LeetCode #3439 — MEDIUM

Reschedule Meetings for Maximum Free Time I

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

Solve on LeetCode
The Problem

Problem Statement

You are given an integer eventTime denoting the duration of an event, where the event occurs from time t = 0 to time t = eventTime.

You are also given two integer arrays startTime and endTime, each of length n. These represent the start and end time of n non-overlapping meetings, where the ith meeting occurs during the time [startTime[i], endTime[i]].

You can reschedule at most k meetings by moving their start time while maintaining the same duration, to maximize the longest continuous period of free time during the event.

The relative order of all the meetings should stay the same and they should remain non-overlapping.

Return the maximum amount of free time possible after rearranging the meetings.

Note that the meetings can not be rescheduled to a time outside the event.

Example 1:

Input: eventTime = 5, k = 1, startTime = [1,3], endTime = [2,5]

Output: 2

Explanation:

Reschedule the meeting at [1, 2] to [2, 3], leaving no meetings during the time [0, 2].

Example 2:

Input: eventTime = 10, k = 1, startTime = [0,2,9], endTime = [1,4,10]

Output: 6

Explanation:

Reschedule the meeting at [2, 4] to [1, 3], leaving no meetings during the time [3, 9].

Example 3:

Input: eventTime = 5, k = 2, startTime = [0,1,2,3,4], endTime = [1,2,3,4,5]

Output: 0

Explanation:

There is no time during the event not occupied by meetings.

Constraints:

  • 1 <= eventTime <= 109
  • n == startTime.length == endTime.length
  • 2 <= n <= 105
  • 1 <= k <= n
  • 0 <= startTime[i] < endTime[i] <= eventTime
  • endTime[i] <= startTime[i + 1] where i lies in the range [0, n - 2].
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 an integer eventTime denoting the duration of an event, where the event occurs from time t = 0 to time t = eventTime. You are also given two integer arrays startTime and endTime, each of length n. These represent the start and end time of n non-overlapping meetings, where the ith meeting occurs during the time [startTime[i], endTime[i]]. You can reschedule at most k meetings by moving their start time while maintaining the same duration, to maximize the longest continuous period of free time during the event. The relative order of all the meetings should stay the same and they should remain non-overlapping. Return the maximum amount of free time possible after rearranging the meetings. Note that the meetings can not be rescheduled to a time outside the event.

Baseline thinking

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

Pattern signal: Array · Greedy · Sliding Window

Example 1

5
1
[1,3]
[2,5]

Example 2

10
1
[0,2,9]
[1,4,10]

Example 3

5
2
[0,1,2,3,4]
[1,2,3,4,5]

Related Problems

  • Meeting Scheduler (meeting-scheduler)
Step 02

Core Insight

What unlocks the optimal approach

  • In a sequence of <code>K</code> meetings and <code>K + 1</code> gaps, you could move all meetings to the start of the sequence to get the max free time.
  • Use a sliding window of <code>K + 1</code> size to store sum of gaps and take the maximum.
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 #3439: Reschedule Meetings for Maximum Free Time I
class Solution {
    public int maxFreeTime(int eventTime, int k, int[] startTime, int[] endTime) {
        int n = endTime.length;
        int[] nums = new int[n + 1];
        nums[0] = startTime[0];
        for (int i = 1; i < n; ++i) {
            nums[i] = startTime[i] - endTime[i - 1];
        }
        nums[n] = eventTime - endTime[n - 1];
        int ans = 0, s = 0;
        for (int i = 0; i <= n; ++i) {
            s += nums[i];
            if (i >= k) {
                ans = Math.max(ans, s);
                s -= nums[i - k];
            }
        }
        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)
Space
O(n)

Approach Breakdown

EXHAUSTIVE
O(2ⁿ) time
O(n) space

Try every possible combination of choices. With n items each having two states (include/exclude), the search space is 2ⁿ. Evaluating each combination takes O(n), giving O(n × 2ⁿ). The recursion stack or subset storage uses O(n) space.

GREEDY
O(n log n) time
O(1) space

Greedy algorithms typically sort the input (O(n log n)) then make a single pass (O(n)). The sort dominates. If the input is already sorted or the greedy choice can be computed without sorting, time drops to O(n). Proving greedy correctness (exchange argument) is harder than the implementation.

Shortcut: Sort + single pass → O(n log n). If no sort needed → O(n). The hard part is proving it works.
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.

Using greedy without proof

Wrong move: Locally optimal choices may fail globally.

Usually fails on: Counterexamples appear on crafted input orderings.

Fix: Verify with exchange argument or monotonic objective before committing.

Shrinking the window only once

Wrong move: Using `if` instead of `while` leaves the window invalid for multiple iterations.

Usually fails on: Over-limit windows stay invalid and produce wrong lengths/counts.

Fix: Shrink in a `while` loop until the invariant is valid again.