Minimum Number of Arrows to Burst Balloons
To find the minimum number of arrows required to burst all balloons, we can follow these steps:
 Sort the Balloons: Sort the balloons by their
xend
values. This helps in determining the overlapping ranges of balloons.  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.
 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:


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
 spherical
 horizontal diameter
 horizontal ______
 vertical 
Define the Interface Input: points (array of arrays)  represents coordinates 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
 Points are lying in big numbers
 Create a frequency array
 Increase all the values from 1 to 2
 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

