# Minimum possible travel cost among N cities

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: 9
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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 `

Output:

```18
```

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