Hello, fellow algorithm enthusiasts! 🧭
Welcome to our detailed exploration of the ‘Maximum Events Attended’ problem, a popular challenge featured on LeetCode 1353. This guide aims to demystify the process of event scheduling using a strategic combination of greedy algorithms and priority queues (heaps). If you’ve ever struggled to pack your calendar with the most impactful meetings possible, this problem offers practical insights into efficient time management. Let’s delve into it together! 💼
## Understanding the Problem
### 🧠 Problem Statement
You’re presented with an array of events, where each event possesses a `startDay` and an `endDay`. Your challenge is to strategically pick the days you attend the events such that you can participate in the maximum number of events possible, under the following conditions:
– You can **only join one event per day**
– You must select a day between the `startDay` and `endDay` of an event
Your goal is to determine the **highest possible number of events** you can attend without any overlaps.
## Breaking Down the Solution
### 💡 Key Ideas
Our strategy hinges on the following steps:
1. **Sort Events by Start Time**: By default, we align our events in ascending order based on their `startDay` to help us efficiently manage availability.
2. **Prioritize Early-Ending Events**: We utilize a min-heap (priority queue) based on the `endDay` of each event. This setup ensures we always pick the event that frees up our schedule the soonest, allowing maximum flexibility for subsequent events.
3. **Daily Event Evaluation**:
– As the day progresses, we check if any new events become available and add them to our queue.
– Simultaneously, we remove any events that have passed their `endDay` to maintain an up-to-date list.
### Strategic Optimization
By adopting a greedy approach, we focus on prioritizing the shortest time-consuming events first. This practice maximizes our chances to incorporate more events into a tightly packed schedule while using minimal processing time.
## Coding Solutions
Let’s translate our strategy into code through three popular programming languages: C++, Python, and JavaScript. Each implementation follows the same core logic while showcasing language-specific nuances.
### 🛠 C++ Implementation
“`cpp
#include
#include
#include
using Event = std::vector; // Assuming each event is structured like [startDay, endDay]
class Solution {
public:
int maxEvents(std::vector& events) {
int day = 1, maxDay = 0, attended = 0;
std::sort(events.begin(), events.end());
for (auto event : events) maxDay = std::max(maxDay, event[1]);
std::priority_queue<int, std::vector, std::greater> pq;
for (int i = 0; day <= maxDay; day++) {
while (i < events.size() && events[i][0] == day) pq.push(events[i++][1]);
while (!pq.empty() && pq.top() int:
days, attended, heap = max(event[1] for event in events), 0, []
events.sort(key=lambda event: event[0])
for day in range(1, days + 1):
for event in events:
if event[0] == day: heapq.heappush(heap, event[1])
while heap and heap[0] a.start – b.start);
this.eventsLength = events.length;
this.eventPointer = 0;
}
push(endDay) {
this.heap.push(endDay);
this._bubbleUp(this.heap.length – 1);
}
_bubbleUp(index) {
if (index <= 0) return;
const parentNode = Math.floor((index – 1) / 2);
if (this.heap[index] < this.heap[parentNode]) {
[this.heap[index], this.heap[parentNode]] = [this.heap[parentNode], this.heap[index]];
this._bubbleUp(parentNode);
}
}
attendEvent(day) {
while (this.eventPointer 0 && this.heap[0] < day) {
this._removeRoot();
}
if (this.heap.length && this.heap[0] === day) {
this._removeRoot();
return true;
}
return false;
}
_removeRoot() {
if (!this.heap.length) return;
const lastElement = this.heap.pop();
if (this.heap.length === 0) return;
this.heap[0] = lastElement;
this._heapify(0);
}
_heapify(index) {
const leftChildIndex = 2 * index + 1,
rightChildIndex = 2 * index + 2,
length = this.heap.length;
let smallestIndex = index;
if (leftChildIndex < length && this.heap[leftChildIndex] < this.heap[smallestIndex])
smallestIndex = leftChildIndex;
if (rightChildIndex < length && this.heap[rightChildIndex] event.end));
const heap = new MinHeap(events);
let attended = 0;
for (let day = 1; day <= maxDay; day++) {
if (heap.attendEvent(day)) attended++;
}
return attended;
}
}
“`
## Conclusion
By employing this structured scheduling approach, we've managed to address a real-world scenario many individuals face daily. This solution utilizes fundamental algorithms to provide a scalable and efficient method for scheduling events, offering a fresh perspective on optimizing time and resources through coding.
Feel free to revisit this guide whenever you need a refresher, and don't hesitate to share your experiences with similar problems in the comments below!
Leave a Reply