feat(euler): 15 - Lattice paths

-

euler/src/15 - Lattice paths.ts

@@ -0,0 +1,14 @@
+// See https://github.com/newtykins/the-honk/tree/main/euler/thoughts/15%20-Lattice%20Paths.md
+export {};
+
+const factorial = (n: number) => {
+    if (n < 0) return -1;
+    else if (n === 0) return 1;
+    else return n * factorial(n - 1);
+};
+
+const countLatticePaths = (width: number, height: number) => {
+    return factorial(width + height) / (factorial(width) * factorial(height));
+};
+
+console.log(countLatticePaths(20, 20));

euler/thoughts/15 - Lattice paths.md

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+For a lattice with dimensions m x n, all paths will have m + n segments. m segments go down, n segments go right. To count m + n slots, count the ways to pick m downward moves - the rest will be rightward moves.
+
+![](assets/15.svg)
+
+### LaTeX
+
+```
+{m + n \choose m} = {m + n \choose n} = \frac{(m+n)!}{m!n!}
+```