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
.
Input: s = "1000", k = 10000 Output: 1 Explanation: The only possible array is [1000]
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.
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]
1 <= s.length <= 105
s
consists of only digits and does not contain leading zeros.1 <= k <= 109
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]