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Hodel_primitives_atomic.py
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Hodel_primitives_atomic.py
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# The following primitives are a subset from Michael's Hodel's DSL that consists of grid-to-grid transformations only.
# Michael Hodel's DSL: https://github.com/michaelhodel/arc-dsl
import inspect
ZERO = 0
ONE = 1
TWO = 2
THREE = 3
FOUR = 4
FIVE = 5
SIX = 6
SEVEN = 7
EIGHT = 8
NINE = 9
TEN = 10
F = False
T = True
NEG_ONE = -1
ORIGIN = (0, 0)
UNITY = (1, 1)
DOWN = (1, 0)
RIGHT = (0, 1)
UP = (-1, 0)
LEFT = (0, -1)
NEG_TWO = -2
NEG_UNITY = (-1, -1)
UP_RIGHT = (-1, 1)
DOWN_LEFT = (1, -1)
ZERO_BY_TWO = (0, 2)
TWO_BY_ZERO = (2, 0)
TWO_BY_TWO = (2, 2)
THREE_BY_THREE = (3, 3)
def execute(func_str, grid):
return eval(func_str)(grid)
def is_color_related(func_str):
if func_str.startswith("set_fg_color") or func_str.startswith("color_swap"):
return True
else:
return False
def is_rotation(func_str):
if func_str.startswith("rot"):
return True
else:
return False
def is_mirroring(func_str):
if func_str.endswith("mirror"):
return True
else:
return False
def is_rep(func_str):
if func_str.startswith("rep"):
return True
else:
return False
def get_prim_func_by_name(name):
return semantics[name]
def get_shortcuts():
shortcuts = {
'TopHalf/LeftHalf': 'FirstQuadrant',
'LeftHalf/TopHalf': 'FirstQuadrant',
'TopHalf/RightHalf': 'SecondQuadrant',
'RightHalf/TopHalf': 'SecondQuadrant',
'BottomHalf/LeftHalf': 'ThirdQuadrant',
'LeftHalf/BottomHalf': 'ThirdQuadrant',
'BottomHalf/RightHalf': 'FourthQuadrant',
'RightHalf/BottomHalf': 'FourthQuadrant',
'VerticallyMirror/HorizontallyMirror': 'RotateHalf',
'HorizontallyMirror/VerticallyMirror': 'RotateHalf'
}
return shortcuts
def get_index(name):
return prim_indices[name]
def inverse_lookup(idx):
for key, val in prim_indices.items():
if val == idx:
return key
def clear_single_colors(grid):
func = fork(paint, identity, chain(lbind(recolor, ZERO), rbind(mfilter, matcher(size, ONE)), partition))
return func(grid)
def clear_double_colors(grid):
func = fork(paint, identity, chain(lbind(recolor, ZERO), rbind(mfilter, matcher(size, TWO)), partition))
return func(grid)
def clear_triple_colors(grid):
func = fork(paint, identity, chain(lbind(recolor, ZERO), rbind(mfilter, matcher(size, THREE)), partition))
return func(grid)
def drag_down_underpaint(grid):
func = fork(underpaint, identity, chain(rbind(shift, DOWN), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_down_paint(grid):
func = fork(paint, identity, chain(rbind(shift, DOWN), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_left_underpaint(grid):
func = fork(underpaint, identity, chain(rbind(shift, LEFT), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_left_paint(grid):
func = fork(paint, identity, chain(rbind(shift, LEFT), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_up_underpaint(grid):
func = fork(underpaint, identity, chain(rbind(shift, UP), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_up_paint(grid):
func = fork(paint, identity, chain(rbind(shift, UP), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_right_underpaint(grid):
func = fork(underpaint, identity, chain(rbind(shift, RIGHT), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_right_paint(grid):
func = fork(paint, identity, chain(rbind(shift, RIGHT), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_diagonally_underpaint(grid):
func = fork(underpaint, identity, chain(rbind(shift, UNITY), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_diagonally_paint(grid):
func = fork(paint, identity, chain(rbind(shift, UNITY), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_counterdiagonally_underpaint(grid):
func = fork(underpaint, identity, chain(rbind(shift, DOWN_LEFT), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def drag_counterdiagonally_paint(grid):
