Minimum total cost incurred to reach the last station

Given an array where each element denotes the number of chocolates corresponding to each station and to move from station i to station i+1, we get A[i] – A[i+1] chocolates for free, if this number is negative, we lose that many chocolates also. 
You can only move from station i to station i+1, if we have non-negative number of chocolates. 
Given the cost of one chocolate p, the task to find the minimum cost incurred in reaching last station from the first station (station 1). 
Note: Initially we have 0 chocolates.
Examples: 

Input : arr[] = {1, 2, 3}   p = 10
Output : 30
Initial choc_buy = 1 (arr[0])
To reach index 0 to 1, arr[0] - arr[1] = -1,
so choc_buy +=1.
Similarly To reach index 2 to 1, 
arr[1] - arr[2] = -1, so choc_buy +=1.
Total choc_buy = 3.
Total cost = choc_by * p = 3*10 = 30.

Input : arr[] = {10, 6, 11, 4, 7, 1}    p = 5
Output : 55
Initial choc_buy = 10 (arr[0])
To reach index 0 to 1, arr[0] - arr[1] = 4, 
so curr_choc =4.
Similarly To reach index 2 to 1, 
arr[1] - arr[2] = -5, so curr_choc=4+-5 = -1.
choc_buy += abs(-1).
So, similarly till last station, Total choc_buy = 11.
Total cost = choc_by * p = 11*5 = 55.

Approach :
1. Initialize choc_buy with the first element of array and curr_choc =0. 
2. Add arr[i]-arr[i+1] to curr_choc for every i. 
a) Check if curr_choc becomes negative. 
choc_buy += abs(arr[i]- arr[i+1]) 
curr_choc = 0 
3. Return choc_buy * p.

C++

// C++ program to calculate
// minimum cost for candies
#include <bits/stdc++.h>
using namespace std;

// Function to find minimum cost
// to be incurred
int findMinCost(int arr[], int n, int choc_cost) {

  // To reach first station, initial
  // chocolates required
  int choc_buy = arr[0];
  int curr_choc = 0;

  // Start traversing
  for (int i = 0; i < n - 1; i++) {

    // Find no. of chocolates
    // lose or gain
    int choc = arr[i] - arr[i + 1];

    // Add into curr_coc
    curr_choc += choc;

    // if no. of chocolates becomes
    // negative that means we have
    // to buy that no. of chocolates
    if (curr_choc < 0) {
      choc_buy += abs(curr_choc);
      curr_choc = 0;
    }
  }

  // Return cost required
  return choc_buy * choc_cost;
}

// Drivers code
int main() {
  int arr[] = {10, 6, 11, 4, 7, 1};
  int n = sizeof(arr) / sizeof(arr[0]);

  // Price of each candy
  int p = 5;

  cout << findMinCost(arr, n, p);

  return 0;
}

Java

// Java program to calculate
// minimum cost for candies
import java.io.*;

class GFG
{
    // Function to find minimum cost
    // to be incurred
    static int findMinCost(int arr[], int n, int choc_cost)
    {

    // To reach first station, initial
    // chocolates required
    int choc_buy = arr[0];
    int curr_choc = 0;

    // Start traversing
    for (int i = 0; i < n - 1; i++)
    {

        // Find no. of chocolates
        // lose or gain
        int choc = arr[i] - arr[i + 1];

        // Add into curr_coc
        curr_choc += choc;

        // if no. of chocolates becomes
        // negative that means we have
        // to buy that no. of chocolates
        if (curr_choc < 0)
        {
            choc_buy += Math.abs(curr_choc);
            curr_choc = 0;
        }
    }

    // Return cost required
    return choc_buy * choc_cost;
    }

    // Drivers code
    public static void main (String[] args)
    {
        int arr[] = {10, 6, 11, 4, 7, 1};
        int n = arr.length;

        // Price of each candy
        int p = 5;

