Minimum time required to fill a cistern using N pipes
Given the time required by a total of N+1 pipes where N pipes are used to fill the Cistern and a single pipe is used to empty the Cistern. The task is to Calculate the amount of time in which the Cistern will get filled if all the N+1 pipes are opened together.
Examples:
Input: n = 2, pipe1 = 12 hours, pipe2 = 14 hours, emptypipe = 30 hours Output: 8 hours Input: n = 1, pipe1 = 12 hours emptypipe = 18 hours Output: 36 hours
Approach:
- If a pipe1 can fill a cistern in ‘n’ hours, then in 1 hour, the pipe1 will able to fill ‘1/n’ Cistern.
- Similarly If a pipe2 can fill a cistern in ‘m’ hours, then in one hour, the pipe2 will able to fill ‘1/m’ Cistern.
- So on…. for other pipes.
So, total work done in filling a Cistern by N pipes in 1 hours is
1/n + 1/m + 1/p…… + 1/z
Where n, m, p ….., z are the number of hours taken by each pipes respectively.The result of the above expression will be the part of work done by all pipes together in 1 hours, let’s say a / b.
To calculate the time taken to fill the cistern will be b / a.
Consider an example of two pipes:
Time taken by 1st pipe to fill the cistern = 12 hours
Time taken by 2nd pipe to fill the cistern = 14 hours
Time taken by 3rd pipe to empty the cistern = 30 hoursWork done by 1st pipe in 1 hour = 1/12
Work done by 2nd pipe in 1 hour = 1/14
Work done by 3nd pipe in 1 hour = – (1/30) as it empty the pipe.
So, total work done by all the pipes in 1 hour is
=> ( 1 / 12 + 1/ 14 ) – (1 / 30)
=> ((7 + 6 ) / (84)) – (1 / 30)
=> ((13) / (84)) – (1 / 30)
=> 51 / 420So, to Fill the cistern time required will be 420 / 51 i.e 8 hours Approx.
Below is the implementation of above approach:
C++
// C++ implementation of above approach #include <bits/stdc++.h> using namespace std; // Function to calculate the time float Time( float arr[], int n, int Emptypipe) { float fill = 0; for ( int i = 0; i < n; i++) fill += 1 / arr[i]; fill = fill - (1 / ( float )Emptypipe); return 1 / fill; } // Driver Code int main() { float arr[] = { 12, 14 }; float Emptypipe = 30; int n = sizeof (arr) / sizeof (arr[0]); cout << floor (Time(arr, n, Emptypipe)) << " Hours" ; return 0; } |
Java
// Java implementation of // above approach import java.io.*; class GFG { // Function to calculate the time static float Time( float arr[], int n, float Emptypipe) { float fill = 0 ; for ( int i = 0 ; i < n; i++) fill += 1 / arr[i]; fill = fill - ( 1 / ( float )Emptypipe); return 1 / fill; } // Driver Code public static void main (String[] args) { float arr[] = { 12 , 14 }; float Emptypipe = 30 ; int n = arr.length; System.out.println(( int )(Time(arr, n, Emptypipe)) + " Hours" ); } } // This code is contributed // by inder_verma. |
Python3
# Python3 implementation of # above approach # Function to calculate the time def Time(arr, n, Emptypipe) : fill = 0 for i in range ( 0 ,n) : fill + = ( 1 / arr[i]) fill = fill - ( 1 / float (Emptypipe)) return int ( 1 / fill) # Driver Code if __name__ = = '__main__' : arr = [ 12 , 14 ] Emptypipe = 30 n = len (arr) print ((Time(arr, n, Emptypipe)) , "Hours" ) # This code is contributed by # Smitha Dinesh Semwal |
C#
// C# implementation of // above approach using System; class GFG { // Function to calculate the time static float Time( float []arr, int n, float Emptypipe) { float fill = 0; for ( int i = 0; i < n; i++) fill += 1 / arr[i]; fill = fill - (1 / ( float )Emptypipe); return 1 / fill; } // Driver Code public static void Main () { float []arr = { 12, 14 }; float Emptypipe = 30; int n = arr.Length; Console.WriteLine(( int )(Time(arr, n, Emptypipe)) + " Hours" ); } } // This code is contributed // by inder_verma. |
PHP
<?php // PHP implementation of above approach // Function to calculate the time function T_ime( $arr , $n , $Emptypipe ) { $fill = 0; for ( $i = 0; $i < $n ; $i ++) $fill += 1 / $arr [ $i ]; $fill = $fill - (1 / $Emptypipe ); return 1 / $fill ; } // Driver Code $arr = array ( 12, 14 ); $Emptypipe = 30; $n = count ( $arr ); echo (int)T_ime( $arr , $n , $Emptypipe ) . " Hours" ; // This code is contributed // by inder_verma. ?> |
8 Hours
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