983.Minimum Cost For Tickets
===

###### tags: `Medium`,`Array`,`DP`

[983. Minimum Cost For Tickets](https://leetcode.com/problems/minimum-cost-for-tickets/)

### 題目描述

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 for `7` days: `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.*

### 範例

**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

### 解答
#### Javascript
##### 思路：
從頭開始遍歷，只要遇到出遊的日子就要買票，選擇1、7、30天中最便宜的更新`dp[i]`，`dp[i]`為第`i`天的最低花費。

function mincostTickets(days, costs) {
  const n = days[days.length - 1];
  const dp = new Array(n + 1).fill(0);
  for (let i = 1; i < n + 1; i++) {
    if (days.includes(i)) {
      const oneDay = dp[i - 1] + costs[0];
      const sevenDay = dp[Math.max(0, i - 7)] + costs[1];
      const thirtyDay = dp[Math.max(0, i - 30)] + costs[2];
      dp[i] = Math.min(oneDay, sevenDay, thirtyDay);
    } else {
      dp[i] = dp[i - 1];
    }
  }

  return dp[n];
}

> 要注意邊界問題，不然就會有神秘的錯誤QQ
> [name=Marsgoat][time=Mar 28, 2023]

#### Python

class Solution:
    def mincostTickets(self, days: List[int], costs: List[int]) -> int:
        start, end = days[0], days[-1]
        dp = [0] * (end + 1)

        for i in range(start, end + 1):
            if i in days:
                dp[i] = min(dp[i-1] + costs[0], dp[max(0, i-7)] + costs[1], dp[max(0, i-30)] + costs[2])
            else:
                dp[i] = dp[i-1]

        return dp[end]

> [name=Ron Chen][time=Tue, Mar 28, 2023]

### Reference

[回到題目列表](https://hackmd.io/@Marsgoat/leetcode_every_day)