Package g2401_2500.s2477_minimum_fuel_cost_to_report_to_the_capital

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    2477 - Minimum Fuel Cost to Report to the Capital\.

    Medium

    There is a tree (i.e., a connected, undirected graph with no cycles) structure country network consisting of n cities numbered from 0 to n - 1 and exactly n - 1 roads. The capital city is city 0. You are given a 2D integer array roads where <code>roadsi = a<sub>i</sub>, b<sub>i</sub></code> denotes that there exists a bidirectional road connecting cities <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.

    There is a meeting for the representatives of each city. The meeting is in the capital city.

    There is a car in each city. You are given an integer seats that indicates the number of seats in each car.

    A representative can use the car in their city to travel or change the car and ride with another representative. The cost of traveling between two cities is one liter of fuel.

    Return the minimum number of liters of fuel to reach the capital city.

    Example 1:

    Input: roads = \[\[0,1],0,2,0,3], seats = 5

    Output: 3

    Explanation:

    • Representative<sub>1</sub> goes directly to the capital with 1 liter of fuel.

    • Representative<sub>2</sub> goes directly to the capital with 1 liter of fuel.

    • Representative<sub>3</sub> goes directly to the capital with 1 liter of fuel.

    It costs 3 liters of fuel at minimum. It can be proven that 3 is the minimum number of liters of fuel needed.

    Example 2:

    Input: roads = \[\[3,1],3,2,1,0,0,4,0,5,4,6], seats = 2

    Output: 7

    Explanation:

    • Representative<sub>2</sub> goes directly to city 3 with 1 liter of fuel.

    • Representative<sub>2</sub> and representative<sub>3</sub> go together to city 1 with 1 liter of fuel.

    • Representative<sub>2</sub> and representative<sub>3</sub> go together to the capital with 1 liter of fuel.

    • Representative<sub>1</sub> goes directly to the capital with 1 liter of fuel.

    • Representative<sub>5</sub> goes directly to the capital with 1 liter of fuel.

    • Representative<sub>6</sub> goes directly to city 4 with 1 liter of fuel.

    • Representative<sub>4</sub> and representative<sub>6</sub> go together to the capital with 1 liter of fuel.

    It costs 7 liters of fuel at minimum. It can be proven that 7 is the minimum number of liters of fuel needed.

    Example 3:

    Input: roads = [], seats = 1

    Output: 0

    Explanation: No representatives need to travel to the capital city.

    Constraints:

    • <code>1 <= n <= 10<sup>5</sup></code>

    • roads.length == n - 1

    • roads[i].length == 2

    • <code>0 <= a<sub>i</sub>, b<sub>i</sub>< n</code>

    • <code>a<sub>i</sub> != b<sub>i</sub></code>

    • roads represents a valid tree.

    • <code>1 <= seats <= 10<sup>5</sup></code>

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Long minimumFuelCost(Array<IntArray> roads, Integer seats)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait