983. Minimum Cost For Tickets

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. 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

M1: track calendar days
time = O(n) + O(365), space = O(365)

class Solution {
    public int mincostTickets(int[] days, int[] costs) {
        Set<Integer> set = new HashSet<>();
        for(int d : days) {
            set.add(d);
        }
        int[] dp = new int[366];
        Arrays.fill(dp, Integer.MAX_VALUE);
        dp[0] = 0;
        for(int i = 1; i <= 365; i++) {
            if(set.contains(i)) {
                dp[i] = Math.min(dp[i], dp[i - 1] + costs[0]);   // use 1-day pass
                dp[i] = Math.min(dp[i], dp[Math.max(i - 7, 0)] + costs[1]);     // check if used 7-day pass before
                dp[i] = Math.min(dp[i], dp[Math.max(i - 30, 0)] + costs[2]);    // check if used 15-day pass before
            } else {
                dp[i] = dp[i - 1];
            }
        }
        return dp[365];
    }
}

M2: track input days only

track the min cost for each travel day, store {day, cost} for 7-d and 15-d pass in two queues. after a pass 'expires', remove it from the queue

the queues only contains travel days for the last 7 and 30 days, and the cheapest pass prices are in the front of the queues

time = O(n), space = O(1 + 7 + 30)

class Solution {
    public int mincostTickets(int[] days, int[] costs) {
        Queue<int[]> last7 = new LinkedList<>();
        Queue<int[]> last30 = new LinkedList<>();
        int minCost = 0;
        for(int day : days) {
            while(!last7.isEmpty() && last7.peek()[0] + 7 <= day) {
                last7.poll();
            }
            while(!last30.isEmpty() && last30.peek()[0] + 30 <= day) {
                last30.poll();
            }
            last7.offer(new int[] {day, minCost + costs[1]});
            last30.offer(new int[] {day, minCost + costs[2]});
            minCost = Math.min(minCost + costs[0], Math.min(last7.peek()[1], last30.peek()[1]));
        }
        return minCost;
    }
}