<p>A conveyor belt has packages that must be shipped from one port to another within <code>days</code> days.</p>

<p>The <code>i<sup>th</sup></code> package on the conveyor belt has a weight of <code>weights[i]</code>. Each day, we load the ship with packages on the conveyor belt (in the order given by <code>weights</code>). We may not load more weight than the maximum weight capacity of the ship.</p>

<p>Return the least weight capacity of the ship that will result in all the packages on the conveyor belt being shipped within <code>days</code> days.</p>

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

<pre>
<strong>Input:</strong> weights = [1,2,3,4,5,6,7,8,9,10], days = 5
<strong>Output:</strong> 15
<strong>Explanation:</strong> A ship capacity of 15 is the minimum to ship all the packages in 5 days like this:
1st day: 1, 2, 3, 4, 5
2nd day: 6, 7
3rd day: 8
4th day: 9
5th day: 10

Note that the cargo must be shipped in the order given, so using a ship of capacity 14 and splitting the packages into parts like (2, 3, 4, 5), (1, 6, 7), (8), (9), (10) is not allowed.
</pre>

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

<pre>
<strong>Input:</strong> weights = [3,2,2,4,1,4], days = 3
<strong>Output:</strong> 6
<strong>Explanation:</strong> A ship capacity of 6 is the minimum to ship all the packages in 3 days like this:
1st day: 3, 2
2nd day: 2, 4
3rd day: 1, 4
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> weights = [1,2,3,1,1], days = 4
<strong>Output:</strong> 3
<strong>Explanation:</strong>
1st day: 1
2nd day: 2
3rd day: 3
4th day: 1, 1
</pre>

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

<ul>
	<li><code>1 &lt;= days &lt;= weights.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= weights[i] &lt;= 500</code></li>
</ul>

class Solution {
    bool isPossibleAt(const vector<int>&weights, const int current, const int limit, unordered_map<int,bool>&mp) {
        if (mp.find(current) != mp.end()) {
            return mp[current];
        }
        int sum = 0;
        if (current <= 0) {
            mp[current] = false;
            return false;
        }
        int counter = 1;
        for(int i=0;i<weights.size();i++) {
            if (weights[i] > current) {
                mp[current] = false;
                return false;
            }
            if (sum + weights[i] > current) {
                ++counter;
                sum = 0;
            }
            if (counter > limit) {
                mp[current] = false;
                return false;
            }
            sum = sum + weights[i];
        }
        mp[current] = true;
        return true;
    }
    int getIsFeasibleAt(const vector<int>&weights, const int days, const int st, const int ed, unordered_map<int,bool>& mp) {
        if (st > ed) {
            return ed;
        }
        int mid = (st + ed)/2;
        if (isPossibleAt(weights, mid, days, mp)) {
            if (isPossibleAt(weights, mid-1, days, mp)) {
                return getIsFeasibleAt(weights, days, st, mid-1, mp);
            } else {
                return mid;
            }
        } else {
            return getIsFeasibleAt(weights, days, mid+1, ed, mp);
        }
    }
public:
    int shipWithinDays(const vector<int>& weights, const int days) {
        int expectedAns = 0;
        unordered_map<int,bool>mp;
        for(auto pos: weights) {
            expectedAns += pos;
        }
        return getIsFeasibleAt(weights, days, 0, expectedAns, mp);
    }
};
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