Leetcode 306. Additive Number

Problem

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.

Algorithm

Use DFS to solve the problem, keeping track of the previous two numbers on the path, and continue searching forward if the condition is met.

Code

class Solution:
    def isAdditiveNumber(self, num: str) -> bool:
        nlen = len(num)
        def dfs(s, num1, num2, cnts):
            if s == nlen:
                return cnts >= 3

            for i in range(s, nlen):
                if s < i and num[s] == '0':
                    break
                num3 = int(num[s:i+1])
                if cnts >= 2 and num3 != num1 + num2: 
                    continue
                if dfs(i+1, num2, num3, cnts+1):
                    return True
            
            return False

        return dfs(0, 0, 0, 0)