2562. Count Ways To Build Good Strings¶

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2562. Count Ways To Build Good Strings

Medium

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¶

class Solution {
    public int countGoodStrings(int low, int high, int zero, int one) {
        int[] dp = new int[high + 1];
        dp[0] = 1;
        int md = 1000000007;
        for (int i = Math.min(zero, one); i <= high; i++) {
            if (i >= zero) dp[i] = (dp[i] + dp[i - zero]) % md;
            if (i >= one) dp[i] = (dp[i] + dp[i - one]) % md;
        }
        int sum = 0;
        for (int i = low; i <= high; i++) sum = (sum + dp[i]) % md;
        return sum;
    }
}

Complexity Analysis¶

• Time Complexity: O(?)
• Space Complexity: O(?)

Approach¶

Detailed explanation of the approach will be added here