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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 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.
Note:
1 <= days.length <= 365
1 <= days[i] <= 365
days
is in strictly increasing order.costs.length == 3
1 <= costs[i] <= 1000
思路:DP,dp[i]表示能满足i位置的情况下,需要的最小cost
class Solution(object):
def mincostTickets(self, days, costs):
"""
:type days: List[int]
:type costs: List[int]
:rtype: int
"""
days = [0]+days
n = len(days)
dp = [float('inf') for _ in range(n)] # for _ in range(n)]
dp[0] = 0
for i in range(1,n):
dp[i]=min(dp[i],dp[i-1]+costs[0])
for j in range(i):
if days[i]-days[j+1]<7:
dp[i]=min(dp[i], dp[j]+costs[1])
if days[i]-days[j+1]<30:
dp[i]=min(dp[i], dp[j]+costs[2])
return dp[-1]
s=Solution()
print(s.mincostTickets([1,5,8,9,10,12,13,16,17,18,19,20,23,24,29], [3,12,54]))
print(s.mincostTickets(days = [1,4,6,7,8,20], costs = [2,7,15]))
print(s.mincostTickets(days = [1,2,3,4,5,6,7,8,9,10,30,31], costs = [2,7,15]))