622 lines
18 KiB
Python
622 lines
18 KiB
Python
from math import sqrt
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import shelve
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from collections import deque
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from dataclasses import dataclass, replace
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from functools import reduce
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import random
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from typing import TYPE_CHECKING, Callable, Counter, Dict, List, Literal, Set, Tuple
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from functools import lru_cache
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import pytest
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print()
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# twisting the bottom, opposing this color clockwise when this color is facing away
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# RBOG
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Axis = Literal["G", "O", "B", "R"]
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AXES: tuple[Axis, ...] = Axis.__args__
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# How many clockwise twists along an axis has been twisted after being flush with the top or bottom.
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CornerRotState = Literal[0, 1, 2]
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Twist = Literal["G", "O", "B", "R", "g", "o", "b", "r"]
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TWISTS: tuple[Twist, ...] = Twist.__args__
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to_anticlockwise: dict[Axis, Twist] = {"G": "g", "O": "o", "B": "b", "R": "r"}
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to_clockwise: dict[Twist, Axis] = {v: k for k, v in to_anticlockwise.items()}
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to_opposite: dict[Twist, Twist] = {**to_anticlockwise, **to_clockwise}
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@dataclass(frozen=True)
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class Corner:
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col: Axis
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rot: CornerRotState
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def __repr__(self) -> str:
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return f"{self.col}{self.rot}"
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MidRotState = Literal["Y", "O", "R"]
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@dataclass(frozen=True)
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class Middle:
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col: Literal["G", "O", "B", "R", "Y"]
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rot: MidRotState
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def __repr__(self) -> str:
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return f"{self.col}{self.rot}"
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@dataclass(frozen=True)
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class Skewb:
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"""Represents a Rubics cube variant sold as 'Qiyi Twisty Skewb'."""
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# order: vertically below Axis primary color
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top: Tuple[Corner, Corner, Corner, Corner]
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bot: Tuple[Corner, Corner, Corner, Corner]
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mids: Tuple[Middle, Middle, Middle, Middle, Middle]
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# def __post_init__(self):
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# """Check basic constraints such as the correct number of colors"""
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def assert_valid(self):
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assert Counter(
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corner.col for corners in [self.top, self.bot] for corner in corners
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) == {col: 2 for col in AXES}
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assert Counter(mid.col for mid in self.mids) == Counter("RBOGY")
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# forbidden rotations
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assert self.mids[0].rot != "R"
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assert self.mids[1].rot != "O"
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assert self.mids[2].rot != "R"
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assert self.mids[3].rot != "O"
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assert self.mids[4].col == "Y" or self.mids[4].rot != "Y"
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G0 = Corner("G", 0)
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G1 = Corner("G", 1)
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G2 = Corner("G", 2)
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O0 = Corner("O", 0)
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O1 = Corner("O", 1)
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O2 = Corner("O", 2)
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B0 = Corner("B", 0)
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B1 = Corner("B", 1)
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B2 = Corner("B", 2)
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R0 = Corner("R", 0)
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R1 = Corner("R", 1)
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R2 = Corner("R", 2)
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GR = Middle("G", "R")
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OR = Middle("O", "R")
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BR = Middle("B", "R")
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RR = Middle("R", "R")
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GO = Middle("G", "O")
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OO = Middle("O", "O")
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BO = Middle("B", "O")
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RO = Middle("R", "O")
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GY = Middle("G", "Y")
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OY = Middle("O", "Y")
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BY = Middle("B", "Y")
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RY = Middle("R", "Y")
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YY = Middle("Y", "Y")
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def rotate_mid_about_W(m: Middle) -> Middle:
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return Middle(
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col=m.col, rot="Y" if m.rot == "Y" else ("R" if m.rot == "O" else "O")
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)
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def rotate_everything_about_W(s: Skewb) -> Skewb:
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"""Clockwise rotation when looking down upon white."""
