Longest Uploaded Prefix - Complete Solution Guide

Longest Uploaded Prefix is LeetCode problem 2424, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Framing

Longest Uploaded Prefix is a Medium LeetCode problem that rewards careful tracing, edge-case handling, and a clear grasp of Hash Table and Binary Search. The best solutions usually explain why the chosen invariant holds before they optimize for time or space.

Quick Example Mindset

A useful way to test Longest Uploaded Prefix is to start with a tiny input that exposes the boundary conditions, then run the same logic on a slightly larger case to verify the hash table behavior and the binary search interaction. That second pass is where off-by-one mistakes and missing updates usually appear.

Problem Statement

You are given a stream of n videos, each represented by a distinct number from 1 to n that you need to "upload" to a server. You need to implement a data structure that calculates the length of the longest uploaded prefix at various points in the upload process. We consider i to be an uploaded prefix if all videos in the range 1 to i ( inclusive ) have been uploaded to the server. The longest uploaded prefix is the maximum value of i that satisfies this definition. Implement the LUPrefix class:

Detailed Explanation

The problem requires you to implement a data structure, `LUPrefix`, that simulates uploading videos numbered from 1 to `n`. The goal is to efficiently determine the longest uploaded prefix at any given time. A prefix of length `i` is considered uploaded if all videos with numbers from 1 to `i` have been uploaded. The `LUPrefix` class has three methods: `LUPrefix(int n)` to initialize the structure, `upload(int video)` to simulate uploading a video, and `longest()` to return the length of the longest uploaded prefix.

Solution Approach

The solution uses a boolean array `uploaded` to keep track of which videos have been uploaded. The `upload` method marks the specified video as uploaded and then iteratively extends the `prefix_len` variable as long as the next video in the sequence has also been uploaded. The `longest` method simply returns the current value of `prefix_len`. This approach is efficient because it avoids recomputing the longest prefix from scratch each time `longest` is called.

Step-by-Step Algorithm

1. Step 1: Initialize a boolean array `uploaded` of size `n + 2` with all values set to `false`. The extra two elements handle edge cases and array bounds checking.
2. Step 2: Initialize an integer `prefix_len` to 0. This variable stores the length of the longest uploaded prefix.
3. Step 3: In the `upload` method, set `uploaded[video]` to `true` to indicate that the video has been uploaded.
4. Step 4: After uploading the video, use a `while` loop to increment `prefix_len` as long as `uploaded[prefix_len + 1]` is `true`. This extends the longest uploaded prefix.
5. Step 5: In the `longest` method, simply return the value of `prefix_len`.

Key Insights

• Insight 1: The longest uploaded prefix can be efficiently tracked by maintaining a boolean array representing which videos have been uploaded.
• Insight 2: The `upload` operation needs to update the longest prefix length after a new video is uploaded, and the `longest` operation simply returns this cached value.
• Insight 3: The problem can be solved without using more complex data structures like Binary Search Trees or Heaps because the video numbers are consecutive integers.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(n)

Topics

This problem involves: Hash Table, Binary Search, Union Find, Design, Binary Indexed Tree, Segment Tree, Heap (Priority Queue), Ordered Set.

Study Paths

Continue from this problem into the surrounding topic and company clusters to compare how the same pattern appears in other interview settings.

Related topics: Hash Table, Binary Search, Union Find, Design

Frequently Asked Questions