# Minimum possible travel cost among N cities

• Difficulty Level : Medium
• Last Updated : 04 Aug, 2021

There are N cities situated on a straight road and each is separated by a distance of 1 unit. You have to reach the (N + 1)th city by boarding a bus. The ith city would cost of C[i] dollars to travel 1 unit of distance. In other words, cost to travel from the ith city to the jth city is abs(i – j ) * C[i] dollars. The task is to find the minimum cost to travel from city 1 to city (N + 1) i.e. beyond the last city.
Examples:

Input: C[] = {3, 5, 4}
Output:
The bus boarded from the first city has the minimum
cost of all so it will be used to travel (N + 1) unit.
Input: C[] = {4, 7, 8, 3, 4}
Output: 18
Board the bus at the first city then change
the bus at the fourth city.
(3 * 4) + (2 * 3) = 12 + 6 = 18

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Approach: The approach is very simple, just travel by the bus which has the lowest cost so far. Whenever a bus with an even lower cost is found, change the bus from that city. Following are the steps to solve:

2. Travel to the next city until a city j having cost less than the previous city (by which we are travelling, let’s say city i) is found.
3. Calculate cost as abs(j – i) * C[i] and add it to the total cost so far.
4. Repeat the previous steps until all the cities have been traversed.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the minimum cost to``// travel from the first city to the last``int` `minCost(vector<``int``>& cost, ``int` `n)``{` `    ``// To store the total cost``    ``int` `totalCost = 0;` `    ``// Start from the first city``    ``int` `boardingBus = 0;` `    ``for` `(``int` `i = 1; i < n; i++) {` `        ``// If found any city with cost less than``        ``// that of the previous boarded``        ``// bus then change the bus``        ``if` `(cost[boardingBus] > cost[i]) {` `            ``// Calculate the cost to travel from``            ``// the currently boarded bus``            ``// till the current city``            ``totalCost += ((i - boardingBus) * cost[boardingBus]);` `            ``// Update the currently boarded bus``            ``boardingBus = i;``        ``}``    ``}` `    ``// Finally calculate the cost for the``    ``// last boarding bus till the (N + 1)th city``    ``totalCost += ((n - boardingBus) * cost[boardingBus]);``    ``return` `totalCost;``}` `// Driver code``int` `main()``{``    ``vector<``int``> cost{ 4, 7, 8, 3, 4 };``    ``int` `n = cost.size();` `    ``cout << minCost(cost, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{` `// Function to return the minimum cost to``// travel from the first city to the last``static` `int` `minCost(``int` `[]cost, ``int` `n)``{` `    ``// To store the total cost``    ``int` `totalCost = ``0``;` `    ``// Start from the first city``    ``int` `boardingBus = ``0``;` `    ``for` `(``int` `i = ``1``; i < n; i++)``    ``{` `        ``// If found any city with cost less than``        ``// that of the previous boarded``        ``// bus then change the bus``        ``if` `(cost[boardingBus] > cost[i])``        ``{` `            ``// Calculate the cost to travel from``            ``// the currently boarded bus``            ``// till the current city``            ``totalCost += ((i - boardingBus) * cost[boardingBus]);` `            ``// Update the currently boarded bus``            ``boardingBus = i;``        ``}``    ``}` `    ``// Finally calculate the cost for the``    ``// last boarding bus till the (N + 1)th city``    ``totalCost += ((n - boardingBus) * cost[boardingBus]);``    ``return` `totalCost;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `[]cost = { ``4``, ``7``, ``8``, ``3``, ``4` `};``    ``int` `n = cost.length;` `    ``System.out.print(minCost(cost, n));``}``}` `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 implementation of the approach` `# Function to return the minimum cost to``# travel from the first city to the last``def` `minCost(cost, n):` `    ``# To store the total cost``    ``totalCost ``=` `0` `    ``# Start from the first city``    ``boardingBus ``=` `0` `    ``for` `i ``in` `range``(``1``, n):` `        ``# If found any city with cost less than``        ``# that of the previous boarded``        ``# bus then change the bus``        ``if` `(cost[boardingBus] > cost[i]):` `            ``# Calculate the cost to travel from``            ``# the currently boarded bus``            ``# till the current city``            ``totalCost ``+``=` `((i ``-` `boardingBus) ``*``                          ``cost[boardingBus])` `            ``# Update the currently boarded bus``            ``boardingBus ``=` `i` `    ``# Finally calculate the cost for the``    ``# last boarding bus till the (N + 1)th city``    ``totalCost ``+``=` `((n ``-` `boardingBus) ``*``                  ``cost[boardingBus])``    ``return` `totalCost` `# Driver code``cost ``=` `[ ``4``, ``7``, ``8``, ``3``, ``4``]``n ``=` `len``(cost)` `print``(minCost(cost, n))` `# This code is contributed by Mohit Kumar`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `// Function to return the minimum cost to``// travel from the first city to the last``static` `int` `minCost(``int` `[]cost, ``int` `n)``{` `    ``// To store the total cost``    ``int` `totalCost = 0;` `    ``// Start from the first city``    ``int` `boardingBus = 0;` `    ``for` `(``int` `i = 1; i < n; i++)``    ``{` `        ``// If found any city with cost less than``        ``// that of the previous boarded``        ``// bus then change the bus``        ``if` `(cost[boardingBus] > cost[i])``        ``{` `            ``// Calculate the cost to travel from``            ``// the currently boarded bus``            ``// till the current city``            ``totalCost += ((i - boardingBus) *``                          ``cost[boardingBus]);` `            ``// Update the currently boarded bus``            ``boardingBus = i;``        ``}``    ``}` `    ``// Finally calculate the cost for the``    ``// last boarding bus till the (N + 1)th city``    ``totalCost += ((n - boardingBus) *``                  ``cost[boardingBus]);``    ``return` `totalCost;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]cost = { 4, 7, 8, 3, 4 };``    ``int` `n = cost.Length;` `    ``Console.Write(minCost(cost, n));``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:
`18`

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

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