feat(math): add factorial. permutation/combination fns

thi-ng · Jan 9, 2023 · 965af0d · 965af0d
1 parent e69a1c8
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diff --git a/packages/math/package.json b/packages/math/package.json
@@ -113,6 +113,9 @@
 		"./mix": {
 			"default": "./mix.js"
 		},
+		"./permutations": {
+			"default": "./permutations.js"
+		},
 		"./prec": {
 			"default": "./prec.js"
 		},

diff --git a/packages/math/src/index.ts b/packages/math/src/index.ts
@@ -10,6 +10,7 @@ export * from "./interval.js";
 export * from "./libc.js";
 export * from "./min-error.js";
 export * from "./mix.js";
+export * from "./permutations.js";
 export * from "./prec.js";
 export * from "./prime.js";
 export * from "./ratio.js";

diff --git a/packages/math/src/permutations.ts b/packages/math/src/permutations.ts
@@ -0,0 +1,53 @@
+/**
+ * Computes factorial for `n`. Throws an error if `n < 0`.
+ *
+ * @param n
+ */
+export const factorial = (n: number) => {
+	if (n < 0) throw new Error(`illegal argument: ${n}`);
+	let res = 1;
+	for (let i = 1; i <= n; i++) res *= i;
+	return res;
+};
+
+/**
+ * Computes `n ** k`
+ *
+ * @param n number of choices
+ * @param k number of selected
+ */
+export const permutationsWithRep = (n: number, k: number) => n ** k;
+
+/**
+ * Computes `n! / (n - k)!`
+ *
+ * @remarks
+ * Reference:
+ * https://en.wikipedia.org/wiki/Permutation#k-permutations_of_n
+ *
+ * @param n number of choices
+ * @param k number of selected
+ */
+export const permutationsWithoutRep = (n: number, k: number) =>
+	factorial(n) / factorial(n - k);
+
+/**
+ * Computes `(n + k - 1)! / (k! * (n - 1)!)`
+ *
+ * @param n number of choices
+ * @param k number of selected
+ */
+export const combinationsWithRep = (n: number, k: number) =>
+	factorial(n + k - 1) / (factorial(k) * factorial(n - 1));
+
+/**
+ * Computes `n! / (k! * (n - k)!)`
+ *
+ * @remarks
+ * https://en.wikipedia.org/wiki/Combination#Number_of_k-combinations
+ *
+ * @param n number of choices
+ * @param k number of selected
+ */
+export const combinationsWithoutRep = (n: number, k: number) =>
+	factorial(n) / (factorial(k) * factorial(n - k));