README.md

1416. Restore The Array

A program was supposed to print an array of integers. The program forgot to print whitespaces and the array is printed as a string of digits s and all we know is that all integers in the array were in the range [1, k] and there are no leading zeros in the array.

Given the string s and the integer k, return the number of the possible arrays that can be printed as s using the mentioned program. Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: s = "1000", k = 10000
Output: 1
Explanation: The only possible array is [1000]

Example 2:

Input: s = "1000", k = 10
Output: 0
Explanation: There cannot be an array that was printed this way and has all integer >= 1 and <= 10.

Example 3:

Input: s = "1317", k = 2000
Output: 8
Explanation: Possible arrays are [1317],[131,7],[13,17],[1,317],[13,1,7],[1,31,7],[1,3,17],[1,3,1,7]

Constraints:

• 1 <= s.length <= 105
• s consists of only digits and does not contain leading zeros.
• 1 <= k <= 109

Solutions (Python)

1. Solution

class Solution:
    def numberOfArrays(self, s: str, k: int) -> int:
        dp = [0] * (len(s) + 1)
        dp[0] = 1

        for i in range(len(s)):
            if s[i] == '0':
                continue

            x = int(s[i])
            j = 1

            while x <= k and i + j <= len(s):
                dp[i + j] = (dp[i + j] + dp[i]) % 1000000007
                if i + j < len(s):
                    x = x * 10 + int(s[i + j])
                j += 1

        return dp[-1]