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return Skewb(
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top=(s.top[-1],) + s.top[:-1],
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bot=(s.bot[-1],) + s.bot[:-1],
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mids=(
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rotate_mid_about_W(s.mids[3]),
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rotate_mid_about_W(s.mids[0]),
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rotate_mid_about_W(s.mids[1]),
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rotate_mid_about_W(s.mids[2]),
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rotate_mid_about_W(s.mids[4]),
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),
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)
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solved_skewb = Skewb(
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top=(G0, O0, B0, R0),
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bot=(G0, O0, B0, R0),
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mids=(GY, OY, BY, RY, YY),
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)
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@pytest.mark.parametrize("s", [solved_skewb])
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def test_rotate_everything_about_W(s: Skewb):
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ss = [s]
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for i in range(4):
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ss.append(rotate_everything_about_W(ss[-1]))
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assert ss[0] == ss[-1]
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assert all(ss[0] != q for q in ss[1:-1])
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def test_axes():
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assert AXES[0] == "G"
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type CornerRotPermutation = dict[CornerRotState, CornerRotState]
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BOT_LEFT_TO_TOP: CornerRotPermutation = {0: 2, 1: 0, 2: 1}
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TOP_TO_BOT_RIGHT: CornerRotPermutation = {0: 2, 1: 0, 2: 1}
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ROTATE_CORNER_CLOCKWISE: CornerRotPermutation = {0: 1, 1: 2, 2: 0}
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BOT_RIGHT_TO_BOT_LEFT: CornerRotPermutation = {0: 2, 1: 0, 2: 1}
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@pytest.mark.parametrize(
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"p",
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[BOT_LEFT_TO_TOP, TOP_TO_BOT_RIGHT, ROTATE_CORNER_CLOCKWISE, BOT_RIGHT_TO_BOT_LEFT],
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)
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def test_rotation_permutations(p: CornerRotPermutation):
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assert set(p.keys()) == {0, 1, 2}
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assert set(p.values()) == {0, 1, 2}
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MID_DIR_INCREMENT: dict[MidRotState, MidRotState] = {"Y": "O", "R": "Y", "O": "R"}
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def clockwise_twist(s: Skewb, axis: Axis) -> Skewb:
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"""Applies a clockwise twist to the axis.
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Coordinate frame is define as follows:
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- axis goes through the `top` of a solved cube of a given color
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- the axis-top is on top and faces away from the observer twisting it,
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- clockwise is twisting the bottom when looking up from diagonally-below the skewb
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"""
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rot_before, rot_after = {"G": (0, 0), "O": (3, 1), "B": (2, 2), "R": (1, 3)}[axis]
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for _ in range(rot_before):
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s = rotate_everything_about_W(s)
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s = Skewb(
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top=(
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s.top[0],
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s.top[1],
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Corner((c := s.bot[0]).col, BOT_LEFT_TO_TOP[c.rot]),
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s.top[3],
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),
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bot=(
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Corner((c := s.bot[2]).col, BOT_RIGHT_TO_BOT_LEFT[c.rot]),
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s.bot[1],
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Corner((c := s.top[2]).col, TOP_TO_BOT_RIGHT[c.rot]),
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Corner((c := s.bot[3]).col, ROTATE_CORNER_CLOCKWISE[c.rot]),
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),
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mids=(
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s.mids[0],
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s.mids[1],
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Middle(
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(m := s.mids[3]).col,
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"Y" if m.col == "Y" else MID_DIR_INCREMENT[m.rot],
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),
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Middle(
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(m := s.mids[4]).col,
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"Y" if m.col == "Y" else MID_DIR_INCREMENT[m.rot],
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),
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Middle(
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(m := s.mids[2]).col,
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"Y" if m.col == "Y" else ("O" if m.rot == "Y" else "R"),
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),
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),
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)
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for _ in range(rot_after):
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s = rotate_everything_about_W(s)
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return s
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@pytest.mark.parametrize(
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"axis, want",
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[
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(
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"O",
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Skewb(
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top=(G0, O0, B0, O2), bot=(G1, R2, B0, R2), mids=(YY, OY, BY, GR, RR)
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),
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)
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],
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)
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def test_clockwise_twist_from_solved(axis: Axis, want: Skewb):
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want.assert_valid()
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assert clockwise_twist(solved_skewb, axis) == want
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def anticlockwise_twist(s: Skewb, twist: Axis) -> Skewb:
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return clockwise_twist(clockwise_twist(s, twist), twist)
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@pytest.mark.parametrize("start", [solved_skewb])
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@pytest.mark.parametrize("axis", AXES)
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def test_clockwise_twist(start: Skewb, axis: Axis):
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assert anticlockwise_twist(clockwise_twist(start, axis), axis) == start
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assert clockwise_twist(anticlockwise_twist(start, axis), axis) == start
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ss = [start]
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for i in range(3):
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ss.append(clockwise_twist(ss[-1], axis))
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assert len(ss) == 4
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assert ss[0] == ss[-1]
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assert all([ss[0] != q for q in ss[1:-1]])
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for s in ss:
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assert anticlockwise_twist(clockwise_twist(s, axis), axis) == s
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assert clockwise_twist(anticlockwise_twist(s, axis), axis) == s
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def apply_twist(start: Skewb, twist: Twist) -> Skewb:
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if twist in AXES:
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return clockwise_twist(start, twist)
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return anticlockwise_twist(start, to_clockwise[twist])
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def apply_opposite(s: Skewb, twist: Twist) -> Skewb:
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return apply_twist(s, to_opposite[twist])
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def apply_twists(start: Skewb, twists: list[Twist]) -> Skewb:
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return reduce(apply_twist, twists, start)
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def instructions(twists: list[Axis]) -> str:
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out = ""
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axis = "R"
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for twist in twists:
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while axis != twist:
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axis = AXES[(1 + AXES.index(axis)) % 4]
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out += "L"
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out += "."
