Additive Number

Description

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

 

Constraints:

• num consists only of digits '0'-'9'.
• 1 <= num.length <= 35

Follow up:
How would you handle overflow for very large input integers?

Solution(javascript)

/*
 * @lc app=leetcode id=306 lang=javascript
 *
 * [306] Additive Number
 */

// @lc code=start
/**
 * @param {string} num
 * @return {boolean}
 */
const isAdditiveNumber = function (num) {
  const invalid = (s = '') => s.length === 0 || (s[0] === '0' && s.length > 1)
  const dfs = (a = '', b = '', str = '') => {
    if (invalid(a) || invalid(b)) {
      return false
    }
    if (str === '') {
      return true
    }
    for (let i = 0; i < str.length; i++) {
      const c = str.slice(0, i + 1)
      if (!invalid(c) && parseInt(a, 10) + parseInt(b, 10) === parseInt(c, 10)) {
        if (dfs(b, c, str.slice(i + 1))) {
          return true
        }
      }
    }
    return false
  }
  for (let i = 1; i <= num.length - 2; i++) {
    for (let j = i + 1; j <= num.length - 1; j++) {
      if (dfs(num.slice(0, i), num.slice(i, j), num.slice(j))) {
        return true
      }
    }
  }
  return false
}
// @lc code=end

// console.log(
//   isAdditiveNumber(
//     '199100199',
//   ),
// )