mirror of
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4d0a8f2355
* optimized recursive_bubble_sort
* Fixed doctest error due whitespace
* reduce loop times for optimization
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
56 lines
1.6 KiB
Python
56 lines
1.6 KiB
Python
"""
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Starting in the top left corner of a 2×2 grid, and only being able to move to
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the right and down, there are exactly 6 routes to the bottom right corner.
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How many such routes are there through a 20×20 grid?
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"""
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from math import factorial
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def lattice_paths(n):
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"""
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Returns the number of paths possible in a n x n grid starting at top left
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corner going to bottom right corner and being able to move right and down
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only.
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bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 50
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1.008913445455642e+29
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bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 25
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126410606437752.0
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bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 23
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8233430727600.0
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bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 15
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155117520.0
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bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 1
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2.0
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>>> lattice_paths(25)
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126410606437752
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>>> lattice_paths(23)
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8233430727600
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>>> lattice_paths(20)
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137846528820
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>>> lattice_paths(15)
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155117520
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>>> lattice_paths(1)
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2
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"""
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n = 2 * n # middle entry of odd rows starting at row 3 is the solution for n = 1,
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# 2, 3,...
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k = n / 2
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return int(factorial(n) / (factorial(k) * factorial(n - k)))
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if __name__ == "__main__":
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import sys
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if len(sys.argv) == 1:
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print(lattice_paths(20))
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else:
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try:
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n = int(sys.argv[1])
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print(lattice_paths(n))
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except ValueError:
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print("Invalid entry - please enter a number.")
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