[LeetCode] 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 <= D <= weights.length <= 50000
1 <= weights[i] <= 500

解题思路

二分查找。capacity取值的上限是所有获取的总重量，下限是以下两者的最小值：

1. 最大货物的重量。
2. 所有货物的总重量除以D。

实现代码

// Runtime: 7 ms, faster than 90.33% of Java online submissions for Capacity To Ship Packages Within D Days.
// Memory Usage: 42.7 MB, less than 100.00% of Java online submissions for Capacity To Ship Packages Within D Days.
class Solution {
    public int shipWithinDays(int[] weights, int D) {
        int left = 0;
        int right = 0;
        int sum = 0;
        for (int weight : weights) {
            sum += weight;
            left = Math.max(left, weight);
        }
        
        left = Math.max(left, sum / D);
        right = sum;
        while (left < right) {
            int mid = (left + right) / 2;
            int days = countDays(weights, mid);
            if (days <= D) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
    
    public int countDays(int[] weights, int capacity) {
        int days = 0;
        int curWeight = 0;
        for (int weight : weights) {
            if (curWeight + weight > capacity) {
                ++days;
                curWeight = weight;
            } else {
                curWeight += weight;
            }
        }
        
        if (curWeight > 0) {
            ++days;
        }
        
        return days;
    }
}