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# print(f"y = (({a_y}*{p_x})-({a_x}*{p_y})) / (({b_x}*{a_y})-({a_x}*{b_y})), x = (({p_x} - ({y}*{b_x})) / {a_x})")
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# we found a solution in R but quite likely contains numerical errors
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# search the proximity for an exact match
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# epsilon = 0.0001
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# if x > 0 and y > 0:
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# for i in range(-100,100):
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# for j in range(-100,100):
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# if abs(((x+i) * a_x) + ((y+j) * b_x) - p_x) < epsilon and abs(((x+i) * a_y) + ((y+j) * b_y) - p_y) < epsilon:
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# return (int(x),int(y))
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def cost(k,j):
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return k*3 + j
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res = 0
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for i,claw in enumerate(claws):
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print(f"running claw {i+1} of {len(claws)}")
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sol = gensol(claw)
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if sol:
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k,j = sol
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sol_cost = cost(k,j)
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print(f"Found cost for claw {claw}. k={k}, j={j}, cost={sol_cost}")
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print(f"{claw.prize[0]}={k*claw.button_a[0]+j*claw.button_b[0]}")
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res += sol_cost
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print(res)
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def part2_get_the_bfg():
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sol = 0
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for i, claw in enumerate(claws):
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solver = pywraplp.Solver.CreateSolver("SAT")
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if not solver:
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return
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infinity = solver.infinity()
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x = solver.IntVar(lb=0.0, ub=infinity, name="x")
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y = solver.IntVar(lb=0.0, ub=infinity, name="y")
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solver.Add(x*claw.button_a[0] + y*claw.button_b[0] <= claw.prize[0])
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solver.Add(x*claw.button_a[0] + y*claw.button_b[0] >= claw.prize[0])
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solver.Add(x*claw.button_a[1] + y*claw.button_b[1] <= claw.prize[1])
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solver.Add(x*claw.button_a[1] + y*claw.button_b[1] >= claw.prize[1])
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solver.Minimize(3*x + y)
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status = solver.Solve()
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if status == pywraplp.Solver.OPTIMAL:
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x = x.solution_value()
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y = y.solution_value()
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sol += solver.Objective().Value()
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print(f"Claw {i: >3}: {x=:>20.3f}\t{y=:>20.3f}\t{solver.Objective().Value()=:.2f} [{claw}]")
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else:
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print(f"Claw {i: >3}: no solution")
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print(f"{sol:.5f}")
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def part2_get_the_bfg2():
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sol = 0
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for i, claw in enumerate(claws):
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model = mathopt.Model()
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x = model.add_variable(lb=0.0, name="x")
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y = model.add_variable(lb=0.0, name="y")
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model.add_linear_constraint(x*claw.button_a[0] + y*claw.button_b[0] <= claw.prize[0])
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model.add_linear_constraint(x*claw.button_a[0] + y*claw.button_b[0] >= claw.prize[0])
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model.add_linear_constraint(x*claw.button_a[1] + y*claw.button_b[1] <= claw.prize[1])
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model.add_linear_constraint(x*claw.button_a[1] + y*claw.button_b[1] >= claw.prize[1])
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model.minimize(3*x + y)
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result = mathopt.solve(model, mathopt.SolverType.GLOP)
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if result.termination.reason != mathopt.TerminationReason.OPTIMAL:
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print(f"model failed to solve: {result.termination}")
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else:
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print("MathOpt solve succeeded")
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print("Objective value:", result.objective_value())
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print("x:", result.variable_values()[x])
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print("y:", result.variable_values()[y])
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x = result.variable_values()[x]
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y = result.variable_values()[y]
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epsilon = 0.001
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if x>0 and y>0 and abs(x - round(x)) <= epsilon and abs(y - round(y)) <= epsilon:
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sol += result.objective_value()
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print(f"{sol:.5f}")
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