983.MinimumCostForTickets.py

"""
    In a country popular for train travel, you have planned some train 
    travelling one year in advance.  The days of the year that you will travel 
    is given as an array days.  Each day is an integer from 1 to 365.
    Train tickets are sold in 3 different ways:
        - a 1-day pass is sold for costs[0] dollars;
        - a 7-day pass is sold for costs[1] dollars;
        - a 30-day pass is sold for costs[2] dollars.
    The passes allow that many days of consecutive travel.  For example, if we 
    get a 7-day pass on day 2, then we can travel for 7 days: 
    day 2, 3, 4, 5, 6, 7, and 8.
    Return the minimum number of dollars you need to travel every day in the 
    given list of days.

    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.

    Example:
    Input: days = [1,2,3,4,5,6,7,8,9,10,30,31], costs = [2,7,15]
    Output: 17
    Explanation: 
                 For example, here is one way to buy passes that lets you 
                 travel your travel plan:
                 On day 1, you bought a 30-day pass for costs[2] = $15 which 
                 covered days 1, 2, ..., 30.
                 On day 31, you bought a 1-day pass for costs[0] = $2 which 
                 covered day 31.
                 In total you spent $17 and covered all the days of your travel.

    Note:
        1. 1 <= days.length <= 365
        2. 1 <= days[i] <= 365
        3. days is in strictly increasing order.
        4. costs.length == 3
        5. 1 <= costs[i] <= 1000
"""
#Difficulty: Medium
#66 / 66 test cases passed.
#Runtime: 60 ms
#Memory Usage: 18.2 MB

from functools import lru_cache

class Solution:
    
    def mincostTickets(self, days, costs):
        self.costs = costs
        self.days = set(days)
        self.days_range = [1, 7, 30]
        return self.calculateBudget(1)

    @lru_cache(None)
    def calculateBudget(self, day):
            if day > 365:
                return 0
            elif day in self.days:
                return min(self.calculateBudget(day + days_range) + cost for cost, days_range in zip(self.costs, self.days_range))
            else:
                return self.calculateBudget(day + 1)