2562. Count Ways To Build Good Strings

难度: Medium

题目描述

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

解题思路

代码实现

解决方案

java

class Solution {
    public int countGoodStrings(int low, int high, int zero, int one) {
        final int MOD = 1_000_000_007;
        int ans = 0;
        int[] f = new int[high + 1];
        f[0] = 1;

        for (int i = 1; i <= high; i++) {

            if (i >= zero && i >= one) {
                f[i] = (f[i - one] + f[i - zero]) % MOD;

            } else if (i >= zero) {
                f[i] = (f[i - zero]) % MOD;
            } else if (i >= one) {
                f[i] = (f[i - one]) % MOD;
            }
            if (i >= low) {
                ans = (ans + f[i]) % MOD;
            }
        }
        return ans;
    }
}