1011. Capacity To Ship Packages Within D Days

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https://leetcode.com/problems/capacity-to-ship-packages-within-d-days/

A conveyor belt has packages that must be shipped from one port to another within D days.
The i-th package on the conveyor belt has a weight of weights[i].  Each day, we load the ship with packages on the conveyor belt (in the order given by weights). We may not load more weight than the maximum weight capacity of the ship.
Return the least weight capacity of the ship that will result in all the packages on the conveyor belt being shipped within D days.

Example 1:
Input: weights = [1,2,3,4,5,6,7,8,9,10], D = 5
Output: 15
Explanation: 
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.
Example 2:
Input: weights = [3,2,2,4,1,4], D = 3
Output: 6
Explanation: 
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
Example 3:
Input: weights = [1,2,3,1,1], D = 4
Output: 3
Explanation: 
1st day: 1
2nd day: 2
3rd day: 3
4th day: 1, 1

Note:
  1. 1 <= D <= weights.length <= 50000
  2. 1 <= weights[i] <= 500
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Related problems
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Intuition
 Two boundary cases

  1. Ship 1 package every single day => Required ship capacity = max (package weights)
  2. Ship all packages in 1 day => Required ship capacity = sum (all package weights)
Final answer is capacity in between max, and sum of all package weights
We can find answer with binary search, while maintaining answer <= mid 

We can build helper function for checking valid grouping 
Whats valid - number of days <= D => mid is valid, don't discard it, search for lower capacity => h = mid
Whats invalid - number of days > D => capacity = mid is insufficient => search from low = mid + 1

If mid is valid
Maintaining the order of packages is important when computing capacity

So keep adding packages
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