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.
Sample Input: weights = [1,2,3,4,5,6,7,8,9,10], days = 5
Expected Output: 15
Explanation: A ship capacity of 15 is the minimum to ship all the packages in 5 days like this:
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.
Constraints
1 <= days <= weights.length <= 5 * 1041 <= weights[i] <= 500
How We Solve This
- We don’t know the exact ship capacity, so we guess a capacity.
- For each guessed capacity, we simulate shipping:
- Load packages in order until the ship is full.
- Then start a new day.
- If it takes more than D days, the capacity is too small → increase it.
- If it takes D days or less, the capacity works → try a smaller one.
- Keep doing this using binary search until we find the minimum capacity that works.
Edge Cases to Consider
D = 1
weights = [3,2,2,4], D = 111All packages must ship in one day, so capacity is the total sum.
D >= Packages
weights = [5,1,2], D = 35You can ship one package per day, so capacity is the heaviest package.
Single Package
weights = [10], D = 410Capacity must be at least that package’s weight.