func = fork(paint, identity, chain(rbind(shift, DOWN_LEFT), rbind(sfilter, chain(flip, rbind(equality, ZERO), first)), asobject))
return func(grid)
def extend_by_one(grid):
func = fork(paint, compose(lbind(canvas, ZERO), chain(increment, increment, shape)), compose(rbind(shift, UNITY), asobject))
return func(grid)
def extend_by_two(grid):
func = fork(paint, chain(lbind(canvas, ZERO), power(increment, FOUR), shape), compose(rbind(shift, TWO_BY_TWO), asobject))
return func(grid)
def insert_top_row(grid):
func = fork(vconcat, chain(lbind(canvas, ZERO), lbind(astuple, ONE), width), identity)
return func(grid)
def insert_bottom_row(grid):
func = fork(vconcat, identity, chain(lbind(canvas, ZERO), lbind(astuple, ONE), width))
return func(grid)
def insert_left_col(grid):
func = fork(hconcat, chain(lbind(canvas, ZERO), rbind(astuple, ONE), height), identity)
return func(grid)
def insert_right_col(grid):
func = fork(hconcat, identity, chain(lbind(canvas, ZERO), rbind(astuple, ONE), height))
return func(grid)
def stack_rows_horizontally(grid):
func = compose(rbind(repeat, ONE), merge)
return func(grid)
def stack_rows_vertically(grid):
func = chain(dmirror, compose(rbind(repeat, ONE), merge), dmirror)
return func(grid)
def stack_rows_horizontally_compress(grid):
func = chain(rbind(repeat, ONE), lbind(remove, ZERO), chain(first, rbind(repeat, ONE), merge))
return func(grid)
def stack_columns_vertically_compress(grid):
func = chain(dmirror, chain(rbind(repeat, ONE), lbind(remove, ZERO), chain(first, rbind(repeat, ONE), merge)), dmirror)
return func(grid)
def symmetrize_left_around_vertical(grid):
return hconcat(lefthalf(grid), vmirror(lefthalf(grid)))
def symmetrize_right_around_vertical(grid):
return hconcat(vmirror(righthalf(grid)), righthalf(grid))
def symmetrize_top_around_horizontal(grid):
return vconcat(tophalf(grid), hmirror(tophalf(grid)))
def symmetrize_bottom_around_horizontal(grid):
return vconcat(hmirror(bottomhalf(grid)), bottomhalf(grid))
def symmetrize_quad(grid):
func = fork(vconcat, fork(hconcat, compose(lefthalf, tophalf), chain(vmirror, lefthalf, tophalf)), fork(hconcat, chain(hmirror, lefthalf, tophalf), chain(compose(hmirror, vmirror), lefthalf, tophalf)))
return func(grid)
def keep_only_diagonal(grid):
func = fork(paint, identity, compose(lbind(recolor, ZERO), fork(difference, asobject, fork(toobject, fork(connect, compose(ulcorner, asindices), compose(lrcorner, asindices)), identity))))
return func(grid)
def keep_only_counterdiagonal(grid):
func = fork(paint, identity,
compose(lbind(recolor, ZERO),
fork(difference,
asobject,
fork(toobject,
fork(connect,
compose(urcorner, asindices),
compose(llcorner, asindices)), identity))))
return func(grid)
def shear_rows_left(grid):
func = compose(lbind(apply, fork(combine, compose(lbind(apply, first), fork(sfilter, fork(pair, last, chain(rbind(lbind(interval, ZERO), ONE), size, last)), chain(rbind(compose, compose(increment, last)), lbind(rbind, greater), first))), compose(lbind(apply, first), fork(sfilter, fork(pair, last, chain(rbind(lbind(interval, ZERO), ONE), size, last)), chain(rbind(compose, last), lbind(lbind, greater), first))))), fork(pair, compose(rbind(lbind(interval, ZERO), ONE), height), identity))
return func(grid)
def shear_rows_right(grid):
func = chain(vmirror, compose(lbind(apply, fork(combine, compose(lbind(apply, first), fork(sfilter, fork(pair, last, chain(rbind(lbind(interval, ZERO), ONE), size, last)), chain(rbind(compose, compose(increment, last)), lbind(rbind, greater), first))), compose(lbind(apply, first), fork(sfilter, fork(pair, last, chain(rbind(lbind(interval, ZERO), ONE), size, last)), chain(rbind(compose, last), lbind(lbind, greater), first))))), fork(pair, compose(rbind(lbind(interval, ZERO), ONE), height), identity)), vmirror)
return func(grid)
def shear_cols_down(grid):
