#!/usr/bin/env python

# https://adventofcode.com/2025/day/10

from itertools import combinations, product
from sympy import symbols, Matrix, solve_linear_system

f = open("day10input.txt", "r")

# regular input
input = f.readlines()
# testinput
#input = "[.##.] (3) (1,3) (2) (2,3) (0,2) (0,1) {3,5,4,7}\n[...#.] (0,2,3,4) (2,3) (0,4) (0,1,2) (1,2,3,4) {7,5,12,7,2}\n[.###.#] (0,1,2,3,4) (0,3,4) (0,1,2,4,5) (1,2) {10,11,11,5,10,5}".split("\n")

machines = []

for input_line in input:
  line = input_line.rstrip("\n").split(" ")
  machine = {}

  # final state
  fs = line[0][1:-1].replace(".", "0").replace("#", "1")
  machine["fs"] = int(fs, base=2)

  # switches
  switches = []
  for switch in line[1:-1]:
    s = ["0"] * len(fs)
    for i in [int(j) for j in switch[1:-1].split(",")]:
      s[i] = "1"
    switches.append("".join(s))
  machine["s"] = sorted([int(s, base=2) for s in switches], key=int.bit_count)

  # joltage req's
  machine["j"] = [int(n) for n in line[-1][1:-1].split(",")]

  machines.append(machine)


def print_machines(machines: list[dict]) -> None:
  for i in range(len(machines)):
    print(f"Machine no. {i}")
    for k in machines[i].keys():
      print(f"key:\t{k}\tvalue:\t{machines[i][k]}")
  

def part1_bfs(m):
  for steps in range(1, len(m["s"])):
    # check if current step no yields a solution
    for c in list(combinations(m["s"], steps)):
      lights = 0
      for i in c:
        lights ^= i
      if lights == m["fs"]:
        print(f"Success with combo {i} and step count of {steps}")
        return steps
  return None


def part2(m):
  switches = [list(map(int, list("{0:b}".format(switch).zfill(len(m["j"]))))) for switch in m["s"]]
  joltages = m["j"] 

  # define sympy symbols and equations
  x = symbols(f"x:{len(switches)}", integer=True)
  system = Matrix([[switch[j] for switch in switches] + [joltages[j]] for j in range(len(joltages))])
  print(f"Equation system to solve: {system}")

  # solve system with sympy
  solutions = solve_linear_system(system, *x)
  print(f"Solutions: {solutions}")
  
  # isolate free variables
  free_vars = [var for var in x if var not in solutions.keys()]
  print(f"{free_vars=}")

  # find smallest solution
  smallest_sum = None

  # loop over the cartesian product of sensible numbers for button presses times the number of free variables 
  for lv in product(range(max(joltages)), repeat=len(free_vars)):
#    print(f"{lv=}")
    current_sum = sum(lv)
    for v in solutions.values():
      for i in range(len(lv)):
        v = v.subs(free_vars[i], lv[i])
#      print(f"{v=}")
      if v < 0:
#        print(f"negative button press number for {lv=} -> skipping")
        current_sum = -1
        break
      current_sum += v
    if current_sum < 0:
      continue
#    print(f"-> {current_sum=}")
    
    # check current sum
    if not current_sum.is_Integer:
      continue
    elif not smallest_sum or current_sum < smallest_sum: 
      smallest_sum = current_sum
  
  print(f"Smallest number of presses found: {smallest_sum}")
  return smallest_sum


#print_machines(machines)
#print(sum(list(map(part1_bfs, machines))))bin
steps = 0
for machine in machines:
  steps += part2(machine)
  print(f"current total step number: {steps}")
print(f"final total step number: {steps}")