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 <code>specialRoadsi = x1_i, y1_i, x2_i, y2_i, cost_i</code> indicates that the <code>i^th</code> special road can take you from <code>(x1_i, y1_i)</code> to <code>(x2_i, y2_i)</code> with a cost equal to <code>cost_i</code>. 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

• <code>1 <= startX <= targetX <= 10⁵</code>

• <code>1 <= startY <= targetY <= 10⁵</code>

• 1 <= specialRoads.length <= 200

• specialRoads[i].length == 5

• <code>startX <= x1_i, x2_i<= targetX</code>

• <code>startY <= y1_i, y2_i<= targetY</code>

• <code>1 <= cost_i<= 10⁵</code>