LeetCode #1687 — HARD

Delivering Boxes from Storage to Ports

Break down a hard problem into reliable checkpoints, edge-case handling, and complexity trade-offs.

Solve on LeetCode
The Problem

Problem Statement

You have the task of delivering some boxes from storage to their ports using only one ship. However, this ship has a limit on the number of boxes and the total weight that it can carry.

You are given an array boxes, where boxes[i] = [ports​​i​, weighti], and three integers portsCount, maxBoxes, and maxWeight.

  • ports​​i is the port where you need to deliver the ith box and weightsi is the weight of the ith box.
  • portsCount is the number of ports.
  • maxBoxes and maxWeight are the respective box and weight limits of the ship.

The boxes need to be delivered in the order they are given. The ship will follow these steps:

  • The ship will take some number of boxes from the boxes queue, not violating the maxBoxes and maxWeight constraints.
  • For each loaded box in order, the ship will make a trip to the port the box needs to be delivered to and deliver it. If the ship is already at the correct port, no trip is needed, and the box can immediately be delivered.
  • The ship then makes a return trip to storage to take more boxes from the queue.

The ship must end at storage after all the boxes have been delivered.

Return the minimum number of trips the ship needs to make to deliver all boxes to their respective ports.

Example 1:

Input: boxes = [[1,1],[2,1],[1,1]], portsCount = 2, maxBoxes = 3, maxWeight = 3
Output: 4
Explanation: The optimal strategy is as follows: 
- The ship takes all the boxes in the queue, goes to port 1, then port 2, then port 1 again, then returns to storage. 4 trips.
So the total number of trips is 4.
Note that the first and third boxes cannot be delivered together because the boxes need to be delivered in order (i.e. the second box needs to be delivered at port 2 before the third box).

Example 2:

Input: boxes = [[1,2],[3,3],[3,1],[3,1],[2,4]], portsCount = 3, maxBoxes = 3, maxWeight = 6
Output: 6
Explanation: The optimal strategy is as follows: 
- The ship takes the first box, goes to port 1, then returns to storage. 2 trips.
- The ship takes the second, third and fourth boxes, goes to port 3, then returns to storage. 2 trips.
- The ship takes the fifth box, goes to port 2, then returns to storage. 2 trips.
So the total number of trips is 2 + 2 + 2 = 6.

Example 3:

Input: boxes = [[1,4],[1,2],[2,1],[2,1],[3,2],[3,4]], portsCount = 3, maxBoxes = 6, maxWeight = 7
Output: 6
Explanation: The optimal strategy is as follows:
- The ship takes the first and second boxes, goes to port 1, then returns to storage. 2 trips.
- The ship takes the third and fourth boxes, goes to port 2, then returns to storage. 2 trips.
- The ship takes the fifth and sixth boxes, goes to port 3, then returns to storage. 2 trips.
So the total number of trips is 2 + 2 + 2 = 6.

Constraints:

  • 1 <= boxes.length <= 105
  • 1 <= portsCount, maxBoxes, maxWeight <= 105
  • 1 <= ports​​i <= portsCount
  • 1 <= weightsi <= maxWeight
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You have the task of delivering some boxes from storage to their ports using only one ship. However, this ship has a limit on the number of boxes and the total weight that it can carry. You are given an array boxes, where boxes[i] = [ports​​i​, weighti], and three integers portsCount, maxBoxes, and maxWeight. ports​​i is the port where you need to deliver the ith box and weightsi is the weight of the ith box. portsCount is the number of ports. maxBoxes and maxWeight are the respective box and weight limits of the ship. The boxes need to be delivered in the order they are given. The ship will follow these steps: The ship will take some number of boxes from the boxes queue, not violating the maxBoxes and maxWeight constraints. For each loaded box in order, the ship will make a trip to the port the box needs to be delivered to and deliver it. If the ship is already at the correct port, no

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Dynamic Programming · Segment Tree · Monotonic Queue

Example 1

[[1,1],[2,1],[1,1]]
2
3
3

Example 2

[[1,2],[3,3],[3,1],[3,1],[2,4]]
3
3
6

Example 3

[[1,4],[1,2],[2,1],[2,1],[3,2],[3,4]]
3
6
7
Step 02

Core Insight

What unlocks the optimal approach

  • Try to think of the most basic dp which is n^2 now optimize it
  • Think of any range query data structure to optimize
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Largest constraint values
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1687: Delivering Boxes from Storage to Ports
class Solution {
    public int boxDelivering(int[][] boxes, int portsCount, int maxBoxes, int maxWeight) {
        int n = boxes.length;
        long[] ws = new long[n + 1];
        int[] cs = new int[n];
        for (int i = 0; i < n; ++i) {
            int p = boxes[i][0], w = boxes[i][1];
            ws[i + 1] = ws[i] + w;
            if (i < n - 1) {
                cs[i + 1] = cs[i] + (p != boxes[i + 1][0] ? 1 : 0);
            }
        }
        int[] f = new int[n + 1];
        Deque<Integer> q = new ArrayDeque<>();
        q.offer(0);
        for (int i = 1; i <= n; ++i) {
            while (!q.isEmpty()
                && (i - q.peekFirst() > maxBoxes || ws[i] - ws[q.peekFirst()] > maxWeight)) {
                q.pollFirst();
            }
            if (!q.isEmpty()) {
                f[i] = cs[i - 1] + f[q.peekFirst()] - cs[q.peekFirst()] + 2;
            }
            if (i < n) {
                while (!q.isEmpty() && f[q.peekLast()] - cs[q.peekLast()] >= f[i] - cs[i]) {
                    q.pollLast();
                }
                q.offer(i);
            }
        }
        return f[n];
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(n)

Approach Breakdown

RECURSIVE
O(2ⁿ) time
O(n) space

Pure recursion explores every possible choice at each step. With two choices per state (take or skip), the decision tree has 2ⁿ leaves. The recursion stack uses O(n) space. Many subproblems are recomputed exponentially many times.

DYNAMIC PROGRAMMING
O(n × m) time
O(n × m) space

Each cell in the DP table is computed exactly once from previously solved subproblems. The table dimensions determine both time and space. Look for the state variables — each unique combination of state values is one cell. Often a rolling array can reduce space by one dimension.

Shortcut: Count your DP state dimensions → that’s your time. Can you drop one? That’s your space optimization.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

State misses one required dimension

Wrong move: An incomplete state merges distinct subproblems and caches incorrect answers.

Usually fails on: Correctness breaks on cases that differ only in hidden state.

Fix: Define state so each unique subproblem maps to one DP cell.