// https://projecteuler.net/problem=15
/* 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 20×20 grid?
*/

//A lattice path is composed of horizontal and vertical lines that pass through lattice points.

const latticePath = (gridSize) => {

    for (var i = 1, paths = 1; i <= gridSize; i++)
        //The total number of paths can be found using the binomial coefficient (b+a)/a.
        paths = paths * (gridSize + i) / i;
    return paths;
}
console.log(latticePath(20));  //output = 137846528820