Problem Description
There is a bookstore owner that has a store open for n minutes. You are given an integer array customers of length n where customers[i] is the number of the customers that enter the store at the start of the i-th minute and all those customers leave after the end of that minute. During certain minutes, the bookstore owner is grumpy. You are given a binary array grumpy where grumpy[i] is 1 if the bookstore owner is grumpy during the i-th minute, and is 0 otherwise. When the bookstore owner is grumpy, the customers entering during that minute are not satisfied. Otherwise, they are satisfied. The bookstore owner knows a secret technique to remain not grumpy for minutes consecutive minutes, but this technique can only be used once. Return the maximum number of customers that can be satisfied throughout the day.
Key Insights
- When the owner is not grumpy (grumpy[i] == 0), customers[i] are satisfied.
- We can use a sliding window approach to determine the best time to apply the technique to minimize customer dissatisfaction.
- The goal is to maximize the number of satisfied customers by strategically choosing the interval where the owner will not be grumpy.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
We will use a sliding window approach to find the optimal minutes during which the owner should not be grumpy. First, we will calculate the total number of satisfied customers when the owner is grumpy. Then, we will compute the maximum number of customers that can be satisfied by applying the technique over a specific range of minutes. The sliding window will allow us to efficiently calculate the number of unsatisfied customers during the grumpy minutes within the selected window and find the maximum possible satisfaction.