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1553. Minimum Number of Days to Eat N Oranges (Hard)

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.

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.

Example 3:

Input: n = 1
Output: 1

Example 4:

Input: n = 56
Output: 6

 

Constraints:

• 1 <= n <= 2*10^9

Related Topics

[Dynamic Programming]

Hints

Hint 1

In each step, choose between 2 options: minOranges = 1 + min( (n%2) + f(n/2), (n%3) + f(n/3) ) where f(n) is the minimum number of days to eat n oranges.