func = chain(dmirror, compose(lbind(apply, fork(combine, compose(lbind(apply, first), fork(sfilter, fork(pair, last, chain(rbind(lbind(interval, ZERO), ONE), size, last)), chain(rbind(compose, compose(increment, last)), lbind(rbind, greater), first))), compose(lbind(apply, first), fork(sfilter, fork(pair, last, chain(rbind(lbind(interval, ZERO), ONE), size, last)), chain(rbind(compose, last), lbind(lbind, greater), first))))), fork(pair, compose(rbind(lbind(interval, ZERO), ONE), height), identity)), dmirror)
return func(grid)
def shear_cols_up(grid):
func = chain(dmirror, chain(vmirror, compose(lbind(apply, fork(combine, compose(lbind(apply, first), fork(sfilter, fork(pair, last, chain(rbind(lbind(interval, ZERO), ONE), size, last)), chain(rbind(compose, compose(increment, last)), lbind(rbind, greater), first))), compose(lbind(apply, first), fork(sfilter, fork(pair, last, chain(rbind(lbind(interval, ZERO), ONE), size, last)), chain(rbind(compose, last), lbind(lbind, greater), first))))), fork(pair, compose(rbind(lbind(interval, ZERO), ONE), height), identity)), vmirror), dmirror)
return func(grid)
def upscale_horizontal_by_two(grid):
return hupscale(grid, TWO)
def upscale_vertical_by_two(grid):
return vupscale(grid, TWO)
def upscale_horizontal_by_three(grid):
return hupscale(grid, THREE)
def upscale_vertical_by_three(grid):
return vupscale(grid, THREE)
def upscale_by_two(grid):
return upscale(grid, TWO)
def upscale_by_three(grid):
return upscale(grid, THREE)
def clear_outline(grid):
func = fork(paint, identity, chain(lbind(recolor, ZERO), box, asindices))
return func(grid)
def clear_all_but_outline(grid):
func = fork(paint, identity, compose(lbind(recolor, ZERO), fork(difference, asindices, compose(box, asindices))))
return func(grid)
def clear_top_row(grid):
func = fork(paint, identity, compose(lbind(recolor, ZERO), fork(connect, compose(ulcorner, asobject), compose(urcorner, asobject))))
return func(grid)
def clear_bottom_row(grid):
func = chain(hmirror, fork(paint, identity, compose(lbind(recolor, ZERO), fork(connect, compose(ulcorner, asobject), compose(urcorner, asobject)))), hmirror)
return func(grid)
def clear_left_column(grid):
func = chain(rot270, fork(paint, identity, compose(lbind(recolor, ZERO), fork(connect, compose(ulcorner, asobject), compose(urcorner, asobject)))), rot90)
return func(grid)
def clear_right_column(grid):
func = chain(rot90, fork(paint, identity, compose(lbind(recolor, ZERO), fork(connect, compose(ulcorner, asobject), compose(urcorner, asobject)))), rot270)
return func(grid)
def clear_diagonal(grid):
func = fork(paint, identity, compose(lbind(recolor, ZERO), fork(connect, compose(ulcorner, asindices), compose(lrcorner, asindices))))
return func(grid)
def clear_counterdiagonal(grid):
func = fork(paint, identity, compose(lbind(recolor, ZERO), fork(connect, compose(urcorner, asindices), compose(llcorner, asindices))))
return func(grid)
def rep_first_row(grid):
return repeat(first(grid), height(grid))
def rep_last_row(grid):
return repeat(last(grid), height(grid))
def rep_first_col(grid):
rot_grid = rot90(grid)
return rot270(repeat(first(rot_grid), height(rot_grid)))
def rep_last_col(grid):
rot_grid = rot270(grid)
return rot90(repeat(first(rot_grid), height(rot_grid)))
def remove_top_row(grid):
func = fork(subgrid, compose(lbind(insert, DOWN), chain(initset, decrement, shape)), identity)
return func(grid)
def remove_bottom_row(grid):
func = chain(hmirror, fork(subgrid, compose(lbind(insert, DOWN), chain(initset, decrement, shape)), identity), hmirror)
return func(grid)
def remove_left_column(grid):
func = chain(rot270, fork(subgrid, compose(lbind(insert, DOWN), chain(initset, decrement, shape)), identity), rot90)
return func(grid)
def remove_right_column(grid):
func = chain(rot90, fork(subgrid, compose(lbind(insert, DOWN), chain(initset, decrement, shape)), identity), rot270)
return func(grid)
# TODO: test this
def inner_columns(grid):
return subgrid(
insert(add(shape(grid), multiply(LEFT, TWO)), initset(RIGHT)),
grid)
