Minimum time required to transport all the boxes from source to the destination under the given constraints
Given two arrays, box[] and truck[], where box[i] represents the weight of the ith box and truck[i] represents the maximum load that the ith truck can carry. Now each truck takes 1 hour to transport a box from source to destination and another one hour to come back. Now, given that all the boxes are kept at the source, the task is to find the minimum time required to transport all the boxes from the source to the destination.
Note that there will always be some time in which the boxes can be transported and only a single box can be carried by truck at any instance of time.
Examples:
Input: box[] = {7, 6, 5, 4, 3}, truck[] = {10, 3}
Output: 7
1st hour: truck[0] carries box[0] and truck[1] carries box[4]
2nd hour: Both trucks are back at the source location.
Now, truck[1] cannot carry anymore boxes as all the remaining boxes
have weights more than the capacity of a truck[1].
So, truck[0] will carry box[1] and box[2]
in a total of four hours. (source-destination and then destination-source)
And finally, box[3] will take another hour to reach the destination.
So, total time taken = 2 + 4 + 1 = 7Input: box[] = {10, 2, 16, 19}, truck[] = {29, 25}
Output: 3
Approach: The idea is to use binary search and sort the two arrays. Here the lower bound will be 0 and the upper bound will be 2 * size of box[] because in the worst case, the amount of time required to transport all the boxes will be 2 * size of box array. Now compute the mid-value, and for each mid-value check if all the boxes can be transported by the loaders in time = mid. If yes, then update the upper bound as mid – 1 and if not, then update the lower bound as mid + 1.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function that returns true if it is // possible to transport all the boxes // in the given amount of time bool isPossible( int box[], int truck[], int n, int m, int min_time) { int temp = 0; int count = 0; while (count < m) { for ( int j = 0; j < min_time && temp < n && truck[count] >= box[temp]; j += 2) temp++; count++; } // If all the boxes can be // transported in the given time if (temp == n) return true ; // If all the boxes can't be // transported in the given time return false ; } // Function to return the minimum time required int minTime( int box[], int truck[], int n, int m) { // Sort the two arrays sort(box, box + n); sort(truck, truck + m); int l = 0; int h = 2 * n; // Stores minimum time in which // all the boxes can be transported int min_time = 0; // Check for the minimum time in which // all the boxes can be transported while (l <= h) { int mid = (l + h) / 2; // If it is possible to transport all // the boxes in mid amount of time if (isPossible(box, truck, n, m, mid)) { min_time = mid; h = mid - 1; } else l = mid + 1; } return min_time; } // Driver code int main() { int box[] = { 10, 2, 16, 19 }; int truck[] = { 29, 25 }; int n = sizeof (box) / sizeof ( int ); int m = sizeof (truck) / sizeof ( int ); printf ( "%d" , minTime(box, truck, n, m)); return 0; } |
Java
// Java implementation of the approach import java.util.Arrays; class GFG { // Function that returns true if it is // possible to transport all the boxes // in the given amount of time static boolean isPossible( int box[], int truck[], int n, int m, int min_time) { int temp = 0 ; int count = 0 ; while (count < m) { for ( int j = 0 ; j < min_time && temp < n && truck[count] >= box[temp]; j += 2 ) temp++; count++; } // If all the boxes can be // transported in the given time if (temp == n) return true ; // If all the boxes can't be // transported in the given time return false ; } // Function to return the minimum time required static int minTime( int box[], int truck[], int n, int m) { // Sort the two arrays Arrays.sort(box); Arrays.sort(truck); int l = 0 ; int h = 2 * n; // Stores minimum time in which // all the boxes can be transported int min_time = 0 ; // Check for the minimum time in which // all the boxes can be transported while (l <= h) { int mid = (l + h) / 2 ; // If it is possible to transport all // the boxes in mid amount of time if (isPossible(box, truck, n, m, mid)) { min_time = mid; h = mid - 1 ; } else l = mid + 1 ; } return min_time; } // Driver code public static void main(String[] args) { int box[] = { 10 , 2 , 16 , 19 }; int truck[] = { 29 , 25 }; int n = box.length; int m = truck.length; System.out.printf( "%d" , minTime(box, truck, n, m)); } } /* This code contributed by PrinciRaj1992 */ |
Python3
