Package g2601_2700.s2662_minimum_cost_of_a_path_with_special_roads

Class Solution

java.lang.Object
g2601_2700.s2662_minimum_cost_of_a_path_with_special_roads.Solution
public class Solution extends java.lang.Object
2662 - Minimum Cost of a Path With Special Roads.

Medium

You are given an array start where start = [startX, startY] represents your initial position (startX, startY) in a 2D space. You are also given the array target where target = [targetX, targetY] represents your target position (targetX, targetY).

The cost of going from a position (x1, y1) to any other position in the space (x2, y2) is |x2 - x1| + |y2 - y1|.

There are also some special roads. You are given a 2D array specialRoads where specialRoads[i] = [x1i, y1i, x2i, y2i, costi] indicates that the ith special road can take you from (x1i, y1i) to (x2i, y2i) with a cost equal to costi. You can use each special road any number of times.

Return the minimum cost required to go from (startX, startY) to (targetX, targetY).

Example 1:

Input: start = [1,1], target = [4,5], specialRoads = [[1,2,3,3,2],[3,4,4,5,1]]

Output: 5

Explanation: The optimal path from (1,1) to (4,5) is the following:

  • (1,1) -> (1,2). This move has a cost of |1 - 1| + |2 - 1| = 1.
  • (1,2) -> (3,3). This move uses the first special edge, the cost is 2.
  • (3,3) -> (3,4). This move has a cost of |3 - 3| + |4 - 3| = 1.
  • (3,4) -> (4,5). This move uses the second special edge, the cost is 1.

So the total cost is 1 + 2 + 1 + 1 = 5.

It can be shown that we cannot achieve a smaller total cost than 5.

Example 2:

Input: start = [3,2], target = [5,7], specialRoads = [[3,2,3,4,4],[3,3,5,5,5],[3,4,5,6,6]]

Output: 7

Explanation: It is optimal to not use any special edges and go directly from the starting to the ending position with a cost |5 - 3| + |7 - 2| = 7.

Constraints:

  • start.length == target.length == 2
  • 1 <= startX <= targetX <= 105
  • 1 <= startY <= targetY <= 105
  • 1 <= specialRoads.length <= 200
  • specialRoads[i].length == 5
  • startX <= x1i, x2i <= targetX
  • startY <= y1i, y2i <= targetY
  • 1 <= costi <= 105

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    minimumCost(int[] start, int[] target, int[][] specialRoads)
     

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • minimumCost

      public int minimumCost(int[] start, int[] target, int[][] specialRoads)