Minimum time required to complete a work by N persons together

Given the no. of working hours of N people individually to complete a certain piece of work. The task is to find the number of hours they will take when all work together. 
Examples:

Input: n = 2, a = 6.0, b = 3.0
Output: 2 Hours

Input: n = 3, a = 6.0, b = 3.0, c = 4.0
Output: 1.33333 Hours

Solution:

• If a person can do a piece of work in ‘n’ days, then in one day, the person will do ‘1/n’ work.
• Similarly If a person can do a piece of work in ‘m’ days, then in one day, the person will do ‘1/m’ work.
• So on…. for other persons.

So, total work done by N persons in 1 day is

1/n + 1/m + 1/p…… + 1/z 
Where n, m, p ….., z are the number of days taken by each person respectively.
The result of the above expression will be the part of work done by all person together in 1 day, let’s say a / b. 
To calculate the time taken to complete the whole work will be b / a.

Consider an example of two persons:

Time taken by 1st person to complete a work = 6 hours
Time taken by 2nd person to complete the same work = 2 hours

Work done by 1st person in 1 hour = 1/6
Work done by 2nd person in 1 hour = 1/2
So, total work done by them in 1 hour is
=> 1 / 6 + 1/ 2 
=> (2 + 6) / (2 * 6)
=> 8 / 12

So, to complete the whole work, the time taken will be 12/8.

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;

// Function to calculate the time
float calTime(float arr[], int n)
{

    float work = 0;
    for (int i = 0; i < n; i++)
        work += 1 / arr[i];

    return 1 / work;
}

// Driver Code
int main()
{
    float arr[] = { 6.0, 3.0, 4.0 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << calTime(arr, n) << " Hours";

    return 0;
}

Java

// Java implementation
// of above approach
import java.io.*;

class GFG
{

// Function to calculate the time
static double calTime(double arr[], int n)
{
    double work = 0;
    for (int i = 0; i < n; i++)
        work += 1 / arr[i];

    return 1 / work;
}

// Driver Code
public static void main (String[] args)
{
    double arr[] = { 6.0, 3.0, 4.0 };
    int n = arr.length;

    System.out.println(calTime(arr, n) +
                              " Hours");
}
}

// This code is contributed
// by inder_verma.

Python3

# Python3 implementation of
# above approach

# Function to calculate the time
def calTime(arr, n):

    work = 0
    for i in range(n):
        work += 1 / arr[i]

    return 1 / work

# Driver Code
arr = [ 6.0, 3.0, 4.0 ]
n = len(arr)

print(calTime(arr, n), "Hours")

# This code is contributed
# by Sanjit_Prasad

C#

// C# implementation
// of above approach
using System;
class GFG
{

// Function to calculate the time
static double calTime(double []arr,
                      int n)
{
    double work = 0;
    for (int i = 0; i < n; i++)
        work += 1 / arr[i];

    return Math.Round(1 / work, 5);
}

// Driver Code
public static void Main ()
{
    double []arr = { 6.0, 3.0, 4.0 };
    int n = arr.Length;

    Console.Write(calTime(arr, n) +
                         " Hours");
}
}

// This code is contributed by Smitha

PHP

<?php
// PHP implementation of above approach

// Function to calculate the time
function calTime(&$arr, $n)
{
    $work = 0;
    for ($i = 0; $i < $n; $i++)
        $work += 1 / $arr[$i];

    return 1 / $work;
}

// Driver Code
$arr = array(6.0, 3.0, 4.0);
$n = sizeof($arr);

echo calTime($arr, $n);
echo " Hours";

// This code is contributed
// by Shivi_Aggarwal
?>

Javascript

<script>
// javascript implementation
// of above approach

    // Function to calculate the time
    function calTime(arr , n)
    {
        var work = 0;
        for (i = 0; i < n; i++)
            work += 1 / arr[i];

        return 1 / work;
    }

    // Driver Code

    var arr = [ 6.0, 3.0, 4.0 ];
    var n = arr.length;

    document.write(calTime(arr, n).toFixed(5) + " Hours");

// This code is contributed by Rajput-Ji.
</script>

Output:

1.33333 Hours

Time Complexity: O(n), to iterate over the array
Auxiliary Space: O(1)

Note: Here the input array contains hours, it can be days, minutes……so on.