Collision Course | TCS MockVita 2020

Problem Description

On a busy road, multiple cars are passing by. A simulation is run to see what happens if brakes fail for all cars on the road. The only way for them to be safe is if they don’t collide and pass by each other. The goal is to identify whether any of the given cars would collide or pass by each other safely around a Roundabout. Think of this as a reference point O ( Origin with coordinates (0, 0) ), but instead of going around it, cars pass through it.

Considering that each car is moving in a straight line towards the origin with individual uniform speed. Cars will continue to travel in that same straight line even after crossing origin. Calculate the number of collisions that will happen in such a scenario.

Note: Calculate collisions only at origin. Ignore the other collisions. Assume that each car continues on its respective path even after the collision without change of direction or speed for an infinite distance.

Given an array car[] which contains the co-ordinates and their speed for each element. Find the total number of collisions at origin.

Example:



Input: car[] = {(5 12 1), (16 63 5), (-10 24 2), (7 24 2), (-24 7 2)}
Output: 4
Explanation:
Let the 5 cars be A, B, C, D, and E respectively.
4 Collisions are as follows –
A & B, A & C, B & C, D & E

 

Approach: The idea is to find the number of cars colliding at origin. We are given coordinate position of cars, from which we can find the distance of cars from origin.

Let x, y be position of a car then distance from origin will be:

\sqrt{x^2 + y^2}

Dividing this distance with speed will give us time at which a car is present at origin.  So if there are ‘N’ cars present at origin at some instant of time then total collisions will be 

{n}\choose{2}

Adding all collision at a different instance of time will give our required answer.

Below is the implementation of the above approach:

C++

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// C++ implementation to find the
// collision at the origin
  
#include <bits/stdc++.h>
using namespace std;
  
// Structure to store the
// co-ordinates of car and speed
struct Car {
    long long x;
    long long y;
    long long v;
};
  
// Function to find the co-ordinates
// of the car and speed
long long solve(long long c,
                vector<Car>& arr)
{
    map<long long, long long> freq;
  
    long sum = 0;
    for (long long i = 0; i < c; i++) {
        long long x = arr[i].x,
                  y = arr[i].y,
                  v = arr[i].v;
        long long dist_square
            = (x * x) + (y * y);
        long long time_square
            = dist_square / (v * v);
        freq[time_square]++;
    }
  
    // Loop to iterate over the
    // frequency of the elements
    for (auto it = freq.begin();
         it != freq.end(); it++) {
        long long f = it->second;
        if (f <= 0)
            continue;
  
        sum += (f * (f - 1)) / 2;
    }
  
    return sum;
}
  
// Driver Code
int main()
{
    long long c = 5;
  
    vector<Car> arr;
  
    Car tmp;
    tmp.x = 5;
    tmp.y = 12;
    tmp.v = 1;
    arr.push_back(tmp);
  
    tmp.x = 16;
    tmp.y = 63;
    tmp.v = 5;
    arr.push_back(tmp);
  
    tmp.x = -10;
    tmp.y = 24;
    tmp.v = 2;
    arr.push_back(tmp);
  
    tmp.x = 7;
    tmp.y = 24;
    tmp.v = 2;
    arr.push_back(tmp);
  
    tmp.x = -24;
    tmp.y = 7;
    tmp.v = 2;
    arr.push_back(tmp);
  
    cout << solve(c, arr);
  
    return 0;
}

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Output:

4

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