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.

Example:

“112358” is an additive number because 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 “199100199” is also an additive number, the additive sequence is: 1, 99, 100, 199. 1 + 99 = 100, 99 + 100 = 199

Note:

Numbers in the additive sequence cannot have leading zeros, so sequence 1, 2, 03 or 1, 02, 3 is invalid.

Given a string containing only digits ‘0’-‘9’, write a function to determine if it’s an additive number.

Follow up:

How would you handle overflow for very large input integers?

Solution

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

class Solution(object):
    def isAdditiveNumber(self, num):
        """
        :type num: str
        :rtype: bool
        """
  n = len(num)
        for i,j in itertools.combinations(range(1,n),2):
            # 得到第一个数和第二个数
            a, b = num[:i], num[i:j]
            # a = "01" 以0开始
            if a != str(int(a)) or b != str(int(b)):
                continue
            while j < n:
                # c: 第三个数应该是多少
                c = str(int(a) + int(b))

                # 第三个数实际并不是c
                if not num.startswith(c,j):
                    break
                j += len(c)
                a,b = b,c
                if j == n:
                    return True
        return False