#### Minimum Tickets Cost

R
```"""
Author  : Alexander Pantyukhin
Date    : November 1, 2022

Given a list of days when you need to travel. Each day is integer from 1 to 365.
You are able to use tickets for 1 day, 7 days and 30 days.
Each ticket has a cost.

Find the minimum cost you need to travel every day in the given list of days.

Implementation notes:
implementation Dynamic Programming up bottom approach.

Runtime complexity: O(n)

The implementation was tested on the
leetcode: https://leetcode.com/problems/minimum-cost-for-tickets/

Minimum Cost For Tickets
Dynamic Programming: up -> down.
"""

import functools

def mincost_tickets(days: list[int], costs: list[int]) -> int:
"""
>>> mincost_tickets([1, 4, 6, 7, 8, 20], [2, 7, 15])
11

>>> mincost_tickets([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31],  [2, 7, 15])
17

>>> mincost_tickets([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [2, 90, 150])
24

>>> mincost_tickets([2], [2, 90, 150])
2

>>> mincost_tickets([], [2, 90, 150])
0

>>> mincost_tickets('hello', [2, 90, 150])
Traceback (most recent call last):
...
ValueError: The parameter days should be a list of integers

>>> mincost_tickets([], 'world')
Traceback (most recent call last):
...
ValueError: The parameter costs should be a list of three integers

>>> mincost_tickets([0.25, 2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [2, 90, 150])
Traceback (most recent call last):
...
ValueError: The parameter days should be a list of integers

>>> mincost_tickets([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [2, 0.9, 150])
Traceback (most recent call last):
...
ValueError: The parameter costs should be a list of three integers

>>> mincost_tickets([-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [2, 90, 150])
Traceback (most recent call last):
...
ValueError: All days elements should be greater than 0

>>> mincost_tickets([2, 367], [2, 90, 150])
Traceback (most recent call last):
...
ValueError: All days elements should be less than 366

>>> mincost_tickets([2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [])
Traceback (most recent call last):
...
ValueError: The parameter costs should be a list of three integers

>>> mincost_tickets([], [])
Traceback (most recent call last):
...
ValueError: The parameter costs should be a list of three integers

>>> mincost_tickets([2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [1, 2, 3, 4])
Traceback (most recent call last):
...
ValueError: The parameter costs should be a list of three integers
"""

# Validation
if not isinstance(days, list) or not all(isinstance(day, int) for day in days):
raise ValueError("The parameter days should be a list of integers")

if len(costs) != 3 or not all(isinstance(cost, int) for cost in costs):
raise ValueError("The parameter costs should be a list of three integers")

if len(days) == 0:
return 0

if min(days) <= 0:
raise ValueError("All days elements should be greater than 0")

if max(days) >= 366:
raise ValueError("All days elements should be less than 366")

days_set = set(days)

@functools.cache
def dynamic_programming(index: int) -> int:
if index > 365:
return 0

if index not in days_set:
return dynamic_programming(index + 1)

return min(
costs[0] + dynamic_programming(index + 1),
costs[1] + dynamic_programming(index + 7),
costs[2] + dynamic_programming(index + 30),
)

return dynamic_programming(1)

if __name__ == "__main__":
import doctest

doctest.testmod()
```