Description
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 <= 105sconsists of only digits and does not contain leading zeros.1 <= k <= 109
Solution
Python3
class Solution:
def numberOfArrays(self, s: str, k: int) -> int:
N = len(s)
MOD = 10 ** 9 + 7
@cache
def go(index):
if index == N: return 1
if s[index] == '0': return 0
res = curr = 0
for i in range(index, N):
curr = curr * 10 + int(s[i])
if curr > k: break
res += go(i + 1)
res %= MOD
return res % MOD
return go(0)