Minimum Number of Days to Eat N Oranges

Problem

There are n oranges in the kitchen and you decided to eat some of these oranges every day as follows:

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

You can only choose one of the actions per day.

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

Example 1:

Input: n = 10
Output: 4
Explanation: You have 10 oranges.
Day 1: Eat 1 orange,  10 - 1 = 9.  
Day 2: Eat 6 oranges, 9 - 2*(9/3) = 9 - 6 = 3. (Since 9 is divisible by 3)
Day 3: Eat 2 oranges, 3 - 2*(3/3) = 3 - 2 = 1. 
Day 4: Eat the last orange  1 - 1  = 0.
You need at least 4 days to eat the 10 oranges.

Example 2:

Input: n = 6
Output: 3
Explanation: You have 6 oranges.
Day 1: Eat 3 oranges, 6 - 6/2 = 6 - 3 = 3. (Since 6 is divisible by 2).
Day 2: Eat 2 oranges, 3 - 2*(3/3) = 3 - 2 = 1. (Since 3 is divisible by 3)
Day 3: Eat the last orange  1 - 1  = 0.
You need at least 3 days to eat the 6 oranges.

Constraints:

1 <= n <= 2 * 10^9

Solution

class Solution {
    public int minDays(int n) {
        return eat(n, new HashMap<>());
    }

    private int eat(int n, Map<Integer, Integer> cache) {
        if (n <= 1) {
            return n;
        }
        Integer cached = cache.get(n);
        if (cached != null) {
            return cached;
        }
        int result = Math.min(n % 2 + eat(n / 2, cache), n % 3 + eat(n / 3, cache)) + 1;
        cache.put(n, result);
        return result;
    }
}

Explain:

nope.

Complexity:

Time complexity : O(n).
Space complexity : O(n).