# TODO: test this
def inner_rows(grid):
return subgrid(
insert(add(multiply(UP, TWO), shape(grid)), initset(DOWN)),
grid)
def gravitate_right(grid):
func = lbind(apply, fork(combine, compose(lbind(repeat, ZERO), compose(rbind(colorcount, ZERO), rbind(repeat, ONE))), lbind(remove, ZERO)))
return func(grid)
def gravitate_left(grid):
func = lbind(apply, fork(combine, lbind(remove, ZERO), chain(lbind(repeat, ZERO), rbind(colorcount, ZERO), rbind(repeat, ONE))))
return func(grid)
def gravitate_up(grid):
func = chain(rot270, lbind(apply, fork(combine, compose(lbind(repeat, ZERO), compose(rbind(colorcount, ZERO), rbind(repeat, ONE))), lbind(remove, ZERO))), rot90)
return func(grid)
def gravitate_down(grid):
func = chain(rot270, lbind(apply, fork(combine, lbind(remove, ZERO), chain(lbind(repeat, ZERO), rbind(colorcount, ZERO), rbind(repeat, ONE)))), rot90)
return func(grid)
def gravitate_left_right(grid):
func = fork(hconcat, compose(lbind(apply, fork(combine, lbind(remove, ZERO), chain(lbind(repeat, ZERO), rbind(colorcount, ZERO), rbind(repeat, ONE)))), lefthalf), compose(lbind(apply, fork(combine, compose(lbind(repeat, ZERO), compose(rbind(colorcount, ZERO), rbind(repeat, ONE))), lbind(remove, ZERO))), righthalf))
return func(grid)
def gravitate_top_down(grid):
func = fork(vconcat, compose(chain(rot270, lbind(apply, fork(combine, compose(lbind(repeat, ZERO), compose(rbind(colorcount, ZERO), rbind(repeat, ONE))), lbind(remove, ZERO))), rot90), tophalf), compose(chain(rot270, lbind(apply, fork(combine, lbind(remove, ZERO), chain(lbind(repeat, ZERO), rbind(colorcount, ZERO), rbind(repeat, ONE)))), rot90), bottomhalf))
return func(grid)
def shift_left(grid):
tmp = remove_left_column(grid)
tmp = insert_right_col(tmp)
return tmp
def shift_right(grid):
tmp = remove_right_column(grid)
tmp = insert_left_col(tmp)
return tmp
def shift_up(grid):
tmp = remove_top_row(grid)
tmp = insert_bottom_row(tmp)
return tmp
def shift_down(grid):
tmp = remove_bottom_row(grid)
tmp = insert_top_row(tmp)
return tmp
def wrap_left(grid):
func = fork(hconcat, fork(subgrid, compose(compose(lbind(insert, RIGHT), initset), fork(astuple, compose(decrement, height), compose(decrement, width))), identity), fork(subgrid, compose(compose(lbind(insert, ORIGIN), initset), compose(toivec, compose(decrement, height))), identity))
return func(grid)
def wrap_right(grid):
func = chain(vmirror, fork(hconcat, fork(subgrid, compose(compose(lbind(insert, RIGHT), initset), fork(astuple, compose(decrement, height), compose(decrement, width))), identity), fork(subgrid, compose(compose(lbind(insert, ORIGIN), initset), compose(toivec, compose(decrement, height))), identity)), vmirror)
return func(grid)
def wrap_up(grid):
func = chain(rot90, fork(hconcat, fork(subgrid, compose(compose(lbind(insert, RIGHT), initset), fork(astuple, compose(decrement, height), compose(decrement, width))), identity), fork(subgrid, compose(compose(lbind(insert, ORIGIN), initset), compose(toivec, compose(decrement, height))), identity)), rot270)
return func(grid)
def wrap_down(grid):
func = chain(rot270, fork(hconcat, fork(subgrid, compose(compose(lbind(insert, RIGHT), initset), fork(astuple, compose(decrement, height), compose(decrement, width))), identity), fork(subgrid, compose(compose(lbind(insert, ORIGIN), initset), compose(toivec, compose(decrement, height))), identity)), rot90)
return func(grid)
# TODO: test this
def outer_columns(grid):
return hconcat(first(hsplit(grid, width(grid))), last(hsplit(grid, width(grid))))
# TODO: test this
def outer_rows(grid):
return vconcat(first(vsplit(grid, height(grid))), last(vsplit(grid, height(grid))))
# TODO: test this
def left_column(grid):
return first(hsplit(grid, width(grid)))
# TODO: test this
def right_column(grid):
return last(hsplit(grid, width(grid)))
# TODO: test this
def top_row(grid):
return first(vsplit(grid, height(grid)))
# TODO: test this
def bottom_row(grid):
return last(vsplit(grid, height(grid)))
