freeCodeCamp/curriculum/challenges/en/08-coding-interview-prep/project-euler/problem-15-lattice-paths.en.md

id, challengeType, title

id	challengeType	title
5900f37b1000cf542c50fe8e	5	Problem 15: Lattice paths

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

- text: <code>latticePaths(4)</code> should return 70.
  testString: 'assert.strictEqual(latticePaths(4), 70, ''<code>latticePaths(4)</code> should return 70.'');'
- text: <code>latticePaths(9)</code> should return 48620.
  testString: 'assert.strictEqual(latticePaths(9), 48620, ''<code>latticePaths(9)</code> should return 48620.'');'
- text: <code>latticePaths(20)</code> should return 137846528820.
  testString: 'assert.strictEqual(latticePaths(20), 137846528820, ''<code>latticePaths(20)</code> should return 137846528820.'');'

Challenge Seed

function latticePaths(gridSize) {
  // Good luck!
  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;
}