diff --git a/Project-Euler/Problem015.js b/Project-Euler/Problem015.js index f33a48b79..35b1aa807 100644 --- a/Project-Euler/Problem015.js +++ b/Project-Euler/Problem015.js @@ -4,10 +4,13 @@ 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? */ -const latticePath = n => { +//A lattice path is composed of horizontal and vertical lines that pass through lattice points. - for (var i = 1, c = 1; i <= n; i++) - c = c * (n + i) / i; - return c; +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)); +console.log(latticePath(20)); //output = 137846528820