Leetcode #983: Minimum Cost For Tickets
In this guide, we solve Leetcode #983 Minimum Cost For Tickets 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
You have planned some train traveling one year in advance. The days of the year in which you will travel are given as an integer array days.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, 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: days = [1,4,6,7,8,20], costs = [2,7,15]
Output: 11
Explanation: For example, here is one way to buy passes that lets you travel your travel plan:
On day 1, you bought a 1-day pass for costs[0] = $2, which covered day 1.
On day 3, you bought a 7-day pass for costs[1] = $7, which covered days 3, 4, ..., 9.
On day 20, you bought a 1-day pass for costs[0] = $2, which covered day 20.
In total, you spent $11 and covered all the days of your travel.
Python Solution
class Solution:
def mincostTickets(self, days: List[int], costs: List[int]) -> int:
def dfs(i: int) -> int:
if i >= n:
return 0
ans = inf
for c, v in zip(costs, valid):
j = bisect_left(days, days[i] + v)
ans = min(ans, c + dfs(j))
return ans
n = len(days)
valid = [1, 7, 30]
return dfs(0)
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.