1416. Restore The Array
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
Solutions
Solution 1
Thinking
We must split \(s\) into integers in \([1,k]\) with no leading zeros. \(n\le 10^5\) rules out enumerating cuts. \(k\le 10^9\), so a number starting at \(i\) spans at most \(10\) digits.
Let \(f(i)\) be the number of ways to restore \(s[i:]\). A leading zero dies; otherwise try end indices \(j\) while the value is \(\le k\) and add \(f(j+1)\). Memoize or compute right to left.
The solution tabs in this problem are still empty; this is the standard transition the implementation should follow.
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