Lecture 163:-Car Fleet-II

The "Car Fleet II" problem is an extension of the "Car Fleet" problem, where you need to determine the time at which each car fleet will reach the target destination.

Here's how you can approach the "Car Fleet II" problem:

1. Calculate the time it takes for each car to reach the target based on their positions and speeds. The time can be calculated as time = distance / speed.

2. Iterate through the cars in reverse order, calculating the time it takes for each car to catch up with the car ahead of it.

3. Maintain a stack to keep track of cars that are forming a fleet. If the time it takes for the current car to catch up is greater than the time of the car at the top of the stack, a new fleet is formed. Otherwise, update the time of the car at the top of the stack and pop cars from the stack until a valid fleet is formed.

4. Store the calculated times in a result array and return the result.

Here's a C++ implementation to solve the "Car Fleet II" problem:

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#include <iostream> #include <vector> #include <stack> std::vector<double> getCollisionTimes(std::vector<int>& position, std::vector<int>& speed) { int n = position.size(); std::vector<double> collisionTimes(n, -1.0); std::stack<int> stack; for (int i = n - 1; i >= 0; --i) { while (!stack.empty()) { int j = stack.top(); double time = static_cast<double>(position[j] - position[i]) / (speed[i] - speed[j]); if (speed[j] <= speed[i] || (collisionTimes[j] != -1.0 && time >= collisionTimes[j])) { stack.pop(); } else { collisionTimes[i] = time; break; } } stack.push(i); } return collisionTimes; } int main() { std::vector<int> position = {3, 5, 7, 10}; std::vector<int> speed = {5, 3, 7, 10}; std::vector<double> collisionTimes = getCollisionTimes(position, speed); std::cout << "Collision Times: "; for (double time : collisionTimes) { std::cout << time << " "; } std::cout << std::endl; return 0; }

In this example, the getCollisionTimes function calculates the collision times for each car based on the given positions and speeds of the cars. The main function demonstrates how to use this function for a specific input.

For the given input, the output collision times will be:

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Collision Times: 2 -1 1.5 -1

This indicates that the first car will collide with the third car at time 2, the third car will collide with the fourth car at time 1.5, and the second and fourth cars will not collide with any other cars.