#!/usr/bin/env python3

import sys
from functools import cache

@cache
def path(f1,f2):
    path = []
    y, x = f1
    while y != 0:
        y -= 1
        path.append((y,x))
    while x != f2[1]:
        x += 1 if f2[1] > x else -1
        path.append((y,x))
    while y != f2[0]:
        y += 1
        path.append((y,x))
    assert path[-1] == f2
    return path

def pathvalid(path,board):
    for p in path:
        if p in board: return False
    return True

def cost(a,w):
    if a == 'A': return len(w) * 1
    if a == 'B': return len(w) * 10
    if a == 'C': return len(w) * 100
    if a == 'D': return len(w) * 1000

def endstate(board):
    for f,a in board.items():
        if f[1] != target[a]: return False
    return True

def target_position(f,b,lowest):
    a = b[f]
    if f[1] != target[a]: return False
    for y in range(f[0],lowest+1):
        if (y,target[a]) not in b: return False
        if b[(y,target[a])] != a: return False
    return True

def totarget(board,lowest):
    change = False
    costs = 0
    nb = {k: v for k,v in board.items()}
    for f,a in board.items():
        if target_position(f,nb,lowest): continue
        t = (lowest,target[a])
        while t in nb and nb[t] == a:
            t = (t[0]-1,target[a])
        if t == (0,target[a]): continue
        p = path(f,t)
        if pathvalid(p,nb):
            change = True
            nb.pop(f)
            nb[t] = a
            costs += cost(a,p)
    return nb,costs,change

def dfs(board,lowest,costs=0,curmin=sys.maxsize):
    ch = True
    nb = {k: v for k,v in board.items()}
    while ch:
        nb,co,ch = totarget(nb,lowest)
        costs += co
    if endstate(nb): 
        return costs
    if costs > curmin: return None
    board = {k: v for k,v in nb.items()}
    for f,a in board.items():
        if f[0] != 0 and not(target_position(f,board,lowest)):
            for f2 in hallway:
                p = path(f,f2)
                if pathvalid(p, board):
                    cb = {k: v for k,v in board.items()}
                    cb.pop(f)
                    cb[f2] = a
                    nc = dfs(cb,lowest,costs+cost(a,p),curmin)
                    if nc is not None and nc < curmin: curmin = nc
    if curmin < sys.maxsize: return curmin

if __name__ == '__main__':
    # challenge 1
    lines = open(sys.argv[1]).readlines()
    start = {}
    for y,l in enumerate(lines[1:]):
        for x,f in enumerate(l[1:]):
            if f in 'ABCD': start[(y,x)] = f 

    hallway = [(0,0), (0,1), (0,3), (0,5), (0,7), (0,9), (0,10)]
    target = {'A': 2, 'B': 4, 'C': 6, 'D': 8}

    res1 = str(dfs(start,2))
    print("challenge 1:" + "\n" +  res1 + "\n")

    # challenge 2
    lines = open(sys.argv[2]).readlines()
    start = {}
    for y,l in enumerate(lines[1:]):
        for x,f in enumerate(l[1:]):
            if f in 'ABCD': start[(y,x)] = f 

    res2 = str(dfs(start,4))
    print("challenge 2:" + "\n" +  res2 + "\n")