Minimum Cost of a Path With Special Roads
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 i^th special road goes in one direction 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
5The path moves from
(1,1) to (1,2), uses specialRoads[0], moves to (3,4), then uses specialRoads[1], for total cost 1 + 2 + 1 + 1 = 5.Example 2
Input
start = [3,2], target = [5,7], specialRoads = [[5,7,3,2,1],[3,2,3,4,4],[3,3,5,5,5],[3,4,5,6,6]]Output
7It is optimal not to use any special edges and go directly from the starting to the ending position with cost
|5 - 3| + |7 - 2| = 7; specialRoads[0] is directed from (5,7) to (3,2).Constraints
- start.length == target.length == 2
- 1 <= startX <= targetX <= 10^5
- 1 <= startY <= targetY <= 10^5
- 1 <= specialRoads.length <= 200
- specialRoads[i].length == 5
- startX <= x1i, x2i <= targetX
- startY <= y1i, y2i <= targetY
- 1 <= costi <= 10^5