/* 

  Advent of Code 2024 in Picat.

  Problem 13
  https://adventofcode.com/2024/day/13

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import util.
import cp.
import aoc_utils.

main => go.

/*
  Part 1 and 2

  Benchmark 1: picat 13.pi
    Time (mean ± σ):      58.8 ms ±   7.8 ms    [User: 42.7 ms, System: 16.0 ms]
    Range (min … max):    36.9 ms …  69.7 ms    39 runs

  Part 1
  Benchmark 1: picat 13.pi
    Time (mean ± σ):      47.4 ms ±   8.2 ms    [User: 33.2 ms, System: 14.2 ms]
    Range (min … max):    27.2 ms …  62.0 ms    54 runs

  Part 2
  Benchmark 1: picat 13.pi
    Time (mean ± σ):      47.3 ms ±   9.3 ms    [User: 29.8 ms, System: 17.5 ms]
    Range (min … max):    23.6 ms …  60.8 ms    43 runs

*/
go ?=>
  nolog,
  File = "13.txt",
  Split = split2(read_file_chars(File)),
  member(Part,1..2),
  T = cond(Part == 1,0,10000000000000),
  Sum = 0,
  foreach(Line in Split)
    S = Line.split("=+\n, "),
    [AX,AY,BX,BY,PX1,PY1] = [S[I].to_int : I in [4,6,10,12,15,17]],
    PX = PX1 + T,
    PY = PY1 + T,    
    if [_X,_Y,Z] = s(AX,AY,BX,BY,PX,PY) then
      Sum := Sum + Z
    end
  end,
  println(Sum),
  Part == 2.
go => true.

s(AX,AY,BX,BY,PX,PY) = [X,Y,Z] =>
    X #>= 0,
    Y #>= 0,
    PX #= AX*X + BX*Y,
    PY #= AY*X + BY*Y,
    Z #=3*X+Y,
    solve($[min(Z)],[X,Y,Z]).