题解 | 将真分数分解为埃及分数

const readline = require('readline');

const rl = readline.createInterface({
    input: process.stdin,
    output: process.stdout
});
rl.on('line', function (line) {
  const [a, b] = line.split('/').map(Number);
  console.log(toEgyptionFraction(a, b));
});
function toEgyptionFraction(a, b) {
  /**
   * a/b > 1/n => n > b/a
   */
  const n = Math.ceil(b / a);
  /**
   * a/b = 1/n + (a/b - 1/n) = 1/n + (a*n - b)/(b*n)
   * 递归 (a*n - b, b*n) 直到 a*n - b = 0
   */
  a = a * n - b;
  if (a === 0) return '1/' + n;
  b = b * n;
  return '1/' + n + '+' + toEgyptionFraction(a, b);
}