<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:
 unordered_map<int, int> um;
    int tryWeight(int weight, vector<int>& weights, int days) {
        int daysRequired = 1;
        long int runningSum = 0;
        for (int i = 0; i < weights.size(); i++) {
            // cout << runningSum << '+' << weights[i] << '\n';
            if (runningSum + weights[i] > weight) {
                daysRequired++;
                runningSum = weights[i];
            } else {
                runningSum += weights[i];
            }
        }
        // cout << "daysreq " << daysRequired << " weight" << weight << '\n';
        um[weight] = daysRequired;
        return daysRequired;
    }
    int shipWithinDays(vector<int>& weights, int days) {
        // while correct weight not found, try correct weight , see how many
        // days itll take for that weight

        int minWeight = 0;
        int start = 0;
        int end = 0;
        for(int x : weights){
            end += x;
        }
        int mid = (start + end) / 2;
        int ans = 0;
        int minpossibleweight = INT_MIN;
        for(int x : weights){
            minpossibleweight = max(minpossibleweight, x);
        }
        while (start <= end && start <= mid) {
            mid = (start + end) / 2;
            int result = tryWeight(mid, weights, days);
            if (result <= days) {
                end = mid - 1;
                ans = mid;
            }
            if (result > days) {
                start = mid + 1;
                mid = (start + end) / 2;
            }
        }
        if(ans < minpossibleweight){
            ans = minpossibleweight;
        }
        if(days == 1){
            return ans;
        }
        for(int i = ans ; i >= 0; i--){
            int trial = 0;
            if(um.find(i) == um.end()){
                trial = tryWeight(i, weights, days);
            }else{
                trial = um.at(i);
            }
            if(trial <= days && i >= minpossibleweight){
                ans = i;
            }
        }
        return ans;
    }
};
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