additive-number.js

/**
 * Additive Number
 *
 * Additive number is a string whose digits can form additive sequence.
 *
 * A valid additive sequence should contain at least three numbers. Except for the first two numbers,
 * each subsequent number in the sequence must be the sum of the preceding two.
 *
 * Given a string containing only digits '0'-'9', write a function to determine if it's an additive number.
 *
 * Note: Numbers in the additive sequence cannot have leading zeros, so sequence 1, 2, 03 or 1, 02, 3 is invalid.
 *
 * Example 1:
 *
 * Input: "112358"
 * Output: true
 * Explanation: The digits can form an additive sequence: 1, 1, 2, 3, 5, 8.
 *              1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8
 *
 * Example 2:
 *
 * Input: "199100199"
 * Output: true
 * Explanation: The additive sequence is: 1, 99, 100, 199.
 *              1 + 99 = 100, 99 + 100 = 199
 *
 * Follow up:
 * How would you handle overflow for very large input integers?
 */

/**
 * @param {string} num
 * @return {boolean}
 */
const isAdditiveNumber = num => {
  if (!num || num.length < 3) {
    return false;
  }

  for (let i = 0; i < num.length - 2; i++) {
    if (num[0] === '0' && i > 0) {
      break;
    }

    const num1 = parseInt(num.substring(0, i + 1));

    for (let j = i + 1; j < num.length - 1; j++) {
      if (num[i + 1] === '0' && j > i + 1) {
        break;
      }

      const num2 = parseInt(num.substring(i + 1, j + 1));

      if (isValid(num, j + 1, num1, num2)) {
        return true;
      }
    }
  }

  return false;
};

/**
 * @param {string} num
 * @param {number} start
 * @param {number} num1
 * @param {number} num2
 * @return {boolean}
 */
const isValid = (num, start, num1, num2) => {
  if (start === num.length) {
    return true;
  }

  for (let i = start; i < num.length; i++) {
    if (num[start] === '0' && i > start) {
      break;
    }

    const num3 = parseInt(num.substring(start, i + 1));

    if (num3 === num1 + num2) {
      return isValid(num, i + 1, num2, num3);
    }
  }

  return false;
};

export { isAdditiveNumber };