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out = out.replace("..", ":")
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out = out.replace("LLL", "J")
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return out
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def breadth_first_search(
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start: Skewb,
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is_end: Callable[[Skewb], bool],
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max_steps: int = 2000000,
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bidirectional_fallback_threshold: int | None = None,
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) -> list[Twist] | None:
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start.assert_valid()
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if is_end(start):
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return []
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q = deque([start])
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# what action got us to this point
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skewb_to_twist: dict[Skewb, Twist | None] = {skewb: None for skewb in q}
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def get_path(end: Skewb) -> list[Twist]:
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out = []
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s = end
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while twist := skewb_to_twist[s]:
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out.append(twist)
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s = apply_opposite(s, twist)
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out.reverse()
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return out
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step_count = 0
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while q and max_steps > 0:
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if max_steps % 1000 == 0 and step_count:
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print(".", end="", flush=True)
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if (
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bidirectional_fallback_threshold is not None
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and step_count > bidirectional_fallback_threshold
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):
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return bidirectional_search(start, max_steps)
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step_count += 1
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parent = q.popleft()
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for twist in TWISTS:
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child = apply_twist(parent, twist)
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if child in skewb_to_twist:
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continue
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skewb_to_twist[child] = twist
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if is_end(child):
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return get_path(child)
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q.append(child)
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return None
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def test_breadth_first_search():
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for twist in TWISTS:
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assert breadth_first_search(
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apply_opposite(solved_skewb, twist), is_end=lambda s: s == solved_skewb
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) == [twist]
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def print_path(path: list[Axis]):
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x = start
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print(f"S -> {x}")
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for twist in path:
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x = clockwise_twist(x, twist)
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print(f"{twist} -> {x}")
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def bidirectional_search(
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start: Skewb, max_steps: int, end: Skewb = solved_skewb
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) -> list[Twist] | None:
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start.assert_valid()
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q = deque([start])
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q2 = deque([end])
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# what action got us to this point
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skewb_to_twist: dict[Skewb, Twist | None] = {skewb: None for skewb in q}
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skewb_to_twist2: dict[Skewb, Twist | None] = {skewb: None for skewb in q2}
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def get_path(meet: Skewb) -> list[Twist]:
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path = []
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s = meet
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while twist := skewb_to_twist[s]:
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path.append(twist)
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s = apply_opposite(s, twist)
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path.reverse()
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s = meet
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while twist := skewb_to_twist2[s]:
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path.append(twist)
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s = apply_twist(s, twist)
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return path
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def instructions(twists: list[Axis]) -> str:
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out = ""
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axis = "R"
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for twist in twists:
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while axis != twist:
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axis = AXES[(1 + AXES.index(axis)) % 4]
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out += "L"
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out += "."
