Leetcode #1402: Reducing Dishes
In this guide, we solve Leetcode #1402 Reducing Dishes 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
A chef has collected data on the satisfaction level of his n dishes. Chef can cook any dish in 1 unit of time.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Greedy, Array, Dynamic Programming, Sorting
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: satisfaction = [-1,-8,0,5,-9]
Output: 14
Explanation: After Removing the second and last dish, the maximum total like-time coefficient will be equal to (-1*1 + 0*2 + 5*3 = 14).
Each dish is prepared in one unit of time.
Python Solution
class Solution:
def maxSatisfaction(self, satisfaction: List[int]) -> int:
satisfaction.sort(reverse=True)
ans = s = 0
for x in satisfaction:
s += x
if s <= 0:
break
ans += s
return ans
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.