1011. Capacity To Ship Packages Within D Days

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1011. Capacity To Ship Packages Within D Days

Description

Difficulty: Medium

Related Topics: Array, Binary Search

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:

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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:

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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:

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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

Hints/Notes

  • Binary search to find the left boundary
  • Helper function to get how many days with specific capacity

Solution

Language: C++

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class Solution {
public:
    int shipTime(vector<int>& weights, int c) {
        int days = 0;
        for (int i = 0; i < weights.size();) {
            int sum = 0;
            while (sum <= c && i < weights.size()) {
                sum += weights[i++];
            }
            if (sum > c) {
                i--;
            }
            days++;
        }
        return days;
    }

    int shipWithinDays(vector<int>& weights, int days) {
        int left = 0, right = 0;
        for (int weight : weights) {
            if (weight > left) {
                left = weight;
            }
            right += weight;
        }
        while (left <= right) {
            int mid = left + (right - left) / 2;
            int time = shipTime(weights, mid);
            if (time == days) {
                right = mid - 1;
            } else if (time > days) {
                left = mid + 1;
            } else if (time < days) {
                right = mid - 1;
            }
        }
        return left;
    }
};