Eloquent Functions

exponential.ts

const exponential = (base: number, exponent: number): number =>
  exponent === 0 ? 1 : base * exponential(base, exponent - 1);

phi.ts

const calcPhi = (
  table: // TODO: Find a 'cleaner' way to express this!
  [number, number, number, number]
): number =>
  (table[3] * table[0] - table[2] * table[1]) /
  Math.sqrt(
    (table[2] + table[3]) *
      (table[0] + table[1]) *
      (table[1] + table[3]) *
      (table[0] + table[2])
  );

trace.ts

/**
 * TODO: By starting from the number 1 and
 * repeatedly either adding 5 or multiplying by 3,
 * an infinite set of numbers can be produced.
 * How would you write a function that, given a number,
 * tries to find a sequence of such additions and
 * multiplications that produces that number?
 */

const trace = (config: {
  current: number;
  target: number;
  history: string;
}): string | null => {
  // Dun!
  if (config.current === config.target) {
    return config.history;
  }

  // Over shot - trigger recursive unwinding by returning 'falsy'
  if (config.current > config.target) {
    return null;
  }

  return (
    trace({
      current: config.current + 5,
      target: config.target,
      history: `(${config.history} + 5)`,
    }) ||
    trace({
      current: config.current * 3,
      target: config.target,
      history: `(${config.history} * 3)`,
    })
  );
};

console.log(trace({ current: 1, target: 24, history: "1" }));