# 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

**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.**

*distCovered*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; ` `} ` |

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## 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. ` |

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## 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 ` |

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## 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. ` |

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## 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. ` `?> ` |

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**Output :**

5

**Time Complexity**: O(N)

**Auxiliary Space**: O(1)

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