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
class Solution {
Map<Integer, Integer> map;
public int minDays(int n) {
map = new HashMap<>();
return helper(n);
}
private int helper(int n) {
if (n <= 1)
return n;
if (map.containsKey(n))
return map.get(n);
int ans = Integer.MAX_VALUE;
// 1 -> Divide step, n%2 or n%3 represents the steps of -1
// to reach the closest multiple or 2 or 3
ans = Math.min(ans, helper(n / 2) + n % 2 + 1);
ans = Math.min(ans, helper(n / 3) + n % 3 + 1);
map.put(n, ans);
return ans;
}
}