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
. Each day is an integer from 1
to 365
.
Train tickets are sold in three different ways:
- a 1-day pass is sold for
costs[0]
dollars, - a 7-day pass is sold for
costs[1]
dollars, and - 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 for7
days:2
,3
,4
,5
,6
,7
, and8
.
Return the minimum number of dollars you need to travel every day in the given list of days.
Example 1:
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 2:
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.
Constraints:
-
1 <= days.length <= 365
-
1 <= days[i] <= 365
-
days
is in strictly increasing order. -
costs.length == 3
-
1 <= costs[i] <= 1000
SOLUTION:
import bisect
class Solution:
def mincost(self, days: List[int], costs: List[int], i) -> int:
n = len(days)
if i >= n:
return 0
if i in self.cache:
return self.cache[i]
today = days[i]
tomorrow = i + 1
nextweek = bisect.bisect_right(days, today + 6)
nextmonth = bisect.bisect_right(days, today + 29)
cost = min(costs[0] + self.mincost(days, costs, tomorrow), costs[1] + self.mincost(days, costs, nextweek), costs[2] + self.mincost(days, costs, nextmonth))
self.cache[i] = cost
return cost
def mincostTickets(self, days: List[int], costs: List[int], i = 0) -> int:
self.cache = {}
return self.mincost(days, costs, 0)
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