Count Ways To Build Good Strings

Problem

Given the integers zero, one, low, and high, we can construct a string by starting with an empty string, and then at each step perform either of the following:

Append the character '0' zero times.
Append the character '1' one times.

This can be performed any number of times.

A good string is a string constructed by the above process having a length between low and high (inclusive).

Return **the number of *different* good strings that can be constructed satisfying these properties.** Since the answer can be large, return it modulo 109 + 7.

Example 1:

Input: low = 3, high = 3, zero = 1, one = 1
Output: 8
Explanation: 
One possible valid good string is "011". 
It can be constructed as follows: "" -> "0" -> "01" -> "011". 
All binary strings from "000" to "111" are good strings in this example.

Example 2:

Input: low = 2, high = 3, zero = 1, one = 2
Output: 5
Explanation: The good strings are "00", "11", "000", "110", and "011".

Constraints:

1 <= low <= high <= 105
1 <= zero, one <= low

Solution (Java)

class Solution {
    public int countGoodStrings(int low, int high, int zero, int one) {
        int dp[] = new int[high + 1], res = 0, mod = 1000000007;
        dp[0] = 1;
        for (int i = 1; i <= high; ++i) {
            // if we can add 0 string then add 
            if (i >= zero) dp[i] = (dp[i] + dp[i - zero]) % mod;
            // if we can add 1's string i.e i >= len of 1's string
            if (i >= one) dp[i] = (dp[i] + dp[i - one]) % mod;
            // if i is in between low and high add 
            if (i >= low) res = (res + dp[i]) % mod;
        }
        return res;
    }
}

Explain:

nope.

Complexity:

Time complexity : O(n).
Space complexity : O(n).