Additive Number

An additive number is a string whose digits can form an 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, return true if it is an additive number or false otherwise.

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:

• 1 <= num.length <= 35
• num consists only of digits.

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

SOLUTION:

class Solution:
    def getSeq(self, num, i, n, a, b, ctr):
        if i >= n:
            return ctr >= 3
        for j in range(i + 1, n + 1):
            curr = int(num[i:j])
            if a == None or b == None or curr == a + b:
                if self.getSeq(num, j, n, b, curr, ctr + 1):
                    return True
            if num[i] == "0":
                break
        return False

    def isAdditiveNumber(self, num: str) -> bool:
        return self.getSeq(num, 0, len(num), None, None, 0)