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 <= 105s consists of only digits and does not contain leading zeros.1 <= k <= 109class Solution {
public:
int numberOfArrays(string s, int k) {
vector<int> dp(s.size(), -1); // dp[i] is number of ways to print valid arrays from string s start at i
return dfs(s, k, 0, dp);
}
int dfs(const string& s, long k, int i, vector<int>& dp) {
if (i == s.size()) return 1; // base case -> Found a valid way
if (s[i] == '0') return 0; // all numbers are in range [1, k] and there are no leading zeros -> So numbers starting with 0 mean invalid!
if (dp[i] != -1) return dp[i];
int ans = 0;
long num = 0;
for (int j = i; j < s.size(); j++) {
num = num * 10 + s[j] - '0'; // num is the value of the substring s[i..j]
if (num > k) break; // num must be in range [1, k]
ans += dfs(s, k, j + 1, dp);
ans %= 1000000007;
}
return dp[i] = ans;
}
};