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Calculate the average number of moves in a snakes and ladders game
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"""Calculate the average number of moves in a snakes and ladders game. | |
Because as a parent one gets roped into these board (boring?) games | |
every so often, and I wanted to calculate the average duration of a | |
snakes and ladders game. Turns out it's about 36 moves (though | |
admittedly that's for a single-player game). :-) | |
> python snakes_and_ladders.py | |
Played 10000 rounds, averaged 36.0559 moves, max 324 moves, took 0.508s | |
""" | |
from __future__ import division | |
import random | |
import time | |
try: | |
range = xrange # Make range a generator on Python 2.7 | |
except NameError: | |
pass | |
# Defines the snakes and ladders on the board. A low:high item | |
# represents a ladder going from low to high, whereas a high:low | |
# item represents a snake going from high to low. | |
SNAKES_LADDERS = { | |
1: 38, 4: 14, 9: 31, | |
16: 6, | |
21: 42, 28: 84, | |
36: 44, | |
48: 26, 49: 11, | |
51: 67, 56: 53, | |
62: 19, 64: 60, | |
71: 91, 80: 100, | |
87: 24, | |
93: 73, 95: 75, 98: 78, | |
} | |
MAX_SQUARE = 100 | |
MAX_MOVES = 100000 | |
def play_one(): | |
"""Play one game and return the number of moves it took.""" | |
square = 0 | |
for num_moves in range(1, MAX_MOVES + 1): | |
dice_roll = random.randrange(1, 7) | |
square += dice_roll | |
square = SNAKES_LADDERS.get(square, square) | |
if square >= MAX_SQUARE: | |
return num_moves | |
return MAX_MOVES | |
def play_all(num_rounds): | |
"""Play num_rounds games and return tuple of (total, max, time).""" | |
start_time = time.time() | |
total_moves = 0 | |
max_moves = 0 | |
for _ in range(num_rounds): | |
num_moves = play_one() | |
total_moves += num_moves | |
max_moves = max(max_moves, num_moves) | |
elapsed_time = time.time() - start_time | |
return (total_moves, max_moves, elapsed_time) | |
if __name__ == '__main__': | |
import argparse | |
parser = argparse.ArgumentParser() | |
parser.add_argument('-n', '--num-rounds', type=int, default=10000, | |
help='number of rounds (games) to play') | |
args = parser.parse_args() | |
total_moves, max_moves, elapsed_time = play_all(args.num_rounds) | |
print('Played {} rounds, averaged {} moves, max {} moves, took {:.3f}s'.format( | |
args.num_rounds, | |
total_moves / args.num_rounds, | |
max_moves, | |
elapsed_time, | |
)) |
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