Hello friends today we are going to talk about **Busy Intersection LeetCode Problem: Intersection Time Intervals for Cars?** Are you looking to improve your coding skills and ace your next technical interview? LeetCode is a great platform to practice coding problems and prepare for coding interviews.

One of the interesting problems on LeetCode is “**Busy Intersection**“, which tests your understanding of algorithms and data structures. In this article, we’ll dive into the problem statement, its significance, approaches to solve it, and how to write optimized code for it.

## Introduction

Busy Intersection is a coding problem that tests your problem-solving skills and coding abilities. Given two lists of cars, where each car is represented as a pair of integers (start_time, end_time), you need to find the time intervals when both cars are present at the intersection. The problem is taken from LeetCode, which is a popular platform for coding interviews and problem-solving.

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## Understanding the Problem

Before we dive into solving the problem, let’s understand its requirements in detail. The problem statement can be summarized as follows:

- Given two lists of cars, each represented as a pair of integers (start_time, end_time), find the time intervals when both cars are present at the intersection.
- The intersection time intervals should be returned as a list of pairs, where each pair represents the start and end times of the interval.
- If there are no time intervals when both cars are present at the intersection, return an empty list.

For example, consider the following input:

```
cars1 =[[0, 4], [2, 10], [3, 5], [6, 11]]
cars2 = [[1, 2], [3, 7], [4, 9], [8, 10]]
```

In this case, the intersection time intervals are:

```
[[3, 4], [6, 7], [8, 9]]
```

## Approaches to Solve the Problem

To solve the problem, we can start with a brute-force approach that compares every car in the first list with every car in the second list. This approach has a time complexity of O(n^2) and is not efficient for large inputs.

A more optimized approach is to sort the two lists of cars based on their start times and use a two-pointer approach to find the intersection time intervals. This approach has a time complexity of O(n log n), where n is the total number of cars.

Let’s understand the optimized approach in detail:

- Sort both lists of cars based on their start times.
- Initialize two pointers i and j to point to the first car in each list.
- While i and j are within bounds: a. Check if the current cars overlap (i.e., their end times are greater than or equal to each other’s start times). b. If they overlap, add the intersection time interval to the result list and move the pointer of the car that ends earlier. c. If they do not overlap, move the pointer of the car that starts earlier.
- Return the result list of intersection time intervals.

## Writing Code

Now that we have an understanding of the optimized approach, let’s write code to solve the problem. Here’s the implementation in Python:

```
def find_intersection(cars1, cars2):
cars1.sort()
cars2.sort()
i, j = 0, 0
result = []
while i < len(cars1) and j < len(cars2):
car1_start, car1_end = cars1[i]
car2_start, car2_end = cars2[j]
if car1_end >= car2_start and car2_end >= car1_start:
```

```
intersection_start = max(car1_start, car2_start)
intersection_end = min(car1_end, car2_end)
result.append([intersection_start, intersection_end])
if car1_end < car2_end:
i += 1
else:
j += 1
return result
```

The code sorts both lists of cars and initializes two pointers to point to the first car in each list. It then compares each car in the two lists and checks for overlapping time intervals. If there is an overlap, the code adds the intersection time interval to the result list and moves the pointer of the car that ends earlier. If there is no overlap, it moves the pointer of the car that starts earlier. Finally, the code returns the result list of intersection time intervals.

## Testing and Debugging

To test the code, let’s consider the input example we discussed earlier:

```
cars1 = [[0, 4], [2, 10], [3, 5], [6, 11]]
cars2 = [[1, 2], [3, 7], [4, 9], [8, 10]]
result = find_intersection(cars1, cars2)
print(result) # Output: [[3, 4], [6, 7], [8, 9]]
```

The code should output

, which are the intersection time intervals for the input cars.**[[3, 4], [6, 7], [8, 9]]**

## Additionally

**Alternative Approaches to Solve the Problem**:

While the two-pointer approach is a commonly used technique to solve the Busy Intersection problem, there are other approaches you can consider as well. For instance, you could use a hash table to keep track of the start and end times of each car and find the intersection intervals by checking if there is any overlap between the time intervals of the cars.

Explaining these approaches and comparing their pros and cons can provide more insights into the problem-solving process.

**Real-world Applications of the Problem**:

The Busy Intersection problem has several real-world applications, such as in traffic management systems, autonomous vehicles, and logistics planning. Explaining how the problem relates to these domains and how it can be used to optimize their performance can make the article more engaging and relevant.

**Advanced Topics Related to the Problem**: The Busy Intersection problem is a classic example of a problem that involves time intervals and overlapping events. Discussing advanced topics related to this problem, such as interval scheduling algorithms, can provide readers with a deeper understanding of the problem and its applications.

**Examples and Edge Cases**: Providing more examples of the problem and its variations can help readers understand the problem better. Additionally, discussing edge cases and how to handle them can make the article more informative and useful.

**Optimizing the Code Further**: While the code presented in the article is already optimized, there may be ways to make it even more efficient. Discussing these optimization techniques, such as using bitwise operations or pre-sorting the input data, can be helpful for readers who are interested in coding optimization.

## Conclusion

The **Busy Intersection LeetCode problem** is an interesting challenge that tests your problem-solving skills and coding abilities. In this article, we discussed the problem statement, its significance, and approaches to solve it.

We also went through how to write optimized code for the problem and how to test and debug it. Practicing coding problems on platforms like LeetCode is an excellent way to improve your coding skills and prepare for coding interviews. Keep practicing and happy coding!

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