Number of refills to complete the journey of N km

Given a number N which represents the total distance in km to be covered by a car on a single road. There are N petrol pumps at a distance of 1 km each(1, 2, 3, ..N). The capacity of the fuel tank of the car is such that at full tank it goes till a distance of K km. The car has to compulsorily stop at M petrol tanks whose distance from the starting position is given as M integers. The task is to find the number of times, the car has to refill its tank including the compulsory stops to complete its journey of N km. 

Examples :

Input: N = 5, K = 2, M = 1 
arr[] = {3} 
Output: 2 
The car starts at 0, with its tank full, travels for 2 km and then refills its tank at 2 km. The car makes the compulsory stop at 3 where its tank if refilled again. It travels for 2 km more to reach its destination of 5 km. 

Input: N = 10, K = 2, M = 3 
arr[] = { 6, 7, 8 } 
Output: 5 
The car starts from 0, stops at 2, 4 for refilling its tank, before making compulsory stops at 6, 7, 8. It travels 2 km from 8 km to make its journey of 10 km complete. 

Approach: As total journey is of N km, so keep a track of distance covered till now in a variable, say distCovered, which will be initialized by 0. Increment distCovered by K km till distCovered is less than N because K is the amount of distance vehicle can travel since the last refill. Also, with each increment, check if there is a compulsory petrol pump to stop between distCovered and distCovered + K, if yes, then distCovered will be K plus the last compulsory petrol pump to stop at between distCovered and distCovered + K. Also, keep counting the number of refills taken to reach the destination of N km. 

Below is the implementation of the above approach:  

C++

// CPP program for finding the total
// number of stops for refilling to
// reach destination of N km
#include <iostream>
using namespace std;

// Function that returns the total number of
// refills made to reach the destination of N km
int countRefill(int N, int K, int M, int compulsory[])
{
    int count = 0;
    int i = 0;
    int distCovered = 0;

    // While we complete the whole journey.
    while (distCovered < N) {
        // If must visited petrol pump lie
        // between distCovered and distCovered+K.
        if (i < M && compulsory[i] <= (distCovered + K)) {
            // make last mustVisited as distCovered
            distCovered = compulsory[i];

            // increment the index of compulsory visited.
            i++;
        }

        // if no such must visited pump is
        // there then increment distCovered by K.
        else
            distCovered += K;

        // Counting the number of refill.
        if (distCovered < N)
            count++;
    }

    return count;
}

// Driver Code
int main()
{
    int N = 10;
    int K = 2;
    int M = 3;
    // compulsory petrol pumps to refill at
    int compulsory[] = { 6, 7, 8 };

    // function call that returns the answer to the problem
    cout << countRefill(N, K, M, compulsory) << endl;
    return 0;
}

Java

// Java program for finding the
// total number of stops for
// refilling to reach
// destination of N km
import java.io.*;

class GFG
{

;

// Function that returns the
// total number of refills made
// to reach the destination of N km
static int countRefill(int N, int K,
                       int M, int compulsory[])
{
    int count = 0;
    int i = 0;
    int distCovered = 0;

    // While we complete
    // the whole journey.
    while (distCovered < N)
    {
        // If must visited petrol pump lie
        // between distCovered and distCovered+K.
        if (i < M && compulsory[i] <=
                                (distCovered + K))
        {
            // make last mustVisited
            // as distCovered
            distCovered = compulsory[i];

            // increment the index
            // of compulsory visited.
            i++;
        }

        // if no such must visited
        // pump is there then
        // increment distCovered by K.
        else
            distCovered += K;

        // Counting the number of refill.
        if (distCovered < N)
            count++;
    }

    return count;
}

// Driver Code
public static void main (String[] args)
{
    int N = 10;
    int K = 2;
    int M = 3;
    // compulsory petrol
    // pumps to refill at
    int compulsory[] = { 6, 7, 8 };

    // function call that returns
    // the answer to the problem
    System.out.println(countRefill(N, K,
                        M, compulsory));
}
}

// This code is contributed by anuj_67.

