Leetcode #1553: Minimum Number of Days to Eat N Oranges
In this guide, we solve Leetcode #1553 Minimum Number of Days to Eat N Oranges in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Memoization, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
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.
Python Solution
class Solution:
def minDays(self, n: int) -> int:
def dfs(n: int) -> int:
if n < 2:
return n
return 1 + min(n % 2 + dfs(n // 2), n % 3 + dfs(n // 3))
return dfs(n)
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.