109 lines
2.6 KiB
Python
109 lines
2.6 KiB
Python
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from copy import copy
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from typing import Optional, Tuple
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CACHE = {}
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EMPTY = '⬛'
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FIELDS = ['🔴', '🟠', '🟡', '🟢', '🔵', '🟣', '⚪', '🟤', '⭐']
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# We use [row, col] indexing.
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BLOCKS = [
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((0, 0), (0, 1), (0, 2)), # dark blue
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((0, 0), (1, 0), (2, 0)), # black
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((0, 0), (0, 1), (1, 0)), # red
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((0, 0), (0, 1), (1, 1)), # green
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((0, 0), (1, 0), (1, 1)), # blue
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((0, 0), (1, 0), (1, -1)), # orange
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]
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class Field:
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def __init__(self, N_COLS, N_ROWS):
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self.N_COLS = N_COLS
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self.N_ROWS = N_ROWS
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self.state = 0
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def __hash__(self):
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return hash(self.state)
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def get_first_empty(self) -> Optional[Tuple[int, int]]:
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for row in range(self.N_ROWS):
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for col in range(self.N_COLS):
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if self.is_empty(row, col):
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return (row, col)
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return None
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def is_empty(self, row: int, col: int) -> bool:
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index = row * self.N_COLS + col
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result = not bool(self.state & (1 << index))
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return result
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def set(self, row: int, col: int):
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index = row * self.N_COLS + col
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self.state |= (1 << index)
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def __getitem__(self, row: int):
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return [self.is_empty(row, col) for col in range(self.N_COLS)]
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def print(self):
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for row in range(self.N_ROWS):
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row_str = ""
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for col in range(self.N_COLS):
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row_str += '⬛' if self.is_empty(row, col) else '⚪'
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print(row_str)
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def fits(field, block, coord):
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N_ROWS = field.N_ROWS
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N_COLS = field.N_COLS
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for rel_coord in block:
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abs_row = coord[0] + rel_coord[0]
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abs_col = coord[1] + rel_coord[1]
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if abs_row < 0 or abs_col < 0 or abs_row >= N_ROWS or abs_col >= N_COLS:
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return None
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if not field.is_empty(abs_row, abs_col):
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return None
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new_field = copy(field)
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for rel_coord in block:
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abs_row = coord[0] + rel_coord[0]
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abs_col = coord[1] + rel_coord[1]
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new_field.set(abs_row, abs_col)
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return new_field
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def count(field):
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global CACHE
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if hash(field) in CACHE:
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return CACHE[hash(field)]
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first_empty = field.get_first_empty()
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if first_empty is None:
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return 1
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result = 0
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for block in BLOCKS:
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if (new_field := fits(field, block, first_empty)) is not None:
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result += count(new_field)
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CACHE[hash(field)] = result
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return result
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def euler_161():
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return count(Field(9, 12))
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if __name__ == "__main__":
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solution = euler_161()
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print("e161.py: " + str(solution))
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assert(solution == 20574308184277971)
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