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out = out.replace("..", ":")
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out = out.replace("LLL", "J")
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return out
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def on_meet(meet: Skewb) -> list[Twist]:
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path = get_path(meet)
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assert apply_twists(start, path) == end
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return path
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# print(f"{heuristic_list(end)=} {''.join(path)=} {instructions(path)=}")
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# return
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while q and max_steps > 0:
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max_steps -= 1
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if max_steps % 1000 == 0:
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print(".", end="", flush=True)
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parent2 = q2.popleft()
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for twist in TWISTS:
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child = apply_opposite(parent2, twist)
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if child in skewb_to_twist2:
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continue
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skewb_to_twist2[child] = twist
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if child in skewb_to_twist:
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return on_meet(child)
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q2.append(child)
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parent = q.popleft()
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for twist in TWISTS:
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child = apply_twist(parent, twist)
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if child in skewb_to_twist:
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continue
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skewb_to_twist[child] = twist
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if child in skewb_to_twist2:
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return on_meet(child)
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q.append(child)
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print(f"{len(skewb_to_twist)}")
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return None
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def heuristic(got: Skewb) -> float:
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return sum(heuristic_list(got))
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def heuristic_list(got: Skewb) -> list[float]:
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out = []
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want = solved_skewb
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out.append(10000 * (got.top[0] == want.top[0]))
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out.append(1000 * (got.bot[3] == want.bot[3]))
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out.append(1000 * (got.mids[3] == want.mids[3]))
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out.append(100 * (got.top[1] == want.top[1]))
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out.append(100 * (got.mids[0] == want.mids[0]))
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out.append(100 * (got.bot[0] == want.bot[0]))
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out.append(100 * (got.mids[4] == want.mids[4]))
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for c_got, c_want in zip(got.top + got.bot, want.top + want.bot):
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out.append(1 * (c_got.col == c_want.col) + 2 * (c_got.rot == c_want.rot))
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for m_got, m_want in zip(got.mids, want.mids):
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out.append(1 * (m_got.rot == m_want.rot) + 4 * (m_got.col == m_want.col))
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return out
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def get_heuristic_matches(s: Skewb) -> List[int]:
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"""
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format:
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[0:4] top
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[4:8] bot
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[8:13] mids
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"""
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out = [
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int((c_got.col == c_want.col) and (c_got.rot == c_want.rot))
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for c_got, c_want in zip(s.top + s.bot, solved_skewb.top + solved_skewb.bot)
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]
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out.extend(
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int((m_got.rot == m_want.rot) and (m_got.col == m_want.col))
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for m_got, m_want in zip(s.mids, solved_skewb.mids)
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)
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return out
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def element_multiply(a: list[int], b: list[int]) -> list[int]:
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assert len(a) == len(b)
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return [x * y for x, y in zip(a, b)]
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def test_heuristic():
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assert heuristic(apply_twist(solved_skewb, "O")) < heuristic(solved_skewb)
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def random_skewb(seed: int = 4, twists: int = 20) -> Skewb:
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return apply_twists(solved_skewb, random_skewb_twists(seed, twists))
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def random_skewb_twists(seed: int = 4, twists: int = 20) -> list[Twist]:
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out: list[Twist] = []
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rng = random.Random(seed)
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ax_i = rng.randint(0, 3)
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for _ in range(twists):
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twist = AXES[ax_i]
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if rng.getrandbits(1):
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twist = to_opposite[twist]
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out.append(twist)
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ax_i = (ax_i + rng.randint(1, 3)) % len(AXES)
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return out
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def double_clockwise_to_anticlockwise(twists: list[Axis]) -> list[Twist]:
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i = 0
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n = len(twists)
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out: list[Twist] = []
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while i < n:
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twist = twists[i]
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if i < n - 1 and twist == twists[i + 1]:
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out.append(to_anticlockwise[twist])
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i += 2
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else:
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out.append(twist)
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i += 1
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return out
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|
@pytest.mark.parametrize(
|
|
"twists, want",
|
|
[
|
|
("RBOG", "RBOG"),
|
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("RRBBOOGG", "rbog"),
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|
("RRR", "rR"),
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|
("RROR", "rOR"),
|
|
("RORR", "ROr"),
|
|
],
|
|
)
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|
def test_double_clockwise_to_anticlockwise(twists: list[Axis], want: list[Twist]):
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assert double_clockwise_to_anticlockwise(twists) == list(want)
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|
|
|
|
|
def test_random_skewb():
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twist_count = 50
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twists = random_skewb_twists(twists=twist_count)
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assert len(twists) == twist_count
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|
|
|
|
|
def shelve_it(file_name):
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|
d = shelve.open(file_name)
|
|
|
|
def decorator(func):
|
|
def new_func(*args, **kwargs):
|
|
key = str(args) + str(kwargs)
|
|
if key not in d:
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|
d[key] = func(*args, **kwargs)
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|
return d[key]
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|
|
|
return new_func
|
|
|
|
return decorator
|
|
|
|
|
|
def get_paths_from_heuristic(
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|
start: Skewb, heuristic_permutation: list[int]
|
|
) -> list[list[Twist]]:
|
|
out: list[list[Twist]] = []
|
|
s = start
|
|
mask = [0 for _ in heuristic_permutation]
|
|
total_path_length = 0
|
|
for heuristic_i in heuristic_permutation:
|
|
mask[heuristic_i] = 1
|
|
|
|
def step_finished(candidate: Skewb) -> bool:
|
|
matches = get_heuristic_matches(candidate)
|
|
assert len(matches) == len(mask)
|
|
return all(match >= m for match, m in zip(matches, mask))
|
|
|
|
print(f"{mask=} {s=}", end=" ")
|
|
if heuristic_i == len(heuristic_permutation) - 3:
