842.Split Array into Fibonacci Sequence

Given a string S of digits, such as S = "123456579", we can split it into a Fibonacci-like sequence [123, 456, 579].

Formally, a Fibonacci-like sequence is a list F of non-negative integers such that:

• 0 <= F[i] <= 2^31 - 1, (that is, each integer fits a 32-bit signed integer type);
• F.length >= 3;
• and F[i] + F[i+1] = F[i+2] for all 0 <= i < F.length - 2.

Also, note that when splitting the string into pieces, each piece must not have extra leading zeroes, except if the piece is the number 0 itself.

Return any Fibonacci-like sequence split from S, or return [] if it cannot be done.

Example 1:

Input: "123456579"
Output: [123,456,579]

Example 2:

Input: "11235813"
Output: [1,1,2,3,5,8,13]

Example 3:

Input: "112358130"
Output: []
Explanation: The task is impossible.

Example 4:

Input: "0123"
Output: []
Explanation: Leading zeroes are not allowed, so "01", "2", "3" is not valid.

Example 5:

Input: "1101111"
Output: [110, 1, 111]
Explanation: The output [11, 0, 11, 11] would also be accepted.

Note:

1. 1 <= S.length <= 200
2. S contains only digits.

class Solution:
    def splitIntoFibonacci(self, S):
        """
        :type S: str
        :rtype: List[int]
        """
        MAX = 2**31-1
        if len(S)<=2:
            return []
        def judge(s): #judge a string valid or not
            if len(s)==1:
                return True
            if len(s)==0:
                return False
            if s[0]=='0':
                return False
            return True
        def solve(i,j,res): #judge this method vaild or not
            res = []
            a,b = S[:i],S[i:j]
            if judge(a) is False or judge(b) is False:
                return []
            n1,n2 = int(a),int(b)
            if n1>MAX or n2>MAX:
                return []
            # print(n1,n2)
            res.append(n1)
            res.append(n2)
            while True:
                n3 = n1 + n2
                res.append(n3)
                c = str(n3)
                if j+len(c)>len(S) or n3!=int(S[j:j+len(c)]) or n3>MAX:
                    return []
                if j+len(c)==len(S):
                    return res
                n1 = n2
                n2 = n3
                j = j+len(c)
                # print('n2:',n2,'n1:',n1,'j:',j)
        for i in range(1,len(S)//2+1):
            for j in range(i+1,len(S)):
                # print(i,j)
                res = solve(i,j,[])
                if len(res)>0:
                    return res
        return []

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