Problem 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 10^9 + 7.
Key Insights
- The integers in the array must be in the range
[1, k]. - No leading zeros are allowed in any of the integers.
- We can use dynamic programming to count the number of ways to split the string into valid integers.
- Each valid split must respect the constraints imposed by
k.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(n)
Solution
To solve the problem, we can use dynamic programming. We define a DP array dp where dp[i] represents the number of ways to split the substring s[0:i] into valid integers. The base case is dp[0] = 1, representing the empty string.
We iterate through each position i in the string s, and for each position, we check all possible ending positions j (where j ranges from i-1 to max(0, i - len(str(k)))), ensuring that the substring s[j:i] forms a valid integer within the range [1, k]. If it does, we update our DP array accordingly.
Finally, the answer will be stored in dp[s.length()].