## Algorithm

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.

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const n = num.length
for (let i = 1; i  < = (n / 2) >> 0; ++i) {
if (num.charAt(0) === '0' && i > 1) return false
const x1 = +num.slice(0, i)
for (let j = 1; Math.max(j, i)  < = n - i - j; ++j) {
if (num.charAt(i) == '0' && j > 1) break
const x2 = +num.slice(i, i + j)
if (isValid(x1, x2, j + i, num)) return true
}
}
return false
}

function isValid(x1, x2, start, num) {
if (start === num.length) return true
x2 = x2 + x1
x1 = x2 - x1
const sum = x2 + ''
return num.startsWith(sum, start) && isValid(x1, x2, start + sum.length, num)
}
``````
Copy The Code &

Input

cmd
"112358"

Output

cmd
true

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def getStarter():
arr = []
for i in range(1, len(num) - 1):
for j in range(i + 1, len(num)):
s1, s2 = num[:i], num[i:j]
if (s1[0] == "0" and len(s1) > 1) or (s2[0] == "0" and len(s2) > 1):
continue
arr.append((int(s1), int(s2), j))
return arr
def dfs(pre1, pre2, i):
if i == len(num):
return True
sm = pre1 + pre2
l = len(str(sm))
new = int(num[i:i + l])
return new == sm and dfs(pre2, new, i + l)
q = getStarter()
return any(dfs(p1, p2, i) for p1, p2, i in q)
``````
Copy The Code &

Input

cmd
"112358"

Output

cmd
true