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dbl-linear.ts
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dbl-linear.ts
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/**
* @file dblLinear
* @module dblLinear
* @see https://codewars.com/kata/5672682212c8ecf83e000050
*/
/**
* Consider a sequence `u` where `u` is defined as follows:
*
* 1. The number `u(0) = 1` is the first one in `u`
* 2. For each `x` in `u`, `y = 2x + 1` and `z = 3x + 1` must be in `u` too
* 3. There are no other numbers in `u`
*
* Given an index, `n`, the function returns the element at `u(n)`.
*
* @example
* await dblLinear(0) // 1
* @example
* await dblLinear(10) // 22
* @example
* await dblLinear(100) // 447
* @example
* await dblLinear(7687) // 111718
*
* @param {number} n - Sequence element index
* @return {number} Element at `u(n)`
*/
function dblLinear(n: number): number {
/**
* Sequence.
*
* @const {number[]} u
*/
const u: number[] = [1]
/**
* Index of x in {@linkcode u} used to calculate y.
*
* @var {number} j
*/
let j: number = 0
/**
* Index of x in {@linkcode u} used to calculate z.
*
* @var {number} j
*/
let k: number = 0
// build sequence up to index n (inclusive)
for (let i = 1; i <= n; i++) {
/**
* `y`.
*
* @const {number} y
*/
const y: number = 2 * u[j]! + 1
/**
* `z`.
*
* @const {number} z
*/
const z: number = 3 * u[k]! + 1
// set sequence value to smallest value in [y, z]
u[i] = Math.min(y, z)
if (u[i] === y) j++
if (u[i] === z) k++
}
return u[n]!
}
export default dblLinear