1553. Minimum Number of Days to Eat N Oranges

Description

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 * 109

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(logn)
• Space complexity: O(logn)

 

JavaScript

/**
 * @param {number} n
 * @return {number}
 */
const minDays = function (n) {
  const memo = new Map();

  const eatOrange = oranges => {
    if (oranges <= 1) return oranges;
    if (memo.has(oranges)) return memo.get(oranges);
    const days2 = eatOrange(Math.floor(oranges / 2)) + (oranges % 2);
    const days3 = eatOrange(Math.floor(oranges / 3)) + (oranges % 3);
    const result = 1 + Math.min(days2, days3);

    memo.set(oranges, result);

    return result;
  };

  return eatOrange(n);
};