|
|
# print("going bidirectional now.")
|
|
path = bidirectional_search(s, max_steps=200000)
|
|
else:
|
|
path = breadth_first_search(
|
|
s, step_finished, bidirectional_fallback_threshold=20000
|
|
)
|
|
print(f" {path=}")
|
|
if path is None:
|
|
raise ValueError("oh no! solver could not find solution")
|
|
out.append(path)
|
|
s = apply_twists(s, path)
|
|
total_path_length += len(path)
|
|
return out
|
|
|
|
|
|
# def get_total_path_length(start: Skewb, heuristic_permutation: list[int]) -> int:
|
|
# return sum(len(p) for p in get_paths_from_heuristic(start, heuristic_permutation))
|
|
|
|
|
|
# close_to_wrongly_solved = Skewb(top=(R0, B0, O0, G0), bot=(B0, O0, G0, R0), mids=(BY, GRB, ORG, RY, YY))
|
|
near_end = Skewb(top=(O0, B0, R0, G2), bot=(B0, R0, G1, O0), mids=(BY, RY, GY, OY, YY))
|
|
start = near_end
|
|
# start = Skewb(top=(O0, B0, R1, G1), bot=(B0, R2, G2, O0), mids=(BY, RY, GY, OY, YY))
|
|
|
|
HURISTIC_PERMUTATION_LENGTH = 4 + 4 + 5
|
|
|
|
|
|
def quadratic_mean(values: list[float]) -> float:
|
|
return sqrt(sum(x * x for x in values) / len(values))
|
|
|
|
|
|
def score_fn(values: list[float]) -> float:
|
|
return -sum(2**i * v for i, v in enumerate(sorted(values)))
|
|
|
|
|
|
@shelve_it("skewb_solver.evaluate_permutation.shelve.sqlite")
|
|
def evaluate_permutation(
|
|
heuristic_permutation: list[int], seed=4, sample_size: int = 10
|
|
) -> float:
|
|
scores = []
|
|
for i in range(sample_size):
|
|
paths = get_paths_from_heuristic(start, heuristic_permutation)
|
|
score = score_fn([len(p) for p in paths])
|
|
print(f"{score=}")
|
|
scores.append(score)
|
|
return sum(scores) / len(scores)
|
|
|
|
|
|
def evaluate_all_1_swaps(hp: list[int]):
|
|
for i in range(len(hp)):
|
|
for j in range(i):
|
|
hp[i], hp[j] = hp[j], hp[i]
|
|
evaluate_permutation(hp, sample_size=22)
|
|
hp[i], hp[j] = hp[j], hp[i]
|
|
|
|
|
|
def evaluate_all_1_swaps_except_first(hp: list[int]):
|
|
for i in range(len(hp)):
|
|
for j in range(1, i):
|
|
hp[i], hp[j] = hp[j], hp[i]
|
|
evaluation = evaluate_permutation(hp, sample_size=100)
|
|
print(f"{hp=} {evaluation=}")
|
|
hp[i], hp[j] = hp[j], hp[i]
|
|
|
|
|
|
if __name__ == "__main__":
|
|
hp = top_bot_mids = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
|
|
hp = top_down = [0, 1, 2, 3, 8, 9, 10, 11, 12, 4, 5, 6, 7]
|
|
# evaluate_all_1_swaps(top_down)
|
|
evaluate_all_1_swaps_except_first(hp)
|
|
|
|
start = Skewb((G0, O0, B0, R0), (G0, R1, B2, O2), (BY, OY, RO, GR, YY))
|
|
# print(bidirectional_search(start, max_steps=1000000))
|
|
# print(get_paths_from_heuristic(start, hp))
|