Find the sum of remaining sticks after each iterations

Given N number of sticks of varying lengths in an array arr, the task is to determine the sum of the count of sticks that are left after each iteration. At each iteration, cut the length of the shortest stick from remaining sticks.

Examples: 

Input: N = 6, arr = {5, 4, 4, 2, 2, 8}
Output: 7
Explanation:
Iteration 1: 
Initial arr = {5, 4, 4, 2, 2, 8}
Shortest stick = 2
arr with reduced length = {3, 2, 2, 0, 0, 6}
Remaining sticks = 4

Iteration 2: 
arr = {3, 2, 2, 4}
Shortest stick = 2
Left stick = 2

Iteration 3: 
arr = {1, 2}
Shortest stick = 1
Left stick = 1

Iteration 4: 
arr = {1}
Min length = 1
Left stick = 0

Input: N = 8, arr = {1, 2, 3, 4, 3, 3, 2, 1}
Output: 11

Approach: The approach to solving this problem is to sort the array and then find the number of minimum length sticks that are of the same length while traversing and update the sum accordingly at each step and in the end return the sum.

7

Time Complexity: O(Nlog(N)) where N is the number of sticks.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

Another Approach: 
 

• Store the frequency of stick lengths in a map
• In each iteration, 
  • Find the frequency of min length’s stick
  • Decrease the frequency of min length’s stick from each stick’s frequency
  • Add the count of non-zero sticks to the resultant stick.

Below is the implementation of above approach:

7

Time Complexity:where N is the number of sticks
Auxiliary Space: O(N), where N is the number of sticks.