LeetCode #2332 — MEDIUM

The Latest Time to Catch a Bus

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given a 0-indexed integer array buses of length n, where buses[i] represents the departure time of the ith bus. You are also given a 0-indexed integer array passengers of length m, where passengers[j] represents the arrival time of the jth passenger. All bus departure times are unique. All passenger arrival times are unique.

You are given an integer capacity, which represents the maximum number of passengers that can get on each bus.

When a passenger arrives, they will wait in line for the next available bus. You can get on a bus that departs at x minutes if you arrive at y minutes where y <= x, and the bus is not full. Passengers with the earliest arrival times get on the bus first.

More formally when a bus arrives, either:

  • If capacity or fewer passengers are waiting for a bus, they will all get on the bus, or
  • The capacity passengers with the earliest arrival times will get on the bus.

Return the latest time you may arrive at the bus station to catch a bus. You cannot arrive at the same time as another passenger.

Note: The arrays buses and passengers are not necessarily sorted.

Example 1:

Input: buses = [10,20], passengers = [2,17,18,19], capacity = 2
Output: 16
Explanation: Suppose you arrive at time 16.
At time 10, the first bus departs with the 0th passenger. 
At time 20, the second bus departs with you and the 1st passenger.
Note that you may not arrive at the same time as another passenger, which is why you must arrive before the 1st passenger to catch the bus.

Example 2:

Input: buses = [20,30,10], passengers = [19,13,26,4,25,11,21], capacity = 2
Output: 20
Explanation: Suppose you arrive at time 20.
At time 10, the first bus departs with the 3rd passenger. 
At time 20, the second bus departs with the 5th and 1st passengers.
At time 30, the third bus departs with the 0th passenger and you.
Notice if you had arrived any later, then the 6th passenger would have taken your seat on the third bus.

Constraints:

  • n == buses.length
  • m == passengers.length
  • 1 <= n, m, capacity <= 105
  • 2 <= buses[i], passengers[i] <= 109
  • Each element in buses is unique.
  • Each element in passengers is unique.
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 are given a 0-indexed integer array buses of length n, where buses[i] represents the departure time of the ith bus. You are also given a 0-indexed integer array passengers of length m, where passengers[j] represents the arrival time of the jth passenger. All bus departure times are unique. All passenger arrival times are unique. You are given an integer capacity, which represents the maximum number of passengers that can get on each bus. When a passenger arrives, they will wait in line for the next available bus. You can get on a bus that departs at x minutes if you arrive at y minutes where y <= x, and the bus is not full. Passengers with the earliest arrival times get on the bus first. More formally when a bus arrives, either: If capacity or fewer passengers are waiting for a bus, they will all get on the bus, or The capacity passengers with the earliest arrival times will get on

Baseline thinking

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

Pattern signal: Array · Two Pointers · Binary Search

Example 1

[10,20]
[2,17,18,19]
2

Example 2

[20,30,10]
[19,13,26,4,25,11,21]
2

Related Problems

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  • Maximum Matching of Players With Trainers (maximum-matching-of-players-with-trainers)
  • Time Taken to Cross the Door (time-taken-to-cross-the-door)
  • Time to Cross a Bridge (time-to-cross-a-bridge)
  • Rearranging Fruits (rearranging-fruits)
Step 02

Core Insight

What unlocks the optimal approach

  • Sort the buses and passengers arrays.
  • Use 2 pointers to traverse buses and passengers with a simulation of passengers getting on a particular bus.
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
Upper-end input sizes
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 #2332: The Latest Time to Catch a Bus
class Solution {
    public int latestTimeCatchTheBus(int[] buses, int[] passengers, int capacity) {
        Arrays.sort(buses);
        Arrays.sort(passengers);
        int j = 0, c = 0;
        for (int t : buses) {
            c = capacity;
            while (c > 0 && j < passengers.length && passengers[j] <= t) {
                --c;
                ++j;
            }
        }
        --j;
        int ans = c > 0 ? buses[buses.length - 1] : passengers[j];
        while (j >= 0 && ans == passengers[j]) {
            --ans;
            --j;
        }
        return ans;
    }
}
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 × log n + m × log m)
Space
O(log n + log m)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair of elements. The outer loop picks one element, the inner loop scans the rest. For n elements that is n × (n−1)/2 comparisons = O(n²). No extra memory — just two loop variables.

TWO POINTERS
O(n) time
O(1) space

Each pointer traverses the array at most once. With two pointers moving inward (or both moving right), the total number of steps is bounded by n. Each comparison is O(1), giving O(n) overall. No auxiliary data structures are needed — just two index variables.

Shortcut: Two converging pointers on sorted data → O(n) time, O(1) space.
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.

Moving both pointers on every comparison

Wrong move: Advancing both pointers shrinks the search space too aggressively and skips candidates.

Usually fails on: A valid pair can be skipped when only one side should move.

Fix: Move exactly one pointer per decision branch based on invariant.

Boundary update without `+1` / `-1`

Wrong move: Setting `lo = mid` or `hi = mid` can stall and create an infinite loop.

Usually fails on: Two-element ranges never converge.

Fix: Use `lo = mid + 1` or `hi = mid - 1` where appropriate.