LC_Capacity_To_ship_packages_within_d_Days.py

"""
A conveyor belt has packages that must be shipped from one port to another within days days.

The ith 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 days days.

 

Example 1:

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

Constraints:

1 <= days <= weights.length <= 5 * 104
1 <= weights[i] <= 500
"""

class Solution:
    def shipWithinDays(self, weights: List[int], days: int) -> int:
        # Concepetually if we load capacity within days, we can certainly load up capacity+ within the days
        def isValid(capacity):
            # Start witht the first day
            d = 1
            rsum = 0
            
            # See if we can load it up
            for i in weights:
                rsum += i
                
                # anytime the weight goes over the capacity we need another day.
                if (rsum > capacity):
                    d += 1
                    rsum = i
                
                # No point if we have already crossed the allowed days
                if d > days:
                    return False
            # Since within return true
            return True
        
        # the minimum weight of the ship is the maximum of all the cargos on the conveyer belt
        start = max(weights)
        
        # The maximum weight is the sum of all the cargos considering we load everything up in a ship
        end = sum(weights)
        
        ans = -1
        # binary search between the two ends
        while(start <= end):
            mid = start + (end - start)//2
            
            # Check the validity condition
            if isValid(mid):
                # If valid move left and continue
                ans = mid
                end = mid-1
            else:
                # If false move right and continue
                start = mid+1
        return ans