1011. Capacity To Ship Packages Within D Days

LeetCode 1011. Capacity To Ship Packages Within D Days

Description

A conveyor belt has packages that must be shipped from one port to another within D 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 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

Constraints:

• 1 <= D <= weights.length <= 5 * 10^4

• 1 <= weights[i] <= 500

Tags

Array, Binary Search

Solution

We can perform binary search on capacities to find the least qualified weight capacity of the ship. The lower bound and the upper bound are max(weights) and sum(weights) respectively. We also adopt the greedy strategy, where we make each ship of certain capacity load packages as much as possible, to obtain the minimum days required given the weights and capacity. If the computed days is larger than the required days D, move lower bound to mid+1; otherwise, move upper bound to mid. Finally, we return the lower bound as we need the least weight capacity.

Complexity

• Time complexity: $O(n\log(\Sigma weights))$

• Space complexity: $O(1)$

Code

func shipWithinDays(weights []int, D int) int {
	var l, r int
	for _, w := range weights {
		if w > l {
			l = w
		}
		r += w
	}
	for l < r {
		mid := l + (r-l)/2
		if daysRequired(weights, mid) > D {
			l = mid + 1
		} else {
			r = mid
		}
	}
	return l
}

func daysRequired(weights []int, cap int) int {
	days, C := 1, cap // 1 for the last day
	for _, w := range weights {
		if w > cap {
			days++
			cap = C - w
		} else {
			cap -= w
		}
	}
	return days
}

Reference

1. 在 D 天内送达包裹的能力