英文:
How to calculate the shortest path?
问题
import java.util.LinkedList;
public class ShortestPathBetweenCellsBFS {
private static class Cell {
int x;
int y;
int dist; //distance
Cell prev; //parent cell in the path
Cell(int x, int y, int dist, Cell prev) {
this.x = x;
this.y = y;
this.dist = dist;
this.prev = prev;
}
@Override
public String toString() {
return "(" + x + "," + y + ")";
}
}
public static void shortestPath(int[][] matrix, int[] start, int[] end) {
int sx = start[0], sy = start[1];
int dx = end[0], dy = end[1];
int m = matrix.length;
int n = matrix[0].length;
Cell[][] cells = new Cell[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (matrix[i][j] != 1) {
cells[i][j] = new Cell(i, j, Integer.MAX_VALUE, null);
}
}
}
LinkedList<Cell> queue = new LinkedList<>();
Cell src = cells[sx][sy];
src.dist = 0;
queue.add(src);
System.out.println(src);
Cell dest = null;
Cell p;
while ((p = queue.poll()) != null) {
// find destination
if (p.x == dx && p.y == dy) {
dest = p;
break;
}
// moving up
visit(cells, queue, p.x - 1, p.y, p);
// moving down
visit(cells, queue, p.x + 1, p.y, p);
// moving left
visit(cells, queue, p.x, p.y - 1, p);
// moving right
visit(cells, queue, p.x, p.y + 1, p);
}
if (dest == null) {
return;
} else {
LinkedList<Cell> path = new LinkedList<>();
p = dest;
do {
path.addFirst(p);
} while ((p = p.prev) != null);
System.out.println(path);
}
}
// function to update cell visiting status
static void visit(Cell[][] cells, LinkedList<Cell> queue, int x, int y, Cell parent) {
if (x < 0 || x >= cells.length || y < 0 || y >= cells[0].length || cells[x][y] == null) {
return;
}
int dist = parent.dist + 1;
Cell p = cells[x][y];
if (dist < p.dist && isAdjacentToZero(cells, x, y)) {
p.dist = dist;
p.prev = parent;
queue.add(p);
}
}
// function to check if a cell is adjacent to a zero cell
static boolean isAdjacentToZero(Cell[][] cells, int x, int y) {
int[] dx = {-1, 0, 1, 0};
int[] dy = {0, 1, 0, -1};
for (int i = 0; i < 4; i++) {
int newX = x + dx[i];
int newY = y + dy[i];
if (newX >= 0 && newX < cells.length && newY >= 0 && newY < cells[0].length) {
if (cells[newX][newY] != null && cells[newX][newY].dist == 0) {
return true;
}
}
}
return false;
}
public static void main(String[] args) {
int[][] matrix = {
{1, 0, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 1, 1, 1, 1, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 1, 1, 0, 1, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 1, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 0}
};
int[] start = {4, 0};
int[] end = {5, 5};
shortestPath(matrix, start, end);
}
}
英文:
I implemented a code to calculate the shortest route,but i want to add a condition.If i got a matrix like this :
1 0 0 0 0 0 0 0
1 0 0 1 1 1 1 0
0 0 0 0 0 0 0 0
0 0 1 1 1 0 1 0
A 0 0 0 0 0 0 0
0 0 1 1 0 B 0 1
0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0
How can i add a condition that from cell A to cell B it can move only if there is a distance of one row or one column of 0 , so the shortest path from A to B (A is on [4;0] and B is on [5;5]) is : [4;0] , [5;0] , [6;0] , [7;0] , [7;1] , [7;2] , [7,3] , [7,4] , [7,5] , [6,5] , [5;5] .
This is what i have at the moment:
import java.util.LinkedList;
public class ShortestPathBetweenCellsBFS {
private static class Cell {
int x;
int y;
int dist; //distance
Cell prev; //parent cell in the path
Cell(int x, int y, int dist, Cell prev) {
this.x = x;
this.y = y;
this.dist = dist;
this.prev = prev;
}
@Override
public String toString(){
return "(" + x + "," + y + ")";
}
}
public static void shortestPath(int[][] matrix, int[] start, int[] end) {
int sx = start[0], sy = start[1];
int dx = end[0], dy = end[1];
int m = matrix.length;
int n = matrix[0].length;
Cell[][] cells = new Cell[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (matrix[i][j] != 1) {
cells[i][j] = new Cell(i, j, Integer.MAX_VALUE, null);
}
}
}
LinkedList<Cell> queue = new LinkedList<>();
Cell src = cells[sx][sy];
src.dist = 0;
queue.add(src);
System.out.println(src);
Cell dest = null;
Cell p;
while ((p = queue.poll()) != null) {
//find destination
if (p.x == dx && p.y == dy) {
dest = p;
break;
}
// moving up
visit(cells, queue, p.x - 1, p.y, p);
// moving down
visit(cells, queue, p.x + 1, p.y, p);
// moving left
visit(cells, queue, p.x, p.y - 1, p);
//moving right
visit(cells, queue, p.x, p.y + 1, p);
}
if (dest == null) {
return;
} else {
LinkedList<Cell> path = new LinkedList<>();
p = dest;
do {
path.addFirst(p);
} while ((p = p.prev) != null);
System.out.println(path);
}
}
//function to update cell visiting status
static void visit(Cell[][] cells, LinkedList<Cell> queue, int x, int y, Cell parent) {
if (x < 0 || x >= cells.length || y < 0 || y >= cells[0].length || cells[x][y] == null) {
return;
}
int dist = parent.dist + 1;
Cell p = cells[x][y];
if (dist < p.dist) {
p.dist = dist;
p.prev = parent;
queue.add(p);
}
}
public static void main(String[] args) {
int[][] matrix = {
{1, 0, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 1, 1, 1, 1, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 1, 1, 0, 1, 0},
{0, 0, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 1, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 0}
};
int[] start = {4, 0};
int[] end = {5, 5};
shortestPath(matrix, start, end);
}
}
答案1
得分: 0
以下是翻译好的内容:
一个可能解决方案的基本思路是,只有当单元格到任何墙壁的距离至少为一时,才将它们添加到路径查找算法的队列中。
例如,在你的 visit
方法中,你需要检查所有相邻的单元格,而不仅仅是 cells[x][y]
。
一种做法是循环遍历相邻的单元格,并在找到障碍单元格时中止。
for (int x_test = Math.max(0, x - 1); x_test <= Math.min(cells.length - 1, x + 1); x_test++) {
for (int y_test = Math.max(0, y - 1); y_test <= Math.min(cells[0].length - 1, y + 1); y_test++) {
if (cells[x][y] == null) {
return;
}
}
}
请注意,在循环中我使用了 Math.min
和 Math.max
来防止越界访问。
英文:
The basic idea of one possible solution would be to only add cells to the queue of your pathfinding algorithm if they have a distance of at least one to any wall.
So for example in your visit
method, you would have to check all the neighbouring cells as well instead of only cells[x][y]
.
One way to do this would be to loop over the neighbouring cells and abort, when you find a cell that is an obstacle.
for (int x_test = Math.max(0, x - 1); x_test <= Math.min(cells.length - 1; x + 1); x_test++) {
for (int y_test = Math.max(0, y - 1); y_test <= Math.min(cells[0].length - 1; y + 1); y_test++) {
if (cells[x][y] == null) {
return;
}
}
}
Note that I am using Math.min
and Math.max
in the loops to prevent out of bounds accesses.
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