Today is another game. This time I’m given a list of numbers and asked to mix it according to some given rules a certain number of times. Today is also the first time this year where I wrote part one, and then completely started over given part two.

## Challenge

The puzzle can be found here. I’m given a list of numbers, which represent numbered cups in a circle, such that the first comes after the last. The rules are simple. The active cup starts as the first cup in the original list. The next three cups are removed from the circle. The target is found to be cup with the value one less than the active cup (and if that cup isn’t in the circle, decrement again until it is found in the circle). The three cups are then inserted after the target cup, and the active cup moves to the new cup that is after the previous active cup.

In part one, there are 100 rounds with the given list.

In part two, the rules are the same, but there are two differences. First, while the input gives the order for cups 1-9, cups ten through one million are then also joined into the circle in numerical order. Second, instead of 100 rounds, there will be ten million.

## Solution

### Part 1

The scope of the problem in part one made it that I could solve this with a list of numbers, slicing and recombining to make the updated list:

#!/usr/bin/env python3

import sys

game = [int(x) for x in sys.argv[1]]
num_moves = int(sys.argv[2]) if len(sys.argv) > 2 else 100
glen = len(game)

for _ in range(num_moves):
pick = game[1:4]
game = game[0:1] + game[4:]
sgame = sorted(game)
dest = sgame[(sgame.index(game[0]) - 1) % (glen - 3)]
dest_idx = game.index(dest) + 1
game = game[1:dest_idx] + pick + game[dest_idx:] + game[0:1]

idx1 = game.index(1)
res = "".join([str(c) for c in game[idx1 + 1 :] + game[:idx1]])
print(f'Part 1: {res}')


Rather than track the active cup, I just moved the list such that the active cup was always at the front of the list. This made it easier so I didn’t have to worry about slicing beyond the end of the list.

This runs in less than 0.1 second, and solves the challenge.

### Part 2

In theory, one might think I could just change the numbers and construct this new list for part two, but my solution above will be way too slow. slicing and building lists is a very slow action in Python. I’ll change strategies so that I keep a linked list. It will be a simple Python dictionary, where the key is a cup, and the value is the next cup after it. So to find out which cup comes after cup one, it’s kept in cuplist[1]. That also means to move a cup, I only have to change the value for the cup that used to point to it, the new cup that points to it, and the cup it points to.

I’ll create a function that takes a list of cups, the full padded length of the game, and the number of moves. I’ll make sure this function works on both part one and part two.

First, I’ll build the linked list. For part one, it’s as simple as looping over the cups, and taking the cup number as the key, and the next cup number as the value, and putting it into the dictionary. When I reach the last cup, I’ll just set it to point to the value of the first cup.

    cuplist = {}
for i in range(full_len):
if i < len(cups) - 1:
cuplist[cups[i]] = cups[i + 1]
elif i == len(cups) - 1 and len(cups) == full_len:
cuplist[cups[i]] = cups[0]


With the part two extension, I’ll start adding a count up after, and that will take a few more conditions:

        elif i == len(cups) - 1 and len(cups) < full_len:
cuplist[cups[i]] = max(cups) + 1
elif i < full_len - 1:
cuplist[i + 1] = i + 2
elif i == full_len - 1:
cuplist[i + 1] = cups[0]


Once the list is built, the game is played. To pull three cups out, I’ll record their values, and set the pointer in the active cup to the cup four down:

        # remove three cups
c1 = cuplist[ptr]
c2 = cuplist[c1]
c3 = cuplist[c2]
cuplist[ptr] = cuplist[c3]


To find the destination, I’ll use modular arithmetic. I really want to subtract one and take the mod length. But that produce results in the zero to length minus one range. So I’ll actually subtract two, take the mod, and then add one, giving results in the one to length range. I’ll use a while loop to make sure the cup isn’t in the removed cups:

        # find dest
dest = ((ptr - 2) % full_len) + 1
while dest in [c1, c2, c3]:
dest = ((dest - 2) % full_len) + 1


Now I’ll just inset the cups by updating two pointers, and get the next active cup:

        # reinsert cups after dest
cuplist[c3] = cuplist[dest]
cuplist[dest] = c1

# move ptr forward
ptr = cuplist[ptr]


I’ll do that all in a for loop over the number of iterations required, and return that list.

### Final Code

Part one is quick, but part two runs for twenty seconds:

\$ time python3 day23.py 219748365
Part 1: 35827964
Part 2: 5403610688

real    0m22.701s
user    0m22.601s
sys     0m0.065s

#!/usr/bin/env python3

import sys

def solve_game(cups, full_len, num_moves):

# prep list
cuplist = {}
for i in range(full_len):
if i < len(cups) - 1:
cuplist[cups[i]] = cups[i + 1]
elif i == len(cups) - 1 and len(cups) == full_len:
cuplist[cups[i]] = cups[0]
elif i == len(cups) - 1 and len(cups) < full_len:
cuplist[cups[i]] = max(cups) + 1
elif i < full_len - 1:
cuplist[i + 1] = i + 2
elif i == full_len - 1:
cuplist[i + 1] = cups[0]

ptr = cups[0]
for _ in range(num_moves):

# remove three cups
c1 = cuplist[ptr]
c2 = cuplist[c1]
c3 = cuplist[c2]
cuplist[ptr] = cuplist[c3]

# find dest
dest = ((ptr - 2) % full_len) + 1
while dest in [c1, c2, c3]:
dest = ((dest - 2) % full_len) + 1

# reinsert cups after dest
cuplist[c3] = cuplist[dest]
cuplist[dest] = c1

# move ptr forward
ptr = cuplist[ptr]

return cuplist

cups = [int(x) for x in sys.argv[1]]

solved = solve_game(cups, len(cups), 100)
res = ""
x = solved[1]
while x != 1:
res += str(x)
x = solved[x]
print(f"Part 1: {res}")

solved = solve_game(cups, 1000000, 10000000)
res = solved[1] * solved[solved[1]]
print(f"Part 2: {res}")