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# 1416.Restore-The-Array

## 题目描述

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 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. There can be multiple ways to restore the array.
Return the number of possible array that can be printed as a string s using the mentioned program.
The number of ways could be very large so return it modulo 10^9 + 7
Example 1:
Input: s = "1000", k = 10000
Output: 1
Explanation: The only possible array is 
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 ,[131,7],[13,17],[1,317],[13,1,7],[1,31,7],[1,3,17],[1,3,1,7]
Example 4:
Input: s = "2020", k = 30
Output: 1
Explanation: The only possible array is [20,20].  is invalid because 2020 > 30. [2,020] is ivalid because 020 contains leading zeros.
Example 5:
Input: s = "1234567890", k = 90
Output: 34
Constraints:
1 <= s.length <= 10^5.
s consists of only digits and doesn't contain leading zeros.
1 <= k <= 10^9.

## 代码

### Approach #1 DFS

Time: `O(n * log10(k))` && Space: O(n)
Explain: There are total `n` states, each state needs maximum `log10(k)` iteration loops to calculate the result.
class Solution {
public int numberOfArrays(String s, int k) {
int[] memo = new int[s.length()];
Arrays.fill(memo, -1);
return dfs(s, k, memo, 0);
}
private int dfs(String s, int k, int[] memo, int i) {
if (i == s.length()) return 1;
if (s.charAt(i) == '0') return 0;
if (memo[i] != -1) return memo[i];
int ans = 0;
long num = 0;
for (int j = i; j < s.length(); j++) {
num = num * 10 + s.charAt(j) - '0';
if (num > k) break;
ans += dfs(s, k, memo, j + 1);
ans %= 1000_000_007;
}
memo[i] = ans;
return ans;
}
}

### Approach #2 DP

Time: `O(n log k)` Space: `O(n)`
class Solution {
int mod = (int)1e9 + 7;
public int numberOfArrays(String s, int k) {
if (s == null || s.length() == 0) return 0;
int n = s.length();
int[] dp = new int[n + 1];
dp[n] = 1; // initial
for (int i = n - 1; i >= 0; i--) {
long num = s.charAt(i) - '0'; // long
if (num != 0) {
for (int j = i + 1; j <= n; j++) {
if (num > k) break;
dp[i] = (dp[i] + dp[j]) % mod;
if (j < n) {
num = num * 10 + s.charAt(j) - '0';
}
}
} else {
dp[i] = 0;
}
}
return dp;
}
}