def first_quadrant(grid):
return tophalf(lefthalf(grid))
def second_quadrant(grid):
return tophalf(righthalf(grid))
def third_quadrant(grid):
return bottomhalf(lefthalf(grid))
def fourth_quadrant(grid):
return bottomhalf(righthalf(grid))
def identity(x):
""" identity function """
return x
def add(a, b):
""" addition """
if isinstance(a, int) and isinstance(b, int):
return a + b
elif isinstance(a, tuple) and isinstance(b, tuple):
return (a[0] + b[0], a[1] + b[1])
elif isinstance(a, int) and isinstance(b, tuple):
return (a + b[0], a + b[1])
return (a[0] + b, a[1] + b)
def subtract(a, b):
""" subtraction """
if isinstance(a, int) and isinstance(b, int):
return a - b
elif isinstance(a, tuple) and isinstance(b, tuple):
return (a[0] - b[0], a[1] - b[1])
elif isinstance(a, int) and isinstance(b, tuple):
return (a - b[0], a - b[1])
return (a[0] - b, a[1] - b)
def multiply(a, b):
""" multiplication """
if isinstance(a, int) and isinstance(b, int):
return a * b
elif isinstance(a, tuple) and isinstance(b, tuple):
return (a[0] * b[0], a[1] * b[1])
elif isinstance(a, int) and isinstance(b, tuple):
return (a * b[0], a * b[1])
return (a[0] * b, a[1] * b)
def divide(a, b):
""" floor division """
if isinstance(a, int) and isinstance(b, int):
return a // b
elif isinstance(a, tuple) and isinstance(b, tuple):
return (a[0] // b[0], a[1] // b[1])
elif isinstance(a, int) and isinstance(b, tuple):
return (a // b[0], a // b[1])
return (a[0] // b, a[1] // b)
def invert(n):
""" inversion with respect to addition """
return -n if isinstance(n, int) else (-n[0], -n[1])
def even(n):
""" evenness """
return n % 2 == 0
def double(n):
""" scaling by two """
return n * 2 if isinstance(n, int) else (n[0] * 2, n[1] * 2)
def halve(n):
""" scaling by one half """
return n // 2 if isinstance(n, int) else (n[0] // 2, n[1] // 2)
def flip(b):
""" logical not """
return not b
def equality(a, b):
""" equality """
return a == b
def contained(value, container):
""" element of """
return value in container
def combine(a, b):
""" union """
return type(a)((*a, *b))
def intersection(a, b):
""" returns the intersection of two containers """
return a & b
def difference(a, b):
""" difference """
return type(a)(e for e in a if e not in b)
def dedupe(iterable):
""" remove duplicates """
return tuple(e for i, e in enumerate(iterable) if iterable.index(e) == i)
def order(container, compfunc):
""" order container by custom key """
return tuple(sorted(container, key=compfunc))
def repeat(item, num):
""" repetition of item within vector """
return tuple(item for i in range(num))
def greater(a, b):
""" greater """
return a > b
def size(container):
""" cardinality """
return len(container)
def merge(containers):
""" merging """
return type(containers)(e for c in containers for e in c)
def maximum(container):
""" maximum """
return max(container, default=0)
def minimum(container):
""" minimum """
return min(container, default=0)
def valmax(container, compfunc):
""" maximum by custom function """
return compfunc(max(container, key=compfunc, default=0))
def valmin(container, compfunc):
""" minimum by custom function """
return compfunc(min(container, key=compfunc, default=0))
def argmax(container, compfunc):
""" largest item by custom order """
return max(container, key=compfunc, default=None)
def argmin(container, compfunc):
""" smallest item by custom order """
return min(container, key=compfunc, default=None)
def mostcommon(container):
""" most common item """
return max(set(container), key=container.count)
def leastcommon(container):
""" least common item """
return min(set(container), key=container.count)
def initset(value):
""" initialize container """
return frozenset({value})
def both(a, b):
""" logical and """
return a and b
def either(a, b):
""" logical or """
return a or b
def increment(x):
""" incrementing """
return x + 1 if isinstance(x, int) else (x[0] + 1, x[1] + 1)
def decrement(x):
