Find instances at end of time frame after auto scaling

Given an integer, instances, and an array, arr[] of size N representing the average utilization percentage of the computing system at each second, the task is to find the number of instances at the end of the time frame such that the computing system auto-scales the number of instances according to the following rules: 

• Average utilization < 25%: Reduce the number of instances by half if the number of instances is greater than 1.
• 25% ≤ Average utilization ≤ 60%: Take no action.
• Average utilization > 60%: Double the number of instances if the doubled value does not exceed 2* 10⁸.

Once an action of adding or reducing the number of instances is performed, the system will stop monitoring for 10 seconds. During that time, the number of instances does not change.

Examples:

Input: instances = 2, arr[] = {25, 23, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 76, 80}
Output: 2
Explanation:
At second 1, arr[0] = 25 ≤ 25, so take no action.
At second 2, arr[1] = 23 < 25, so an action is instantiated to halve the number of instances to ceil(2/2) = 1. The system will stop checking for 10 seconds, so from arr[2] through arr[11] no actions will be taken.
At second 13, arr[12] = 76 > 60, so the number of instances is doubled from 1 to 2.

There are no more readings to consider and 2 is the final value.

Input: instances = 5, arr = {30, 5, 4, 8, 19, 89}
Output: 3
Explanation:
At second 1, 25 ≤ arr[0] = 30 ≤ 60, so take no action.
At second 2, arr[1] = 5 < 25, so an action is instantiated to halve the number of instances to ceil(5/2) = 3.
The system will stop checking for 10 seconds, so from arr[2] through arr[5] no actions will be taken.

There are no more readings to consider and 3 is the final answer.

Approach: The given problem can be solved by traversing the given array arr[] and if the current element is less than 25 then divide the number of instances by 2 if the number of instances is greater than 1. Otherwise, if the current value is greater than 60 multiply the number of instances by 2 if the number of instances is not greater than 10⁸, after performing either of the two operations increment the current index by 10. Follow the steps to solve the problem:

• Traverse the array, arr[] using the variable i and perform the following steps:
  • If arr[i] is less than 25 and instances is greater than 1, divide the instances by 2 and increment i by 10.
  • If arr[i] is greater than 60 and instances is less than or equal to 10⁸, multiply instances by 2 and increment i by 10.
  • Increment the index i by 1.
• After completing the above steps, print the number of instances as the result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the number of
// instances after compintion
void finalInstances(int instances,
                                  int arr[], int N)
{
    int i = 0;

    // Traverse the array, arr[]
    while (i < N)
    {

        // If current element is less
        // than 25
        if (arr[i] < 25 && instances > 1)
        {

            // Divide instances by 2 and take ceil value
            double temp = (instances / 2.0);
            instances = (int)(ceil(temp));
            i = i + 10;
        }

        // If the current element is
        // greater than 60
        else if (arr[i] > 60 &&
                 instances <= (2*pow(10, 8)))
        {

            // Double the instances
            instances = instances * 2;
            i = i + 10;
        }
        i = i + 1;
    }

    // Print the instances at the end
    // of the traversal
    cout << instances;
}

// Driver Code
int main()
{
    int instances = 2;
    int arr[] = { 25, 23, 1, 2, 3, 4, 5,
                  6, 7, 8, 9, 10, 76, 80 };

    int N = sizeof(arr) / sizeof(arr[0]);

    // Function Call
    finalInstances(instances, arr, N);
}

// This code is contributed by splevel62

Java

// Java program for above approach
class GFG{

// Function to find the number of
// instances after compintion
public static void finalInstances(int instances,
                                  int[] arr)
{
    int i = 0;

    // Traverse the array, arr[]
    while (i < arr.length)
    {

        // If current element is less
        // than 25
        if (arr[i] < 25 && instances > 1)
        {

            // Divide instances by 2
            instances = (instances / 2);
            i = i + 10;
        }

        // If the current element is
        // greater than 60
        else if (arr[i] > 60 &&
                 instances <= Math.pow(10, 8))
        {

            // Double the instances
            instances = instances * 2;
            i = i + 10;
        }
        i = i + 1;
    }

    // Print the instances at the end
    // of the traversal
    System.out.println(instances);
}

// Driver Code
public static void main(String args[])
{
    int instances = 2;
    int[] arr = { 25, 23, 1, 2, 3, 4, 5,
                  6, 7, 8, 9, 10, 76, 80 };

    // Function Call
    finalInstances(instances, arr);
}
}

// This code is contributed by _saurabh_jaiswal

Python3

# Python program for the above approach
from math import ceil

# Function to find the number of
# instances after completion
def finalInstances(instances, arr):
    i = 0

    # Traverse the array, arr[]
    while i < len(arr):

        # If current element is less
        # than 25
        if arr[i] < 25 and instances > 1:

            # Divide instances by 2
            instances = ceil(instances / 2)
            i += 10

        # If the current element is
        # greater than 60
        elif arr[i] > 60 and instances <= 10**8:

            # Double the instances
            instances *= 2
            i += 10
        i += 1

    # Print the instances at the end
    # of the traversal
    print(instances)

# Driver Code
instances = 2

arr = [25, 23, 1, 2, 3, 4, 5,
       6, 7, 8, 9, 10, 76, 80]

# Function Call
finalInstances(instances, arr)

C#

// C# program for above approach
using System;

class GFG{

// Function to find the number of
// instances after compintion
static void finalInstances(int instances, int[] arr)
{
        int i = 0;

        // Traverse the array, arr[]
        while (i < arr.Length) {

            // If current element is less
            // than 25
            if (arr[i] < 25 && instances > 1) {

                // Divide instances by 2
                instances = (instances / 2);
                i = i + 10;
            }

            // If the current element is
            // greater than 60
            else if (arr[i] > 60 && instances <= Math.Pow(10, 8))
            {

                // Double the instances
                instances = instances * 2;
                i = i + 10;

            }
            i = i + 1;

        }
        // Print the instances at the end
        // of the traversal
        Console.Write(instances);
    }


// Driver Code
static void Main()
{
    int instances = 2;

    int[] arr = {25, 23, 1, 2, 3, 4, 5,
        6, 7, 8, 9, 10, 76, 80};

    // Function Call
    finalInstances(instances, arr);
}
}

// This code is contributed by sanjoy_62.

Javascript

<script>

        // JavaScript Program for the above approach

        // Function to find the number of
        // instances after completion
        function finalInstances(instances, arr) {
            let i = 0;

            // Traverse the array, arr[]
            while (i < arr.length) {

                // If current element is less
                // than 25
                if (arr[i] < 25 && instances > 1) {

                    // Divide instances by 2
                    instances = Math.ceil(instances / 2);
                    i = i + 10;
                }

                // If the current element is
                // greater than 60
                else if (arr[i] > 60 && instances <= Math.pow(10, 8))
                {

                    // Double the instances
                    instances = instances * 2;
                    i = i + 10;

                }
                i = i + 1;

            }
            // Print the instances at the end
            // of the traversal
            document.write(instances);
        }
        // Driver Code
        let instances = 2;

        let arr = [25, 23, 1, 2, 3, 4, 5,
            6, 7, 8, 9, 10, 76, 80];

        // Function Call
        finalInstances(instances, arr);

    // This code is contributed by Potta Lokesh

</script>

Output:

2

Time Complexity: O(N)
Auxiliary Space: O(1)