# Schedule elevator to reduce the total time taken

Given an integer k and an array arr[] representing the destination floors for N people waiting currently at the ground floor and k is the capacity of the elevator i.e. maximum number of people it can hold at the same time. It takes 1 unit time for the elevator to reach any consecutive floor from the current floor. The task is to schedule the elevator in a way to minimize the total time taken to get all the people to their destination floor and then return back to the ground floor.

Examples:

Input: arr[] = {2, 3, 4}, k = 2
Output: 12
Second and the third persons (destination floors 3 and 4) shall go in the first turn taking 8 (4 + 4) unit time. The only person left will take 2 unit time to get to the destination
And then the elevator will take another 2 unit time to get back to the ground floor.
Total time taken = 8 + 2 + 2 = 12

Input: arr[] = {5, 5, 4}, k = 3
Output: 10
Every person can get on the elevator at the same time
Time required will be 10 (5 + 5).

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Sort the given array in decreasing order of destination. Create groups of K (starting from the highest floor), the cost for each group will be 2 * (max(Elements in current group)). The summation across all groups will be the answer.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the minimum time taken ` `// by the elevator when operating optimally ` `int` `minTime(``int` `n, ``int` `k, ``int` `a[]) ` `{ ` `    ``// Sort in descending order ` `    ``sort(a, a + n, greater<``int``>()); ` `    ``int` `minTime = 0; ` ` `  `    ``// Iterate through the groups ` `    ``for` `(``int` `i = 0; i < n; i += k) ` ` `  `        ``// Update the time taken for each group ` `        ``minTime += (2 * a[i]); ` ` `  `    ``// Return the total time taken ` `    ``return` `minTime; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `k = 2; ` `    ``int` `arr[] = { 2, 3, 4 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``cout << minTime(n, k, arr); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the minimum time taken ` `// by the elevator when operating optimally ` `static` `int` `minTime(``int` `n, ``int` `k, ``int` `a[]) ` `{ ` `    ``// Sort in descending order ` `    ``int` `temp; ` `    ``for``(``int` `i = ``0``; i < n; i++) ` `    ``{      ` `        ``for``(``int` `j = i + ``1``; j < n; j++) ` `        ``{ ` `            ``if``(a[i] < a[j]) ` `            ``{ ` `                ``temp = a[i]; ` `                ``a[i] = a[j]; ` `                ``a[j] = temp; ` `            ``} ` `        ``} ` `    ``} ` ` `  ` `  `    ``int` `minTime = ``0``; ` ` `  `    ``// Iterate through the groups ` `    ``for` `(``int` `i = ``0``; i < n; i += k) ` ` `  `        ``// Update the time taken for each group ` `        ``minTime += (``2` `* a[i]); ` ` `  `    ``// Return the total time taken ` `    ``return` `minTime; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `k = ``2``; ` `    ``int` `arr[] = { ``2``, ``3``, ``4` `}; ` `    ``int` `n = arr.length; ` `    ``System.out.println(minTime(n, k, arr)); ` `} ` `} ` ` `  `// This code is contributed by ` `// Surendra_Gangwar `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to return the minimum time taken  ` `# by the elevator when operating optimally  ` `def` `minTime(n, k, a) : ` `     `  `    ``# Sort in descending order  ` `    ``a.sort(reverse ``=` `True``);  ` `     `  `    ``minTime ``=` `0``;  ` ` `  `    ``# Iterate through the groups  ` `    ``for` `i ``in` `range``(``0``, n, k) : ` ` `  `        ``# Update the time taken for  ` `        ``# each group  ` `        ``minTime ``+``=` `(``2` `*` `a[i]);  ` ` `  `    ``# Return the total time taken  ` `    ``return` `minTime;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `: ` `     `  `    ``k ``=` `2``;  ` `    ``arr ``=` `[ ``2``, ``3``, ``4` `];  ` `    ``n ``=` `len``(arr) ; ` `    ``print``(minTime(n, k, arr));  ` `     `  `# This code is contributed by Ryuga `

## C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG  ` `{  ` ` `  `// Function to return the minimum time taken  ` `// by the elevator when operating optimally  ` `static` `int` `minTime(``int` `n, ``int` `k, ``int` `[]a)  ` `{  ` `    ``// Sort in descending order  ` `    ``int` `temp;  ` `    ``for``(``int` `i = 0; i < n; i++)  ` `    ``{  ` `        ``for``(``int` `j = i + 1; j < n; j++)  ` `        ``{  ` `            ``if``(a[i] < a[j])  ` `            ``{  ` `                ``temp = a[i];  ` `                ``a[i] = a[j];  ` `                ``a[j] = temp;  ` `            ``}  ` `        ``}  ` `    ``}  ` ` `  ` `  `    ``int` `minTime = 0;  ` ` `  `    ``// Iterate through the groups  ` `    ``for` `(``int` `i = 0; i < n; i += k)  ` ` `  `        ``// Update the time taken for each group  ` `        ``minTime += (2 * a[i]);  ` ` `  `    ``// Return the total time taken  ` `    ``return` `minTime;  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main(String []args)  ` `{  ` `    ``int` `k = 2;  ` `    ``int` `[]arr = { 2, 3, 4 };  ` `    ``int` `n = arr.Length;  ` `    ``Console.Write(minTime(n, k, arr));  ` `}  ` `}  ` ` `  `// This code is contributed by Arnab Kundu `

Output:

```12
```

Time Complexity: O(N * log(N))

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