<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:
    int shipWithinDays(vector<int>& weights, int days) {
        vector<int> pre_sum{weights.at(0)};
        for (int i = 1; i < weights.size(); ++i) {
            pre_sum.push_back(pre_sum.at(i - 1) + weights.at(i));
        }
        int lo = pre_sum.at(0), hi = pre_sum.at(pre_sum.size() - 1);
        while (lo < hi) {
            int mid = (lo + hi) / 2;
            if (IsDaysGreaterTarget(pre_sum, mid, days)) {
                lo = mid + 1;
            } else {
                hi = mid;
            }
        }
        return hi;
    }
private:
    bool IsDaysGreaterTarget(const vector<int>& pre_sums, int load, const int days) {
        int pre_index = 0, pre_sum = 0;
        for (int day = 1; day <= days; ++day) {
            int cur_index = FindLowerBound(pre_sums, pre_sum + load, pre_index);
            if (cur_index == pre_sums.size() - 1) {
                return false;
            }
            pre_index = cur_index;
            pre_sum = pre_sums.at(cur_index);
        }
        return true;
    }
    int FindLowerBound(const vector<int>& pre_sum, int load, int start_index) {
        int lo = start_index, hi = pre_sum.size() - 1;
        while (lo < hi) {
            int mid = (lo + hi + 1) / 2;
            if (pre_sum.at(mid) > load) {
                hi = mid - 1;
            } else {
                lo = mid;
            }
        }
        return lo;
    }
};
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