        System.out.println ( findMinCost(arr, n, p));
    }
}

// This code is contributed by vt_m

Python3

# Python 3 program to calculate
# minimum cost for candies

# Function to find minimum cost
# to be incurred
def findMinCost(arr, n, choc_cost):

    # To reach first station,
    # initial chocolates required
    choc_buy = arr[0]
    curr_choc = 0

    # Start traversing
    for i in range(0,n - 1):

        # Find no. of chocolates lose
        # or gain
        choc = arr[i] - arr[i + 1]

        # Add into curr_coc
        curr_choc += choc

        # if no. of chocolates becomes
        # negative that means we have
        # to buy that no. of chocolates
        if (curr_choc < 0):
            choc_buy += abs(curr_choc)
            curr_choc = 0

    # Return cost required
    return choc_buy * choc_cost


# Drivers code
arr = [10, 6, 11, 4, 7, 1]
n = len(arr)

# Price of each candy
p = 5

print(findMinCost(arr, n, p))

# This code is contributed by Smitha Dinesh Semwal

C#

// C# program to calculate
// minimum cost for candies
using System;

class GFG
{
    // Function to find minimum cost
    // to be incurred
    static int findMinCost(int []arr,
                    int n, int choc_cost)
    {

        // To reach first station, initial
        // chocolates required
        int choc_buy = arr[0];
        int curr_choc = 0;

        // Start traversing
        for (int i = 0; i < n - 1; i++)
        {

            // Find no. of chocolates
            // lose or gain
            int choc = arr[i] - arr[i + 1];

            // Add into curr_coc
            curr_choc += choc;

            // if no. of chocolates becomes
            // negative that means we have
            // to buy that no. of chocolates
            if (curr_choc < 0)
            {
                choc_buy += Math.Abs(curr_choc);
                curr_choc = 0;
            }
    }

    // Return cost required
    return choc_buy * choc_cost;
    }

    // Drivers code
    public static void Main ()
    {
        int []arr = {10, 6, 11, 4, 7, 1};
        int n = arr.Length;

        // Price of each candy
        int p = 5;

    Console.WriteLine( findMinCost(arr, n, p));
    }
}

// This code is contributed by vt_m

PHP

<?php
// PHP program to calculate
// minimum cost for candies

// Function to find minimum cost
// to be incurred
function findMinCost($arr, $n, $choc_cost)
{

    // To reach first station, initial
    // chocolates required
    $choc_buy = $arr[0];
    $curr_choc = 0;

    // Start traversing
    for ($i = 0; $i < $n - 1; $i++) {

        // Find no. of chocolates
        // lose or gain
        $choc = $arr[$i] - $arr[$i + 1];

        // Add into curr_coc
        $curr_choc += $choc;

        // if no. of chocolates becomes
        // negative that means we have
        // to buy that no. of chocolates
        if ($curr_choc < 0) {
        $choc_buy += abs($curr_choc);
        $curr_choc = 0;
        }
    }

    // Return cost required
    return $choc_buy * $choc_cost;
}

// Driver Code
$arr = array(10, 6, 11, 4, 7, 1);
$n = count($arr);

// Price of each candy
$p = 5;

echo findMinCost($arr, $n, $p);

// This code is contributed by Sam007
?>

Javascript

<script>
// Javascript program to calculate
// minimum cost for candies


// Function to find minimum cost
// to be incurred
function findMinCost(arr,  n,  choc_cost) {

// To reach first station, initial
// chocolates required
var choc_buy = arr[0];
var curr_choc = 0;

// Start traversing
for (var i = 0; i < n - 1; i++) {

    // Find no. of chocolates
    // lose or gain
    var choc = arr[i] - arr[i + 1];

    // Add into curr_coc
    curr_choc += choc;

    // if no. of chocolates becomes
    // negative that means we have
    // to buy that no. of chocolates
    if (curr_choc < 0) {
    choc_buy += Math.abs(curr_choc);
    curr_choc = 0;
    }
}

// Return cost required
return (choc_buy * choc_cost);
}

var  arr = [10, 6, 11, 4, 7, 1];
var n = 6;

// Price of each candy
var p = 5;

document.write(findMinCost(arr, n, p));



</script>

Output:

55

Time Complexity: O(n)
Auxiliary Space: O(1)