""" decrementing """
return x - 1 if isinstance(x, int) else (x[0] - 1, x[1] - 1)
def crement(x):
""" incrementing positive and decrementing negative """
if isinstance(x, int):
return 0 if x == 0 else (x + 1 if x > 0 else x - 1)
return (
0 if x[0] == 0 else (x[0] + 1 if x[0] > 0 else x[0] - 1),
0 if x[1] == 0 else (x[1] + 1 if x[1] > 0 else x[1] - 1)
)
def sign(x):
""" sign """
if isinstance(x, int):
return 0 if x == 0 else (1 if x > 0 else -1)
return (
0 if x[0] == 0 else (1 if x[0] > 0 else -1),
0 if x[1] == 0 else (1 if x[1] > 0 else -1)
)
def positive(x):
""" positive """
return x > 0
def toivec(i):
""" vector pointing vertically """
return (i, 0)
def tojvec(j):
""" vector pointing horizontally """
return (0, j)
def sfilter(container, condition):
""" keep elements in container that satisfy condition """
return type(container)(e for e in container if condition(e))
def mfilter(container, function):
""" filter and merge """
return merge(sfilter(container, function))
def extract(container, condition):
""" first element of container that satisfies condition """
return next(e for e in container if condition(e))
def totuple(container):
""" conversion to tuple """
return tuple(container)
def first(container):
""" first item of container """
return next(iter(container))
def last(container):
""" last item of container """
return max(enumerate(container))[1]
def insert(value, container):
""" insert item into container """
return container.union(frozenset({value}))
def remove(value, container):
""" remove item from container """
return type(container)(e for e in container if e != value)
def other(container, value):
""" other value in the container """
return first(remove(value, container))
def interval(start, stop, step):
""" range """
return tuple(range(start, stop, step))
def astuple(a, b):
""" constructs a tuple """
return (a, b)
def product(a, b):
""" cartesian product """
return frozenset((i, j) for j in b for i in a)
def pair(a, b):
""" zipping of two tuples """
return tuple(zip(a, b))
def branch(condition, if_value, else_value):
""" if else branching """
return if_value if condition else else_value
def compose(outer, inner):
""" function composition """
return lambda x: outer(inner(x))
def chain(h, g, f):
""" function composition with three functions """
return lambda x: h(g(f(x)))
def matcher(function, target):
""" construction of equality function """
return lambda x: function(x) == target
def rbind(function, fixed):
""" fix the rightmost argument """
n = function.__code__.co_argcount
if n == 2:
return lambda x: function(x, fixed)
elif n == 3:
return lambda x, y: function(x, y, fixed)
else:
return lambda x, y, z: function(x, y, z, fixed)
def lbind(function, fixed):
""" fix the leftmost argument """
n = function.__code__.co_argcount
if n == 2:
return lambda y: function(fixed, y)
elif n == 3:
return lambda y, z: function(fixed, y, z)
else:
return lambda y, z, a: function(fixed, y, z, a)
def power(function, n):
""" power of function """
if n == 1:
return function
return compose(function, power(function, n - 1))
def fork(outer, a, b):
""" creates a wrapper function """
return lambda x: outer(a(x), b(x))
def apply(function, container):
""" apply function to each item in container """
return type(container)(function(e) for e in container)
def rapply(functions, value):
""" apply each function in container to value """
return type(functions)(function(value) for function in functions)
def mapply(function, container):
""" apply and merge """
return merge(apply(function, container))
def papply(function, a, b):
""" apply function on two vectors """
return tuple(function(i, j) for i, j in zip(a, b))
def mpapply(function, a, b):
""" apply function on two vectors and merge """
return merge(papply(function, a, b))
def prapply(function, a, b):
""" apply function on cartesian product """
return frozenset(function(i, j) for j in b for i in a)
def mostcolor(element):
