recur to loop

recur-to-loop.ts

import { test, expect, describe } from "vitest";

function recur(n: number, cur?: number): number {
  if (!cur) {
    cur = 0;
  }
  if (n < 2) {
    throw new Error("Invalid input");
  }
  if (n === 2) {
    return 1 / n + cur;
  }
  return recur(n - 1, cur + 1 / (n * (n - 1)));
}

function loop(n: number): number {
  let cur = 0;
  for (let i = n; i > 2; i--) {
    cur += 1 / (i * (i - 1));
  }
  cur += 1 / 2;
  return cur;
}

describe("test recur", () => {
  test("n = 2", () => {
    expect(loop(2)).toBe(recur(2));
  });
  test("n = 3", () => {
    expect(loop(3)).toBe(recur(3));
  });
  test("n = 4", () => {
    expect(loop(4)).toBe(recur(4));
  });
  test("n = 5", () => {
    expect(loop(5)).toBe(recur(5));
  });
});