permutation

Calculates the number of permutations (n permute r) using iterative method. Computes P(n, r) = n! / (n-r)! representing the number of ways to arrange r items from n total items where order matters. Uses efficient iterative calculation avoiding full factorial computation to prevent overflow.

Signature

const permutation: (n: number, r: number) => number

Parameters

Name	Type	Description
n	-	Total number of items (must be non-negative integer)
r	-	Number of items to arrange (must be non-negative integer)

Returns

Number of ways to arrange r items from n items

Examples

Basic permutation calculations

import { permutation } from '@winglet/common-utils';

console.log(permutation(5, 2)); // 20 (5×4 arrangements)
console.log(permutation(4, 3)); // 24 (4×3×2 arrangements)
console.log(permutation(6, 1)); // 6 (single item from 6)
console.log(permutation(3, 0)); // 1 (empty arrangement)
console.log(permutation(5, 5)); // 120 (all items: 5!)

Edge cases and impossible arrangements

// Impossible cases (r > n)
console.log(permutation(3, 5)); // 0
console.log(permutation(2, 10)); // 0

// Identity cases
console.log(permutation(10, 0)); // 1
console.log(permutation(0, 0)); // 1

// Large permutations
console.log(permutation(10, 3)); // 720
console.log(permutation(8, 4)); // 1680

Playground

import { permutation } from '@winglet/common-utils';

console.log(permutation(5, 2)); // 20 (5×4 arrangements)
console.log(permutation(4, 3)); // 24 (4×3×2 arrangements)
console.log(permutation(6, 1)); // 6 (single item from 6)
console.log(permutation(3, 0)); // 1 (empty arrangement)
console.log(permutation(5, 5)); // 120 (all items: 5!)

Notes

Mathematical Properties:

• P(n, 0) = 1 (empty arrangement)
• P(n, 1) = n (single item selection)
• P(n, n) = n! (full arrangement)
• P(n, r) = 0 when r > n
• Order matters (unlike combinations)

Use Cases:

• Arranging people in seats or positions
• Password generation with position constraints
• Tournament bracket arrangements
• Task scheduling with ordered dependencies
• Code generation with positional requirements
• Probability calculations for ordered outcomes

Performance: O(r) time complexity, O(1) space complexity. Much more efficient than factorial division for large n values.