<p>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 <code>days</code>. Each day is an integer from <code>1</code> to <code>365</code>.</p>

<p>Train tickets are sold in <strong>three different ways</strong>:</p>

<ul>
	<li>a <strong>1-day</strong> pass is sold for <code>costs[0]</code> dollars,</li>
	<li>a <strong>7-day</strong> pass is sold for <code>costs[1]</code> dollars, and</li>
	<li>a <strong>30-day</strong> pass is sold for <code>costs[2]</code> dollars.</li>
</ul>

<p>The passes allow that many days of consecutive travel.</p>

<ul>
	<li>For example, if we get a <strong>7-day</strong> pass on day <code>2</code>, then we can travel for <code>7</code> days: <code>2</code>, <code>3</code>, <code>4</code>, <code>5</code>, <code>6</code>, <code>7</code>, and <code>8</code>.</li>
</ul>

<p>Return <em>the minimum number of dollars you need to travel every day in the given list of days</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> days = [1,4,6,7,8,20], costs = [2,7,15]
<strong>Output:</strong> 11
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> days = [1,2,3,4,5,6,7,8,9,10,30,31], costs = [2,7,15]
<strong>Output:</strong> 17
<strong>Explanation:</strong> 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.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= days.length &lt;= 365</code></li>
	<li><code>1 &lt;= days[i] &lt;= 365</code></li>
	<li><code>days</code> is in strictly increasing order.</li>
	<li><code>costs.length == 3</code></li>
	<li><code>1 &lt;= costs[i] &lt;= 1000</code></li>
</ul>

class Solution {
public:
    unordered_map<int, unordered_map<int, int>> dp;

    int dfs(vector<pair<int, int>>& tickets, vector<int>& days, int i, int remanining) {
        int o_i = i;
        int o_r = remanining;

        if (dp.find(o_i) != dp.end() && dp[o_i].find(o_r) != dp[o_i].end())
            return dp[o_i][o_r];

        do {
            if (i < days.size() && i - 1 >= 0)
                remanining = remanining - (days[i] - days[i - 1]);
            if (remanining > 0)
                ++i;
        } while(remanining > 0 && i < days.size());

        if (i >= days.size())
            return 0;

        int min_cost = INT32_MAX;
        for (pair<int, int>& p : tickets) {
            min_cost = min(min_cost, dfs(tickets, days, i + 1, p.first) + p.second);
        }

        dp[o_i][o_r] = min_cost;
        return min_cost;
    }

    int mincostTickets(vector<int>& days, vector<int>& costs) {
        vector<pair<int, int>> tickets;
        tickets.push_back({ 1, costs[0] });
        tickets.push_back({ 7, costs[1] });
        tickets.push_back({ 30, costs[2] });

        return dfs(tickets, days, 0, 0);
    }
};

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