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.
2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
How many such routes are there through a 2020 grid?
20 grid?Prelude> :m Math.Combinat.Numbers
Prelude Math.Combinat.Numbers> 21 * catalan 20
137846528820
My first code is ... calculate so long long time.
latticeNo (x, 2) = x
latticeNo (2, y) = y
latticeNo (x, 3) = latticeNo (x - 1, 3) + x
latticeNo (3, y) = latticeNo (y - 1, 3) + y
latticeNo (x, y) = latticeNo (x - 1, y) + latticeNo (x, y - 1)
Second code is ... use combination. I'll try to know more general method.
Google tell me about Catalan number. See カタラン数
Google tell me about Catalan number. See カタラン数
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