""" most common color """
values = [v for r in element for v in r] if isinstance(element, tuple) else [v for v, _ in element]
return max(set(values), key=values.count)
def leastcolor(element):
""" least common color """
values = [v for r in element for v in r] if isinstance(element, tuple) else [v for v, _ in element]
return min(set(values), key=values.count)
def height(piece):
""" height of grid or patch """
if len(piece) == 0:
return 0
if isinstance(piece, tuple):
return len(piece)
return lowermost(piece) - uppermost(piece) + 1
def width(piece):
""" width of grid or patch """
if len(piece) == 0:
return 0
if isinstance(piece, tuple):
return len(piece[0])
return rightmost(piece) - leftmost(piece) + 1
def shape(piece):
""" height and width of grid or patch """
return (height(piece), width(piece))
def portrait(piece):
""" whether height is greater than width """
return height(piece) > width(piece)
def colorcount(element, value):
""" number of cells with color """
if isinstance(element, tuple):
return sum(row.count(value) for row in element)
return sum(v == value for v, _ in element)
def colorfilter(objs, value):
""" filter objects by color """
return frozenset(obj for obj in objs if next(iter(obj))[0] == value)
def sizefilter(container, n):
""" filter items by size """
return frozenset(item for item in container if len(item) == n)
def asindices(grid):
""" indices of all grid cells """
return frozenset((i, j) for i in range(len(grid)) for j in range(len(grid[0])))
def ofcolor(grid, value):
""" indices of all grid cells with value """
return frozenset((i, j) for i, r in enumerate(grid) for j, v in enumerate(r) if v == value)
def ulcorner(patch):
""" index of upper left corner """
return tuple(map(min, zip(*toindices(patch))))
def urcorner(patch):
""" index of upper right corner """
return tuple(map(lambda ix: {0: min, 1: max}[ix[0]](ix[1]), enumerate(zip(*toindices(patch)))))
def llcorner(patch):
""" index of lower left corner """
return tuple(map(lambda ix: {0: max, 1: min}[ix[0]](ix[1]), enumerate(zip(*toindices(patch)))))
def lrcorner(patch):
""" index of lower right corner """
return tuple(map(max, zip(*toindices(patch))))
def crop(grid, start, dims):
""" subgrid specified by start and dimension """
return tuple(r[start[1]:start[1]+dims[1]] for r in grid[start[0]:start[0]+dims[0]])
def toindices(patch):
""" indices of object cells """
if len(patch) == 0:
return frozenset()
if isinstance(next(iter(patch))[1], tuple):
return frozenset(index for value, index in patch)
return patch
def recolor(value, patch):
""" recolor patch """
return frozenset((value, index) for index in toindices(patch))
def shift(patch, directions):
""" shift patch """
if len(patch) == 0:
return patch
di, dj = directions
if isinstance(next(iter(patch))[1], tuple):
return frozenset((value, (i + di, j + dj)) for value, (i, j) in patch)
return frozenset((i + di, j + dj) for i, j in patch)
def normalize(patch):
""" moves upper left corner to origin """
if len(patch) == 0:
return patch
return shift(patch, (-uppermost(patch), -leftmost(patch)))
def dneighbors(loc):
""" directly adjacent indices """
return frozenset({(loc[0] - 1, loc[1]), (loc[0] + 1, loc[1]), (loc[0], loc[1] - 1), (loc[0], loc[1] + 1)})
def ineighbors(loc):
""" diagonally adjacent indices """
return frozenset({(loc[0] - 1, loc[1] - 1), (loc[0] - 1, loc[1] + 1), (loc[0] + 1, loc[1] - 1), (loc[0] + 1, loc[1] + 1)})
def neighbors(loc):
""" adjacent indices """
return dneighbors(loc) | ineighbors(loc)
def objects(grid, univalued, diagonal, without_bg):
""" objects occurring on the grid """
bg = mostcolor(grid) if without_bg else None
objs = set()
occupied = set()
h, w = len(grid), len(grid[0])
unvisited = asindices(grid)
diagfun = neighbors if diagonal else dneighbors
for loc in unvisited:
if loc in occupied:
continue
val = grid[loc[0]][loc[1]]
if val == bg:
continue
obj = {(val, loc)}
cands = {loc}
while len(cands) > 0:
