Minimum Number of Arrows to Burst Balloons

To find the minimum number of arrows required to burst all balloons, we can follow these steps:

1. Sort the Balloons: Sort the balloons by their xend values. This helps in determining the overlapping ranges of balloons.
2. Find Overlaps: Iterate through the sorted list of balloons and find overlaps. Whenever a balloon overlaps with the previous one, they can be burst by the same arrow.
3. Count Arrows: Keep track of the number of arrows required. If a balloon does not overlap with the previous one, it requires a new arrow.

Here’s the code:

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class Solution:
    def findMinArrowShots(self, points: List[List[int]]) -> int:
        # Step 1: Sort the balloons by their ending points
        points.sort(key=lambda x: x[1])

        arrows = 0
        end = float('-inf')  # Initializing the end variable to negative infinity

        # Step 2: Iterate through the sorted balloons
        for balloon in points:
            start, current_end = balloon

            # If the current balloon's start is greater than the previous end, shoot a new arrow
            if start > end:
                arrows += 1
                end = current_end  # Update the end point

        return arrows

Example Explanation:

• For points = [[10,16],[2,8],[1,6],[7,12]], the output is 2.
  • The first arrow can be shot at x = 6 to burst balloons [2,8] and [1,6].
  • The second arrow can be shot at x = 11 to burst balloons [10,16] and [7,12].

The time complexity of this solution is (O(n \log n)) due to the sorting step, where (n) is the number of balloons. The space complexity is (O(1)), as we are using only constant extra space.

Fill out the following sections:

Define the Terms

1. spherical
2. horizontal diameter
3. horizontal ______
4. vertical |

Define the Interface Input: points (array of arrays) - represents co-ordinates Output: integer (minimum number of arrows to burst balloons)

Analyze the Input and Output

Identify the Invariants

Identify the constraints

• 0 <= points.length <= 104
• points[i].length == 2
• -231 <= xstart < xend <= 231 - 1

Search the Problem Space Look for clues in the problem statement. minimum number of …

=> Optimization problem

Classify the Problem

• Greedy Approach

Analyze the Examples

Solve the Problem by Hand

• We can use line diagram.

Describe the Pattern

Distill the Observations to Create Insights

Brute Force Approach

1. Points are lying in big numbers
2. Create a frequency array
3. Increase all the values from 1 to 2
4. Iterate through the freqency array

Sort

Should we sort by start or end? It does not matter. Can we get away without sorting. No

Time: O(N) + O(space used) Space: O(N)

Will not be optimal.

Analyze Time and Space Complexity

Time: O( ) Space: O( )

Outline the Solution

Key Takeaways

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# @param {Integer[][]} points
# @return {Integer}
def find_min_arrow_shots(points)
    if points.size == 0
        return 0
    end

    points.sort!{|a, b| a[1] <=> b[1]}

    arrows = 1
    first_end = points[0][1]

    points.each do |point|
      x_start = point[0]
      x_end = point[1]
#         we don't have a overlap
        if first_end < x_start
            arrows += 1  
            first_end = x_end
        end
    end

    return arrows
end