Can You Eat Your Favorite Candy on Your Favorite Day? - Video Solutions

Problem Overview: You are given an array candiesCount where each index represents how many candies exist for a type. Queries ask whether you can eat a candy of a specific type on a specific day while respecting two rules: you must eat at least one candy per day and at most dailyCap candies. The goal is to determine if reaching that candy type on that day is possible.

Approach 1: Direct Simulation (Brute Force) (Time: O(n * q), Space: O(1))

Simulate the candy consumption process for each query. For a query [favoriteType, favoriteDay, dailyCap], calculate how many candies you could have eaten by that day and check if the target candy type is reachable. This may involve iterating through previous candy types to compute totals each time. The method works but becomes slow when both the number of candy types and queries grow large because repeated summation is expensive.

Approach 2: Prefix Sum Calculation (Optimal) (Time: O(n + q), Space: O(n))

Precompute a prefix sum array where prefix[i] stores the total candies from type 0 to i. For each query, compute two ranges: the minimum candies you must have eaten by that day (favoriteDay + 1) and the maximum candies you could have eaten ((favoriteDay + 1) * dailyCap). The candies of the desired type occupy the range (prefix[type-1] + 1) to prefix[type]. If these two ranges overlap, it means reaching that candy type on that day is feasible. Prefix sums eliminate repeated summation and reduce each query to constant-time range checks.

This technique relies on cumulative totals, a common pattern when solving problems involving running counts across an array. The precomputation step transforms repeated work into a single pass, which is why prefix sum methods frequently appear in interview problems with many queries.

Recommended for interviews: The prefix sum approach is the expected solution. It demonstrates understanding of cumulative preprocessing and interval reasoning. Mentioning the direct simulation method first shows baseline reasoning, but using prefix sums to answer each query in O(1) time is what interviewers typically look for.