Python3

# Python 3 program for finding the total
# number of stops for refilling to reach
# destination of N km

# Function that returns the total number of
# refills made to reach the destination of N km
def countRefill(N, K, M, compulsory):
    count = 0
    i = 0
    distCovered = 0

    # While we complete the whole journey.
    while (distCovered < N):

        # If must visited petrol pump lie
        # between distCovered and distCovered+K.
        if (i < M and compulsory[i] <= (distCovered + K)):

            # make last mustVisited as distCovered
            distCovered = compulsory[i]

            # increment the index of
            # compulsory visited.
            i += 1

        # if no such must visited pump is
        # there then increment distCovered by K.
        else:
            distCovered += K

        # Counting the number of refill.
        if (distCovered < N):
            count += 1

    return count

# Driver Code
if __name__ == '__main__':
    N = 10
    K = 2
    M = 3

    # compulsory petrol pumps to refill at
    compulsory = [6, 7, 8]

    # function call that returns the
    # answer to the problem
    print(countRefill(N, K, M, compulsory))

# This code is contributed by
# Sanjit_Prasad

C#

// C# program for finding the
// total number of stops for
// refilling to reach
// destination of N km
using System;

class GFG
{

// Function that returns
// the total number of
// refills made to reach
// the destination of N km
static int countRefill(int N, int K,
                       int M, int []compulsory)
{
    int count = 0;
    int i = 0;
    int distCovered = 0;

    // While we complete
    // the whole journey.
    while (distCovered < N)
    {
        // If must visited petrol pump
        // lie between distCovered and
        // distCovered+K.
        if (i < M && compulsory[i] <=
                (distCovered + K))
        {
            // make last mustVisited
            // as distCovered
            distCovered = compulsory[i];

            // increment the index
            // of compulsory visited.
            i++;
        }

        // if no such must visited
        // pump is there then
        // increment distCovered by K.
        else
            distCovered += K;

        // Counting the number of refill.
        if (distCovered < N)
            count++;
    }

    return count;
}

// Driver Code
public static void Main ()
{
    int N = 10;
    int K = 2;
    int M = 3;

    // compulsory petrol
    // pumps to refill at
    int []compulsory = {6, 7, 8};

    // function call that returns
    // the answer to the problem
    Console.WriteLine(countRefill(N, K,
                       M, compulsory));
}
}

// This code is contributed by anuj_67.

PHP

<?php
// PHP program for finding the total
// number of stops for refilling to
// reach destination of N km

// Function that returns the total
// number of refills made to reach
// the destination of N km
function countRefill($N, $K, $M,
                     $compulsory)
{
    $count = 0;
    $i = 0;
    $distCovered = 0;

    // While we complete
    // the whole journey.
    while ($distCovered < $N)
    {
        // If must visited petrol
        // pump lie between distCovered
        // and distCovered + K.
        if ($i < $M and $compulsory[$i] <=
                       ($distCovered + $K))
        {
            // make last mustVisited
            // as distCovered
            $distCovered = $compulsory[$i];

            // increment the index
            // of compulsory visited.
            $i++;
        }

        // if no such must visited
        // pump is there then
        // increment distCovered by K.
        else
            $distCovered += $K;

        // Counting the number
        // of refill.
        if ($distCovered < $N)
            $count++;
    }

    return $count;
}

// Driver Code
$N = 10;
$K = 2;
$M = 3;

// compulsory petrol
// pumps to refill at
$compulsory = array(6, 7, 8);

// function call that returns
// the answer to the problem
echo countRefill($N, $K, $M,
                 $compulsory) , "\n";

// This code is contributed by anuj_67.
?>

Javascript

<script>

// Javascript program for finding the total
// number of stops for refilling to
// reach destination of N km

// Function that returns the total number of
// refills made to reach the destination of N km
function countRefill(N, K, M, compulsory)
{
    var count = 0;
    var i = 0;
    var distCovered = 0;

    // While we complete the whole journey.
    while (distCovered < N) {
        // If must visited petrol pump lie
        // between distCovered and distCovered+K.
        if (i < M && compulsory[i] <= (distCovered + K))
        {
            // make last mustVisited as distCovered
            distCovered = compulsory[i];

            // increment the index of compulsory visited.
            i++;
        }

        // if no such must visited pump is
        // there then increment distCovered by K.
        else
            distCovered += K;

        // Counting the number of refill.
        if (distCovered < N)
            count++;
    }

    return count;
}

// Driver Code
var N = 10;
var K = 2;
var M = 3;

// compulsory petrol pumps to refill at
var compulsory = [ 6, 7, 8 ];

// function call that returns the answer to the problem
document.write( countRefill(N, K, M, compulsory));

</script>

Output

5

Complexity Analysis:

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