# Python3 implementation of the approach # Function that returns true if it is # possible to transport all the boxes # in the given amount of time def isPossible(box, truck, n, m, min_time) : temp = 0 count = 0 while (count < m) : j = 0 while (j < min_time and temp < n and truck[count] > = box[temp] ): temp + = 1 j + = 2 count + = 1 # If all the boxes can be # transported in the given time if (temp = = n) : return True # If all the boxes can't be # transported in the given time return False # Function to return the minimum time required def minTime(box, truck, n, m) : # Sort the two arrays box.sort(); truck.sort(); l = 0 h = 2 * n # Stores minimum time in which # all the boxes can be transported min_time = 0 # Check for the minimum time in which # all the boxes can be transported while (l < = h) : mid = (l + h) / / 2 # If it is possible to transport all # the boxes in mid amount of time if (isPossible(box, truck, n, m, mid)) : min_time = mid h = mid - 1 else : l = mid + 1 return min_time # Driver code if __name__ = = "__main__" : box = [ 10 , 2 , 16 , 19 ] truck = [ 29 , 25 ] n = len (box) m = len (truck) print (minTime(box, truck, n, m)) # This code is contributed by Ryuga |
C#
// C# implementation of the approach using System; class GFG { // Function that returns true if it is // possible to transport all the boxes // in the given amount of time static bool isPossible( int []box, int []truck, int n, int m, int min_time) { int temp = 0; int count = 0; while (count < m) { for ( int j = 0; j < min_time && temp < n && truck[count] >= box[temp]; j += 2) temp++; count++; } // If all the boxes can be // transported in the given time if (temp == n) return true ; // If all the boxes can't be // transported in the given time return false ; } // Function to return the minimum time required static int minTime( int []box, int []truck, int n, int m) { // Sort the two arrays Array.Sort(box); Array.Sort(truck); int l = 0; int h = 2 * n; // Stores minimum time in which // all the boxes can be transported int min_time = 0; // Check for the minimum time in which // all the boxes can be transported while (l <= h) { int mid = (l + h) / 2; // If it is possible to transport all // the boxes in mid amount of time if (isPossible(box, truck, n, m, mid)) { min_time = mid; h = mid - 1; } else l = mid + 1; } return min_time; } // Driver code public static void Main(String[] args) { int [] box = { 10, 2, 16, 19 }; int []truck = { 29, 25 }; int n = box.Length; int m = truck.Length; Console.WriteLine( "{0}" , minTime(box, truck, n, m)); } } /* This code contributed by PrinciRaj1992 */ |
PHP
<?php // PHP implementation of the approach // Function that returns true if it is // possible to transport all the boxes // in the given amount of time function isPossible( $box , $truck , $n , $m , $min_time ) { $temp = 0; $count = 0; while ( $count < $m ) { for ( $j = 0; $j < $min_time && $temp < $n && $truck [ $count ] >= $box [ $temp ]; $j += 2) $temp ++; $count ++; } // If all the boxes can be // transported in the given time if ( $temp == $n ) return true; // If all the boxes can't be // transported in the given time return false; } // Function to return the minimum time required function minTime( $box , $truck , $n , $m ) { // Sort the two arrays sort( $box ); sort( $truck ); $l = 0; $h = 2 * $n ; // Stores minimum time in which // all the boxes can be transported $min_time = 0; // Check for the minimum time in which // all the boxes can be transported while ( $l <= $h ) { $mid = intdiv(( $l + $h ) , 2); // If it is possible to transport all // the boxes in mid amount of time if (isPossible( $box , $truck , $n , $m , $mid )) { $min_time = $mid ; $h = $mid - 1; } else $l = $mid + 1; } return $min_time ; } // Driver code $box = array ( 10, 2, 16, 19 ); $truck = array ( 29, 25 ); $n = sizeof( $box ); $m = sizeof( $truck ); echo minTime( $box , $truck , $n , $m ); // This code is contributed by ihritik ?> |
Javascript
<script> // Js implementation of the approach // Function that returns true if it is // possible to transport all the boxes // in the given amount of time function isPossible( box, truck, n, m, min_time) { let temp = 0; let count = 0; while (count < m) { for (let j = 0; j < min_time && temp < n && truck[count] >= box[temp]; j += 2) temp++; count++; } // If all the boxes can be // transported in the given time if (temp == n) return true ; // If all the boxes can't be // transported in the given time return false ; } // Function to return the minimum time required function minTime(box, truck, n, m) { // Sort the two arrays box.sort( function (a,b){ return a-b }); truck.sort( function (a,b){ return a-b }); let l = 0; let h = 2 * n; // Stores minimum time in which // all the boxes can be transported let min_time = 0; // Check for the minimum time in which // all the boxes can be transported while (l <= h) { let mid = Math.floor((l + h) / 2); // If it is possible to transport all // the boxes in mid amount of time if (isPossible(box, truck, n, m, mid)) { min_time = mid; h = mid - 1; } else l = mid + 1; } return min_time; } // Driver code let box = [ 10, 2, 16, 19 ]; let truck = [ 29, 25 ]; let n = box.length; let m = truck.length; document.write(minTime(box, truck, n, m)); </script> |
3
Time Complexity: O(N * log(N))
Auxiliary Space: O(1)