Bursting Balloons

Moderate
0/80
Average time to solve is 40m
34 upvotes
Asked in companies
QuikrSamsungOracle

Problem statement

You are given an array 'ARR' of N integers. Each integer represents the height of a balloon. So, there are N balloons lined up.

Your aim is to destroy all these balloons. Now, a balloon can only be destroyed if the player shoots its head. So, to do the needful, he/ she shoots an arrow from the left to the right side of the platform, from an arbitrary height he/she chooses. The arrow moves from left to right, at a chosen height ARR[i] until it finds a balloon. The moment when an arrow touches a balloon, the balloon gets destroyed and disappears and the arrow continues its way from left to right at a height decreased by 1. Therefore, if the arrow was moving at height ARR[i], after destroying the balloon it travels at height ARR[i]-1. The player wins this game if he destroys all the balloons in minimum arrows.

You have to return the minimum arrows required to complete the task.

Detailed explanation ( Input/output format, Notes, Images )
Input Format: 
The first line of input contains an integer N representing the size of the array.

The second line of input contains N space-separated integers representing the height of the balloons.
Output Format: 
Return a single integer i.e. the count of the minimum number of arrows required to complete the task.

Note:

You are not required to print the output, it has already been taken care of. Just implement the function.
Constraints: 
1 <= N <= 10^5
1 <= ARR[i] <= 10^9

Time Limit: 1sec
Sample Input 1:
5
2 1 5 4 3
Sample Output 1:
2
Explanation of the Sample Input1:
We need to shoot the arrow at height 5 - which destroys balloons at the height [5, 4, 3], and shoots an arrow at height 2 - which destroys [2, 1].  Therefore we require a minimum of 2 arrows.
Sample Input 2:
3
3 2 1
Sample Output 2:
1
Explanation of the Sample Input 2:
We need to shoot the arrow at height 3 - which destroys balloons at the height [3,2,1]. Therefore we need to shoot only 1 arrow.
Hint

We would like to shoot a balloon with the maximum height and then whatever other balloons it can hit will be beneficial to us so think of a way to store the heights of the balloons such that for i’th balloon you should be able to know do you have to fire a new arrow or not.

Approaches (1)
Using hashmap

We can see here that balloons need to be destroyed in a minimum number of arrows so we need to reuse the arrows, also it’s clear that we need a new arrow for every balloon which is not getting destroyed by any previous arrow.

So we can solve this problem greedily by adding a new arrow for every balloon which is not getting destroyed by existing arrows.

  • We will use a map data structure that will store the height of fired arrows.
  • Start a loop from i = 0 to i = N - 1 and for the i’th balloon if the map contains the value ARR[i] then it means this balloon will get hit by the previous arrow.
    • Therefore decrease the count of ARR[i] in the map and if it becomes 0 remove the key from the map.
    • Increase the count of ARR[i]-1 in the map because there is an arrow at this height available.
  • If the map does not contain the ARR[i] then We will need to fire a new arrow to increase the count of ARR[i] in the map.
  • Now at the end find the sum of all the arrows present in the map and return it.
Time Complexity

O(N), where N is the number of balloons.

 

As we are visiting every balloon only once and we are also searching and accessing  Hashmap N times whereas hashmap has constant time complexity on average. So overall time complexity is O(N).

Space Complexity

O(N), where N is the number of balloons.

 

As we are storing the heights of balloons in the hashmap and its size can at max grow up to O(N).

Code Solution
(100% EXP penalty)
Bursting Balloons
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