1011. Capacity To Ship Packages Within D Days

Method 1

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

Method 1

【O(n * log(sum-max)) time | O(1) space】

package Leetcode.BinarySearch.FindMinimum;

import java.util.Arrays;

/**
 * @author zhengxingxing
 * @date 2025/04/29
 */
public class CapacityToShipPackagesWithinDDays {

    public static int shipWithinDays(int[] weights, int days) {
        // Initialize binary search boundaries
        // left = maximum single package weight (minimum possible capacity)
        int left = Arrays.stream(weights).max().getAsInt();
        // right = sum of all weights (maximum possible capacity)
        int right = Arrays.stream(weights).sum();

        // Binary search to find minimum capacity
        while (left < right){
            // Calculate middle point avoiding overflow
            int mid = left + (right - left)/2;

            // If current capacity is feasible, try lower capacity
            if (canShipWithinDays(weights, days, mid)){
                right = mid;
            }else {
                // If current capacity is not enough, need higher capacity
                left = mid + 1;
            }
        }
        // Return the minimum feasible capacity
        return left;
    }
    
    private static boolean canShipWithinDays(int[] weights, int days, int capacity) {
        // Start with day 1
        int currentDays = 1;
        // Track current day's load
        int currentLoad = 0;

        // Process each package
        for (int weight: weights) {
            // If adding current package exceeds capacity
            if (currentLoad + weight > capacity){
                // Move to next day
                currentDays++;
                // Start new day with current package
                currentLoad = weight;

                // If exceeded allowed days, return false
                if (currentDays > days){
                    return false;
                }
            }else{
                // Add package to current day's load
                currentLoad += weight;
            }
        }

        // Return true if all packages processed within allowed days
        return true;
    }
    
    public static void main(String[] args) {
        // Test Case 1: Multiple packages with sequential weights
        int[] weights1 = {1,2,3,4,5,6,7,8,9,10};
        int days1 = 5;
        System.out.println("Test Case 1 Result: " +
                shipWithinDays(weights1, days1));  // Expected output: 15

        // Test Case 2: Mixed weights with shorter duration
        int[] weights2 = {3,2,2,4,1,4};
        int days2 = 3;
        System.out.println("Test Case 2 Result: " +
                shipWithinDays(weights2, days2));  // Expected output: 6

        // Test Case 3: Small weights with more days
        int[] weights3 = {1,2,3,1,1};
        int days3 = 4;
        System.out.println("Test Case 3 Result: " +
                shipWithinDays(weights3, days3));  // Expected output: 3

        // Detailed explanation of Test Case 1
        System.out.println("\nShipping plan for Test Case 1:");
        System.out.println("With capacity 15:");
        System.out.println("Day 1: 1,2,3,4,5 (total=15)");
        System.out.println("Day 2: 6,7 (total=13)");
        System.out.println("Day 3: 8 (total=8)");
        System.out.println("Day 4: 9 (total=9)");
        System.out.println("Day 5: 10 (total=10)");
    }
}

Method 1

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