穿过二维阵列中障碍物（地雷）的最短路径（C编程）

Question

I have a problem with a C program, where a 2D array with mines is given (mines = array fields set to 1). I need to find the shortest path from (0,0) to (x-1,y-1), and you can move only in 4 directions (up, down, left, right).

Do you have any ideas, what the algorithm should look like to keep the program fairly simple?

Answer 1

A* and Dijkstra are more complicated than you need for this problem because, in the graph you are searching, all edges (steps between grid squares) have weight 1.

Just use Breadth First Search:

Let Q be a queue of (x,y) pairs
Let V be a set of (x,y) pairs.
Add the start point (x0,y0) to Q.
While Q is not empty
  H = Q.get_head
  for each neighbor pair N of H in the grid
    if N is not in V
      add N to V
      if N is the goal
        Return N. The path is the chain of N.prev references
      N.prev = H
      Q.add_to_tail(N)
Return "goal could not be reached"

Answer 2

Use Dijikstra's Algorithm. It will solve the problem in O(x*y) time

Answer 3

You can also try A-Star (see wikipedia entry ). It is an extension of Dijkstra's algorithm, it's worst-case running time is O(|E|), but can be improved by using heuristics. A-Star will find the lowest cost path through the area, and in your case the cost that you will be using will be the total distance traveled.

Given your limitation on movement, you would probably be best served by using a 'manhattan-distance' heuristic.