## [Leetcode]983. Minimum Cost For Tickets (C++)

### 题目描述

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` dollars; a 7-day pass is sold for `costs` dollars; a 30-day pass is sold for `costs` 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`.

### 例子

#### 例子 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 = \$2, which covered day 1. On day 3, you bought a 7-day pass for costs = \$7, which covered days 3, 4, …, 9. On day 20, you bought a 1-day pass for costs = \$2, which covered day 20. In total you spent \$11 and covered all the days of your travel.

#### 例子 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 = \$15 which covered days 1, 2, …, 30. On day 31, you bought a 1-day pass for costs = \$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`

### 解题思路

• 一天前的最小花费 + 一天票钱
• 七天前的最小花费 + 七天票钱
• 30天前最小花费 + 30天票钱

``````#include <vector>
#include <bits/stdc++.h>

class Solution {
public:
int mincostTickets(std::vector<int>& days, std::vector<int>& costs) {

std::vector<int> min_costs(366, INT_MAX);
min_costs = 0;
for(int day: days) {
min_costs[day] = 0; // mark for travel days
}
for (int i = 1; i < 366; i++) {
if (min_costs[i] == INT_MAX) {
min_costs[i] = min_costs[i - 1];
} else {
int min_cost = min_costs[i - 1] + costs;
min_cost = std::min(min_costs[std::max(0, i - 7)] + costs, min_cost);
min_cost = std::min(min_costs[std::max(0, i - 30)] + costs, min_cost);
min_costs[i] = min_cost;
}
}

return min_costs.back();

}
};
``````
• 时间复杂度：O(1)—-常数时间（366）
• 空间复杂度：O(1)—-常数空间（366）