31 lines
939 B
Python
31 lines
939 B
Python
#!/usr/bin/python3
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# Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner
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# How many such routes are there through a 20×20 grid?
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from math import factorial
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from timeit import default_timer
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def main():
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start = default_timer()
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# Using a combinatorial solution: in a 20x20 grid there will always be
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# 20 movements to the right and 20 movements down, that can be represented
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# as a string of Rs and Ds. The number of routes is the number of combinations.
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# This is obtained calculating n!/(k!*(n-k)!), where n=40 and k=20.
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count = factorial(40)
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tmp = factorial(20)
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tmp = tmp * tmp
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count = count // tmp
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end = default_timer()
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print('Project Euler, Problem 15')
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print('Answer: {}'.format(count))
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print('Elapsed time: {:.9f} seconds'.format(end - start))
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if __name__ == '__main__':
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main()
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