1.3 KiB
1.3 KiB
id | title | challengeType | forumTopicId |
---|---|---|---|
5900f37b1000cf542c50fe8e | Problem 15: Lattice paths | 5 | 301780 |
--description--
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.
How many such routes are there through a given gridSize
?
--hints--
latticePaths(4)
should return a number.
assert(typeof latticePaths(4) === 'number');
latticePaths(4)
should return 70.
assert.strictEqual(latticePaths(4), 70);
latticePaths(9)
should return 48620.
assert.strictEqual(latticePaths(9), 48620);
latticePaths(20)
should return 137846528820.
assert.strictEqual(latticePaths(20), 137846528820);
--seed--
--seed-contents--
function latticePaths(gridSize) {
return true;
}
latticePaths(4);
--solutions--
function latticePaths(gridSize) {
let paths = 1;
for (let i = 0; i < gridSize; i++) {
paths *= (2 * gridSize) - i;
paths /= i + 1;
}
return paths;
}