1.6 KiB
1.6 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f37b1000cf542c50fe8e | 5 | Problem 15: Lattice paths | 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
?
Instructions
Tests
tests:
- text: <code>latticePaths(4)</code> should return a number.
testString: assert(typeof latticePaths(4) === 'number');
- text: <code>latticePaths(4)</code> should return 70.
testString: assert.strictEqual(latticePaths(4), 70);
- text: <code>latticePaths(9)</code> should return 48620.
testString: assert.strictEqual(latticePaths(9), 48620);
- text: <code>latticePaths(20)</code> should return 137846528820.
testString: assert.strictEqual(latticePaths(20), 137846528820);
Challenge Seed
function latticePaths(gridSize) {
return true;
}
latticePaths(4);
Solution
function latticePaths(gridSize) {
let paths = 1;
for (let i = 0; i < gridSize; i++) {
paths *= (2 * gridSize) - i;
paths /= i + 1;
}
return paths;
}