<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 {
public:
    bool check(int capacity, vector<int>& weights, int days) {
        int count = 1;
        int currentWeight = 0;

        for (int weight : weights) {
            if (currentWeight + weight > capacity) {
                count++;
                currentWeight = weight;
                if (count > days) return false;
            } else {
                currentWeight += weight;
            }
        }

        return true;
    }
    
    int shipWithinDays(vector<int>& weights, int days) {
        int n = weights.size();
        int maxWeight = INT_MIN;
        int sumWeight = 0;

        for (int weight : weights) {
            maxWeight = max(maxWeight, weight);
            sumWeight += weight;
        }

        int low = maxWeight;
        int high = sumWeight;
        int minCapacity = sumWeight;

        while (low <= high) {
            int mid = low + (high - low) / 2;
            if (check(mid, weights, days)) {
                minCapacity = mid;
                high = mid - 1;
            } else {
                low = mid + 1;
            }
        }

        return minCapacity;
    }
};

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