Matrix Traversal by expanding outwards from a point?

问题

Sorry if the title isn't clear. I wasn't sure how to phrase it without an example. So the goal is to traverse a matrix in all directions as fast as possible when starting at a single point(could be anywhere in the matrix). My idea was to use a 2D array and expand outwards in all directions from that single point almost like an explosion. The problem I ran into when developing such an algorithm is that it becomes wildly inefficient when pixels are expanding outwards and exploring already explored pixels. Here is an example of what I would like to do.

0,0,0,0,0
0,0,0,0,0
0,0,1,0,0
0,0,0,0,0
0,0,0,0,0

0,0,0,0,0
0,0,1,0,0
0,1,1,1,0
0,0,1,0,0
0,0,0,0,0

0,0,1,0,0
0,1,1,1,0
1,1,1,1,1
0,1,1,1,0
0,0,1,0,0

1,1,1,1,1
1,1,1,1,1
1,1,1,1,1
1,1,1,1,1
1,1,1,1,1

Thank you for any help you can give me!

回答1:

Please consider this example (Explanation in Comments):

import java.util.ArrayList;

public class MatrixTraversal {

  public static void main(String[] main){
      // 5x5 matrix example 
      Byte[][] matrix = {{0,0,0,0,0},{0,0,0,0,0},
                         {0,0,0,0,0},{0,0,0,0,0}, 
                         {0,0,0,0,0}};

      // testing
      expand(matrix, new Point(0,0));
      print(matrix);

      expand(matrix, new Point(2,4));
      print(matrix);

      expand(matrix, new Point(4,1));
      print(matrix);

      expand(matrix, new Point(3,1));
      print(matrix);

      expand(matrix, new Point(2,2));
      print(matrix);

  }


  ////////////////////////////////////////////////////////


  /**
   * This method to expand a given point in the matrix
   * @param matrix
   * @param point
   */
  public static void expand(Byte[][]matrix, Point point){
      // first change the given point to 1
      matrix[point.x][point.y]=1;

      // then get the neighbors points of the given point 
      ArrayList<Point> neighbors = neighbors(matrix, point); 
      // loop through the neighbors ArrayList and convert 
      // the corresponding points to 1's
      for(Point p : neighbors){
          matrix[p.x][p.y]=1;
      }
  }


  ////////////////////////////////////////////////////////


  /**
   * This method to return the VALID neighbors points of 
   * a given point in the matrix
   * @param matrix
   * @param point
   */
  public static ArrayList<Point> neighbors(Byte[][]matrix, Point point){
      int column = point.y;  int row = point.x; 

      ArrayList<Point> neighbors = new ArrayList<Point>();
      if(column>0){
          if(matrix[row][column-1]!=1){
              neighbors.add(new Point(row, column-1));
          }
      }

      if(column<matrix[0].length-1){
          if(matrix[row][column+1]!=1){
              neighbors.add(new Point(row, column+1));
          }
      }

      if(row>0){
          if(matrix[row-1][column]!=1){
              neighbors.add(new Point(row-1, column));
          }
      }

      if(row<matrix.length-1){
          if(matrix[row+1][column]!=1){
              neighbors.add(new Point(row+1, column));
          }
      }
      return neighbors;
  }



  ////////////////////////////////////////////////////////


  /**
   * This method just to print the result
   * @param matrix
   */
  public static void print(Byte[][] matrix){
      for(int i=0; i< matrix.length; i++, System.out.println()){
          for(int j=0; j< matrix[0].length; j++){
              System.out.print(matrix[i][j] + " ");
          }
      }
      System.out.println("---------");
  }


  ////////////////////////////////////////////////////////


  //Inner Class to represent a Point(x,y)
  public static class Point{
      int x,y;

      public Point(int x, int y){
          this.x = x;
          this.y = y;
      } 
  } 
}

Test

来源：https://stackoverflow.com/questions/44318545/matrix-traversal-by-expanding-outwards-from-a-point

标签

java

matrix

traversal