Minimum Number of Days to Eat N Oranges

Problem Description

You have n oranges in the kitchen and you can eat some of these oranges every day in the following ways:

• Eat one orange.
• If the number of remaining oranges n is divisible by 2, you can eat n / 2 oranges.
• If the number of remaining oranges n is divisible by 3, you can eat 2 * (n / 3) oranges.

Given the integer n, return the minimum number of days to eat all n oranges.

Key Insights

• You can choose only one action per day.
• You should prioritize the actions that allow you to eat the maximum number of oranges.
• A recursive approach with memoization can be used to calculate the minimum days efficiently.
• The problem can be broken down into subproblems based on the number of oranges left.

Space and Time Complexity

Time Complexity: O(n) in the worst case, but due to memoization, it is efficient for large n. Space Complexity: O(n) for the memoization storage.

Solution

The solution involves a recursive function that calculates the minimum days needed to eat all oranges. The function considers all three options for eating oranges and uses memoization to avoid redundant calculations. The key data structure used here is a dictionary (or hash map) for storing results of previously computed states.

1. Define a recursive function that takes the number of oranges left.
2. Check if the result for this state is already computed (memoization).
3. Calculate the minimum days by considering the three eating options:
   • Eat one orange.
   • If divisible by 2, consider eating half.
   • If divisible by 3, consider eating two-thirds.
4. Return the minimum number of days required.

Code Solutions