How do you solve Minimum Number of Days to Eat N Oranges on LeetCode?

Minimum Number of Days to Eat N Oranges (LeetCode #1553) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Memoization significantly reduces redundant calculations.

What is the time complexity of Minimum Number of Days to Eat N Oranges?

The optimal solution for Minimum Number of Days to Eat N Oranges runs in O(n) time and uses O(n) space. The complexity is linear because we compute the result for each state from 1 to n only once, storing results in the memoization dictionary.

What is the brute force solution for Minimum Number of Days to Eat N Oranges?

The brute force approach for Minimum Number of Days to Eat N Oranges is Brute Force, with O(3^n) time complexity and O(n) space complexity. The brute force approach involves recursively trying all possible ways to eat the oranges, either by eating one, half, or two-thirds of them. This method explores every possible path until it finds the minimum days required. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Number of Days to Eat N Oranges?

Minimum Number of Days to Eat N Oranges uses the following concepts: Dynamic Programming, Memoization. The recommended patterns to study are: Memoization, Dynamic Programming.

What are the interview tips for Minimum Number of Days to Eat N Oranges?

Explain your thought process clearly, especially when transitioning from brute force to optimal. Discuss the trade-offs of different approaches. Practice explaining your code as if teaching someone else.

What are common mistakes when solving Minimum Number of Days to Eat N Oranges?

Not considering memoization leading to excessive recursion. Forgetting to check for base cases in recursion.

#1553

Minimum Number of Days to Eat N Oranges

Hard

Dynamic ProgrammingMemoizationMemoizationDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(3^n)	O(n)
Space	O(n)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses memoization to store results of previously computed states, avoiding redundant calculations. This significantly reduces the number of recursive calls needed.

⚙️

Algorithm

4 steps

1Step 1: Create a memoization dictionary to store results for each n.
2Step 2: Define a recursive function that checks if n is in the memo; if so, return the stored result.
3Step 3: If n is 0, return 0 (base case).
4Step 4: Calculate the minimum days for each eating option and store the result in the memo before returning it.

solution.py11 lines

1def minDays(n, memo={}) :
2    if n in memo:
3        return memo[n]
4    if n == 0:
5        return 0
6    memo[n] = 1 + min(
7        minDays(n - 1, memo),
8        minDays(n // 2, memo) if n % 2 == 0 else float('inf'),
9        minDays(n // 3, memo) if n % 3 == 0 else float('inf')
10    )
11    return memo[n]

ℹ

Complexity note: The complexity is linear because we compute the result for each state from 1 to n only once, storing results in the memoization dictionary.

1Memoization significantly reduces redundant calculations.
2Choosing the optimal eating strategy minimizes the number of days.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.