What is the Minimum Number of Arrows problem and how can it be solved using a greedy algorithm?

The Minimum Number of Arrows problem is a problem where there are a number of balloons placed on a 2D plane, each with a start and end coordinate. The goal is to find the minimum number of arrows needed to burst all the balloons.

This problem can be solved using a greedy algorithm. The approach is as follows:

1. Sort the balloons based on their end coordinates in ascending order.
2. Initialize a variable to keep track of the number of arrows needed.
3. Iterate through the sorted balloons.
4. For each balloon, if its start coordinate is greater than the current arrow's end coordinate, it means a new arrow is needed. Increment the arrow count and update the current arrow's end coordinate to the end coordinate of the current balloon.
5. If the start coordinate of the balloon is less than or equal to the current arrow's end coordinate, it means the balloon can be burst with the current arrow. Update the current arrow's end coordinate to the minimum of its current value and the end coordinate of the current balloon.
6. Repeat steps 4 and 5 until all balloons have been processed.
7. The final value of the arrow count will be the minimum number of arrows needed to burst all the balloons.

This greedy algorithm works because by sorting the balloons based on their end coordinates, we ensure that the arrows are shot in a way that maximizes the number of balloons burst with each arrow. The algorithm always chooses the balloon with the smallest end coordinate, ensuring that the arrow can burst as many balloons as possible.