# 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

**i**city would cost of

^{th}**C[i]**dollars to travel

**1**unit of distance. In other words, cost to travel from the

**i**city to the

^{th}**j**city is

^{th}**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

**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:

- Start with the first city with a cost of
**C[1]**. - 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. - Calculate cost as
**abs(j – i) * C[i]**and add it to the total cost so far. - 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 <bits/stdc++.h> ` `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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` |

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**Output:**

18

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