Grumpy Bookstore Owner

class Solution {
public:
    int maxSatisfied(vector<int>& clientList, vector<int>& moodyList, int X) {
        int clientCount = clientList.size();
        int currentUnsatisfied = 0;

        // Calculate initial unsatisfied clients in the first X minutes
        for (int j = 0; j < X; j++) {
            currentUnsatisfied += clientList[j] * moodyList[j];
        }

        int maxUnsatisfied = currentUnsatisfied;

        // Sliding window to include one more and exclude the earliest
        for (int j = X; j < clientCount; j++) {
            currentUnsatisfied += clientList[j] * moodyList[j];
            currentUnsatisfied -= clientList[j - X] * moodyList[j - X];

            // Update the max unsatisfied customers in any window period
            maxUnsatisfied = max(maxUnsatisfied, currentUnsatisfied);
        }

        int totalPossibleSatisfied = maxUnsatisfied;

        // Calculate satisfied customers for non-moody periods
        for (int j = 0; j < clientCount; j++) {
            totalPossibleSatisfied += clientList[j] * (1 - moodyList[j]);
        }

        // Return the total possible satisfied customers
        return totalPossibleSatisfied;
    }
};

Solution Summary:

The C++ solution implements a sliding window technique to solve the "Grumpy Bookstore Owner" problem. The goal is to maximize the number of satisfied customers considering the store owner's grumpy periods represented as arrays.

• Initialize and calculate initial unsatisfied clients during the grumpy period of the owner using the first X minutes.
• Use a sliding window of size X to traverse the entire client list:
  • Incrementally calculate the unsatisfied count by adding the impact of the new time segment and subtracting the earliest time segment from the current unsatisfied count.
  • Keep track of the maximum unsatisfied customers for any period using the sliding window.
• After traversing with the sliding window, compute the total possible satisfied customers by summing up all customers who are satisfied when the owner is not grumpy and adding the maximum unsatisfied customers during the owner's grumpy period that could potentially be satisfied if those periods were handled optimally.
• The function ultimately returns the total number of possible satisfied customers given the optimal handling of the grumpy periods.

class Solution {

    public int maximizeSatisfaction(int[] clientele, int[] mood, int duration) {
        int length = clientele.length;
        int tempCustomers = 0;

        // Initial calculation for the first window of 'duration'
        for (int idx = 0; idx < duration; idx++) {
            tempCustomers += clientele[idx] * mood[idx];
        }

        int maxTempCustomers = tempCustomers;

        // Moving the window through the array
        for (int idx = duration; idx < length; idx++) {
            tempCustomers += clientele[idx] * mood[idx];
            tempCustomers -= clientele[idx - duration] * mood[idx - duration];

            maxTempCustomers = Math.max(
                maxTempCustomers,
                tempCustomers
            );
        }

        int maximumSatisfied = maxTempCustomers;

        // Include the satisfied customers when not grumpy
        for (int idx = 0; idx < clientele.length; idx++) {
            maximumSatisfied += clientele[idx] * (1 - mood[idx]);
        }

        return maximumSatisfied;
    }
}

The provided Java solution outlines a method to compute the maximum possible satisfaction in a bookstore, where the satisfaction is affected by the mood of the owner. The mood can either be grumpy or not, and this impacts the satisfaction of the clientele over a certain duration. The key steps of the solution include:

• Initialize temporary variables to store the current and maximum number of satisfied customers.
• Calculate initial satisfaction without the owner being grumpy for the first 'duration' period.
• Iteratively adjust the satisfied customers count by sliding the window of consideration across the entire period, adding the current index's potential satisfaction and removing the satisfaction that falls out of the window.
• Post the iterations, add the satisfaction derived from customers when the owner is not grumpy.
• The final result is the maximum satisfied customers which combine the best window of owner's grumpy mood and normal moods.

This approach leverages a sliding window technique to maintain efficient computation by reusing previously computed values and only updating them based on the current window, achieving an optimal solution.

class Solution:
    def maximumSatisfaction(
        self, customerCounts: List[int], grumpiness: List[int], X: int
    ) -> int:
        total_customers = len(customerCounts)
        potential_gain = 0

        # Calculate potential customers gain in the first 'X' interval
        for i in range(X):
            potential_gain += customerCounts[i] * grumpiness[i]

        max_gain = potential_gain

        # Sliding window method over the customers array
        for i in range(X, total_customers):
            # Adjust potential gain for the sliding window
            potential_gain += customerCounts[i] * grumpiness[i]
            potential_gain -= customerCounts[i - X] * grumpiness[i - X]

            # Record maximum potential gain seen so far
            max_gain = max(max_gain, potential_gain)

        # Calculate initial total satisfaction including alterations
        total_satisfaction = max_gain

        # Factor in the inherently satisfied customers during owner's good mood
        for i in range(total_customers):
            total_satisfaction += customerCounts[i] * (1 - grumpiness[i])

        # Result is the maximized number of satisfied customers
        return total_satisfaction

In Python3, the provided solution optimizes customer satisfaction in a bookstore where the owner has variable grumpiness levels, affecting the satisfaction of the patrons. Utilize a sliding window approach with the parameters customerCounts (number of customers per day), grumpiness (owner's grumpiness level per day as 1 or 0), and X (the number of consecutive days the owner tries to reduce grumpiness). Follow these steps to understand the solution methodology:

1. Initialize total_customers to quantify days under consideration.

2. Start by maximizing the potential number of satisfied customers during the initial window of X days. Multiply each day's customerCounts by grumpiness to add only the impacted customers.

3. Employ a sliding window technique to traverse beyond the first X days:

   • For each new day entering the window, calculate its potential contribution to satisfaction and adjust the potential_gain.
   • Subtract the effect of the day that moves out of the X window.
   • Update max_gain continuously to ensure it holds the maximum value of potential_gain found during sliding.

4. Determine the total satisfaction:

   • Aggregate the max_gain and the satisfaction from non-grumpy days (days when the owner wasn't grumpy regardless of alterations).

5. Output the total_satisfaction, which represents the maximized number of satisfied customers through strategic control of the owner's grumpiness over a defined range of days.

This solution leverages efficient iteration and condition checks, ensuring effective management of customer satisfaction with computational optimization through sliding window mechanics. This algorithm significantly enhances customer handling during the store owner's variable moods, potentially impacting the bookstore's customer relations positively.