neighborhood = set()
for cand in cands:
v = grid[cand[0]][cand[1]]
if (val == v) if univalued else (v != bg):
obj.add((v, cand))
occupied.add(cand)
neighborhood |= {
(i, j) for i, j in diagfun(cand) if 0 <= i < h and 0 <= j < w
}
cands = neighborhood - occupied
objs.add(frozenset(obj))
return frozenset(objs)
def partition(grid):
""" each cell with the same value part of the same object """
return frozenset(
frozenset(
(v, (i, j)) for i, r in enumerate(grid) for j, v in enumerate(r) if v == value
) for value in palette(grid)
)
def fgpartition(grid):
""" each cell with the same value part of the same object without background """
return frozenset(
frozenset(
(v, (i, j)) for i, r in enumerate(grid) for j, v in enumerate(r) if v == value
) for value in palette(grid) - {mostcolor(grid)}
)
def uppermost(patch):
""" row index of uppermost occupied cell """
return min(i for i, j in toindices(patch))
def lowermost(patch):
""" row index of lowermost occupied cell """
return max(i for i, j in toindices(patch))
def leftmost(patch):
""" column index of leftmost occupied cell """
return min(j for i, j in toindices(patch))
def rightmost(patch):
""" column index of rightmost occupied cell """
return max(j for i, j in toindices(patch))
def square(piece):
""" whether the piece forms a square """
return len(piece) == len(piece[0]) if isinstance(piece, tuple) else height(piece) * width(piece) == len(piece) and height(piece) == width(piece)
def vline(patch):
""" whether the piece forms a vertical line """
return height(patch) == len(patch) and width(patch) == 1
def hline(patch):
""" whether the piece forms a horizontal line """
return width(patch) == len(patch) and height(patch) == 1
def hmatching(a, b):
""" whether there exists a row for which both patches have cells """
return len(set(i for i, j in toindices(a)) & set(i for i, j in toindices(b))) > 0
def vmatching(a, b):
""" whether there exists a column for which both patches have cells """
return len(set(j for i, j in toindices(a)) & set(j for i, j in toindices(b))) > 0
def manhattan(a, b):
""" closest manhattan distance between two patches """
return min(abs(ai - bi) + abs(aj - bj) for ai, aj in toindices(a) for bi, bj in toindices(b))
def adjacent(a, b):
""" whether two patches are adjacent """
return manhattan(a, b) == 1
def bordering(patch, grid):
""" whether a patch is adjacent to a grid border """
return uppermost(patch) == 0 or leftmost(patch) == 0 or lowermost(patch) == len(grid) - 1 or rightmost(patch) == len(grid[0]) - 1
def centerofmass(patch):
""" center of mass """
return tuple(map(lambda x: sum(x) // len(patch), zip(*toindices(patch))))
def palette(element):
""" colors occurring in object or grid """
if isinstance(element, tuple):
return frozenset({v for r in element for v in r})
return frozenset({v for v, _ in element})
def numcolors(element):
""" number of colors occurring in object or grid """
return len(palette(element))
def color(obj):
""" color of object """
return next(iter(obj))[0]
def toobject(patch, grid):
""" object from patch and grid """
h, w = len(grid), len(grid[0])
return frozenset((grid[i][j], (i, j)) for i, j in toindices(patch) if 0 <= i < h and 0 <= j < w)
def asobject(grid):
""" conversion of grid to object """
return frozenset((v, (i, j)) for i, r in enumerate(grid) for j, v in enumerate(r))
def rot90(grid):
""" quarter clockwise rotation """
return tuple(row for row in zip(*grid[::-1]))
def rot180(grid):
""" half rotation """
return tuple(tuple(row[::-1]) for row in grid[::-1])
def rot270(grid):
""" quarter anticlockwise rotation """
return tuple(tuple(row[::-1]) for row in zip(*grid[::-1]))[::-1]
def hmirror(piece):
""" mirroring along horizontal """
if isinstance(piece, tuple):
return piece[::-1]
d = ulcorner(piece)[0] + lrcorner(piece)[0]
if isinstance(next(iter(piece))[1], tuple):
return frozenset((v, (d - i, j)) for v, (i, j) in piece)
return frozenset((d - i, j) for i, j in piece)