# The Busy Intersection – A Leetcode Problem

Mar 23, 2023

## The Busy Intersection – A Leetcode Problem

The Busy Intersection is a Leetcode Problem that asks you to find the intersection of two sets. This can be a difficult problem to solve, but with the right techniques, you can solve it quickly.

Before you can solve the Busy Intersection, you need to know how to find intersections in a set. To find the intersection of two sets, you need to find the points where the sets intersect. To find the points where the sets intersect, you need to find the pairs of points where the sets intersect.

To find the pairs of points where the sets intersect, you need to take the intersection of both sets and then find the intersection of the resulting two sets. To find the intersection of the sets, you need to find the point where the two sets meet.Once you know how to find intersections in a set, you can solve the Busy Intersection problem easily.

## 1. The Busy Intersection – A Leetcode Problem

You are given an array of size N. The array contains integers from 1 to N and is a permutation of numbers from 1 to N. You need to find the number of inversions in the array. Inversion is defined as the number of pairs of elements in the array such that the larger element appears before the smaller element.

For example, in the array [2, 4, 1, 3, 5], there are 3 inversions – (2, 1), (4, 1), (4, 3).

Input Format

The first line of the input contains an integer T, denoting the number of test cases. The first line of each test case contains an integer N, denoting the size of the array. The second line of each test case contains N space separated integers, denoting the elements of the array.

Output Format

For each test case, print the number of inversions in the array.

Constraints

1 <= T <= 10
1 <= N <= 100000
1 <= A[i] <= N

Sample Input

2
5
2 4 1 3 5
5
5 4 3 2 1
Sample Output

3
10
Explanation

Test Case 1:

The array [2, 4, 1, 3, 5] has 3 inversions – (2, 1), (4, 1), (4, 3).

Test Case 2:

The array [5, 4, 3, 2, 1] has 10 inversions – every pair except (5, 4), (5, 3), (5, 2), (5, 1).

“””

## 2. The Problem

The problem is simple. You are given a 2D array of 1s and 0s where 1 represents a car and 0 represents an empty space. The goal is to find the number of cars that can pass through the intersection in a single time unit.

The intersection is a grid of roads, each of which can only handle one car per time unit. That is, if two cars are on the same road, they must wait for each other to clear the intersection before either can continue.

The cars can move in any of the four cardinal directions (up, down, left, or right), but they cannot move diagonally.

The number of cars in the 2D array is not known in advance, nor is the size of the array.

Example:

Input:

[[1,0,0,0,0],
[0,0,1,0,0],
[0,0,0,0,1],
[0,0,0,0,0]]

Explanation:

There are three cars that can pass through the intersection in a single time unit:

The car in the top left can move down.
The car in the bottom middle can move up.
The car in the bottom right can move left.

## 3. The Solution

TheBusyIntersection – A Leetcode Problem
Given an array of integer representing the time taken by each car to cross an intersection, find the minimum time needed for all cars to cross the intersection.

This is a classic leetcode problem that can be solved using a greedy approach. The key is to find the maximum time taken by any car to cross the intersection and use that as the time needed for all cars to cross the intersection.

The time taken by a car to cross the intersection is given by the formula:

time taken = max(time taken by car in front, time taken by car behind)

We can use this formula to find the time taken by each car to cross the intersection. We can then find the maximum of all these times and use that as the time needed for all cars to cross the intersection.

The time complexity of this approach is O(n) where n is the number of cars. The space complexity is O(1) as we only need to store the maximum time taken by any car.

def busyIntersection(self, times):

# find the maximum time taken by any car

max_time = 0

for time in times:

max_time = max(max_time, time)

# use the maximum time as the time needed for all cars to cross the intersection

return max_time

## 4. The Results

The Busy Intersection – A Leetcode Problem

In this article, we will be discussing a leetcode problem called “The Busy Intersection”.

Given an array of integers representing the coordinates of objects on a straight line, determine whether or not it is possible to rearrange the objects so that they form a line with the same slope.

For example, given the coordinates [1, 2, 3, 4, 5], you should return true, since it is possible to rearrange the objects to form a line with slope 1.

Given the coordinates [1, 2, 3, 4, 6], you should return false, since it is not possible to rearrange the objects to form a line with slope 1.

The problem can be solved in O(n) time using a greedy approach. We first sort the array of coordinates in ascending order. Then, we start from the first element of the array and keep track of the slope of the line formed by the current element and the last element in the array. If at any point, we find that the slope of the line is not equal to the slope of the line formed by the first element and the last element, then we return false. Otherwise, we return true.

The following is the implementation of the above approach :

def can_rearrange(arr, n) :

if (n < 2) :
return true

arr.sort()

slope = (arr[n – 1] – arr[0]) / (n – 1)

for i in range(1, n – 1) :

curr_slope = (arr[i + 1] – arr[i]) / 1

if (curr_slope != slope) :
return false

return true

arr = [1, 2, 3, 4, 5]
n = len(arr)

if (can_rearrange(arr, n)) :
print(“Yes”)
else :
print(“No”)