2021-07-04 13:53:20 +00:00
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// https://projecteuler.net/problem=15
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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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2021-07-07 19:34:04 +03:00
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// A lattice path is composed of horizontal and vertical lines that pass through lattice points.
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2021-07-04 13:53:20 +00:00
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2021-10-10 18:18:25 +02:00
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export const latticePath = (gridSize) => {
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2021-07-07 23:01:34 +05:30
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let paths
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for (let i = 1, paths = 1; i <= gridSize; i++) {
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2023-10-03 23:08:19 +02:00
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paths = (paths * (gridSize + i)) / i
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2021-07-07 23:01:34 +05:30
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}
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2021-07-07 19:34:04 +03:00
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// The total number of paths can be found using the binomial coefficient (b+a)/a.
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return paths
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2021-07-04 13:53:20 +00:00
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}
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2021-10-10 18:18:25 +02:00
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// > latticePath(20))
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// 137846528820
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