|
|
|
|
package class_2022_01_3_week;
|
|
|
|
|
|
|
|
|
|
import java.util.PriorityQueue;
|
|
|
|
|
|
|
|
|
|
// A*算法
|
|
|
|
|
// 过程和Dijskra高度相处
|
|
|
|
|
// 有到终点的预估函数
|
|
|
|
|
// 只要预估值<=客观上最优距离,就是对的
|
|
|
|
|
// 预估函数是一种吸引力:
|
|
|
|
|
// 1)合适的吸引力可以提升算法的速度
|
|
|
|
|
// 2)吸引力“过强”会出现错误
|
|
|
|
|
// 讲述A*算法
|
|
|
|
|
// 预估终点距离选择曼哈顿距离
|
|
|
|
|
// 要求先在体系学习班图的章节听过"Dijkstra算法"
|
|
|
|
|
public class Code01_AStarAlgorithm {
|
|
|
|
|
|
|
|
|
|
// Dijkstra算法
|
|
|
|
|
// map[i][j] == 0 代表障碍
|
|
|
|
|
// map[i][j] > 0 代表通行代价
|
|
|
|
|
public static int minDistance1(int[][] map, int startX, int startY, int targetX, int targetY) {
|
|
|
|
|
if (map[startX][startY] == 0 || map[targetX][targetY] == 0) {
|
|
|
|
|
return Integer.MAX_VALUE;
|
|
|
|
|
}
|
|
|
|
|
int n = map.length;
|
|
|
|
|
int m = map[0].length;
|
|
|
|
|
// heap小根堆
|
|
|
|
|
// [20,1,7]
|
|
|
|
|
PriorityQueue<int[]> heap = new PriorityQueue<>((a, b) -> a[0] - b[0]);
|
|
|
|
|
// 1,7已经处理过了,closed[1][7] = true
|
|
|
|
|
boolean[][] closed = new boolean[n][m];
|
|
|
|
|
heap.add(new int[] { map[startX][startY], startX, startY });
|
|
|
|
|
int ans = Integer.MAX_VALUE;
|
|
|
|
|
while (!heap.isEmpty()) {
|
|
|
|
|
int[] cur = heap.poll();
|
|
|
|
|
int dis = cur[0];
|
|
|
|
|
int row = cur[1];
|
|
|
|
|
int col = cur[2];
|
|
|
|
|
if (closed[row][col]) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
closed[row][col] = true;
|
|
|
|
|
if (row == targetX && col == targetY) {
|
|
|
|
|
ans = dis;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
add1(dis, row - 1, col, n, m, map, closed, heap);
|
|
|
|
|
add1(dis, row + 1, col, n, m, map, closed, heap);
|
|
|
|
|
add1(dis, row, col - 1, n, m, map, closed, heap);
|
|
|
|
|
add1(dis, row, col + 1, n, m, map, closed, heap);
|
|
|
|
|
}
|
|
|
|
|
return ans;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
public static void add1(int pre, int row, int col, int n, int m, int[][] map, boolean[][] closed,
|
|
|
|
|
PriorityQueue<int[]> heap) {
|
|
|
|
|
if (row >= 0 && row < n && col >= 0 && col < m && map[row][col] != 0 && !closed[row][col]) {
|
|
|
|
|
heap.add(new int[] { pre + map[row][col], row, col });
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// A*算法
|
|
|
|
|
// map[i][j] == 0 代表障碍
|
|
|
|
|
// map[i][j] > 0 代表通行代价
|
|
|
|
|
public static int minDistance2(int[][] map, int startX, int startY, int targetX, int targetY) {
|
|
|
|
|
if (map[startX][startY] == 0 || map[targetX][targetY] == 0) {
|
|
|
|
|
return Integer.MAX_VALUE;
|
|
|
|
|
}
|
|
|
|
|
int n = map.length;
|
|
|
|
|
int m = map[0].length;
|
|
|
|
|
// [20,1,7]
|
|
|
|
|
// [20,?,1,7]
|
|
|
|
|
PriorityQueue<int[]> heap = new PriorityQueue<>((a, b) -> (a[0] + a[1]) - (b[0] + b[1]));
|
|
|
|
|
boolean[][] closed = new boolean[n][m];
|
|
|
|
|
heap.add(new int[] { map[startX][startY], distance(startX, startY, targetX, targetY), startX, startY });
|
|
|
|
|
int ans = Integer.MAX_VALUE;
|
|
|
|
|
while (!heap.isEmpty()) {
|
|
|
|
|
int[] cur = heap.poll();
|
|
|
|
|
int fromDistance = cur[0];
|
|
|
|
|
int row = cur[2];
|
|
|
|
|
int col = cur[3];
|
|
|
|
|
if (closed[row][col]) {
|
|
|
|
|
continue;
|
|
|
|
|
}
|
|
|
|
|
closed[row][col] = true;
|
|
|
|
|
if (row == targetX && col == targetY) {
|
|
|
|
|
ans = fromDistance;
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
add2(fromDistance, row - 1, col, targetX, targetY, n, m, map, closed, heap);
|
|
|
|
|
add2(fromDistance, row + 1, col, targetX, targetY, n, m, map, closed, heap);
|
|
|
|
|
add2(fromDistance, row, col - 1, targetX, targetY, n, m, map, closed, heap);
|
|
|
|
|
add2(fromDistance, row, col + 1, targetX, targetY, n, m, map, closed, heap);
|
|
|
|
|
}
|
|
|
|
|
return ans;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
public static void add2(int pre, int row, int col, int targetX, int targetY, int n, int m, int[][] map,
|
|
|
|
|
boolean[][] closed, PriorityQueue<int[]> heap) {
|
|
|
|
|
if (row >= 0 && row < n && col >= 0 && col < m && map[row][col] != 0 && !closed[row][col]) {
|
|
|
|
|
heap.add(new int[] { pre + map[row][col], distance(row, col, targetX, targetY), row, col });
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 曼哈顿距离
|
|
|
|
|
public static int distance(int curX, int curY, int targetX, int targetY) {
|
|
|
|
|
return Math.abs(targetX - curX) + Math.abs(targetY - curY);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 为了测试
|
|
|
|
|
// map[i][j] == 0 代表障碍
|
|
|
|
|
// map[i][j] > 0 代表通行代价
|
|
|
|
|
public static int[][] randomMap(int len, int value) {
|
|
|
|
|
int[][] ans = new int[len][len];
|
|
|
|
|
for (int i = 0; i < len; i++) {
|
|
|
|
|
for (int j = 0; j < len; j++) {
|
|
|
|
|
if (Math.random() < 0.2) {
|
|
|
|
|
ans[i][j] = 0;
|
|
|
|
|
} else {
|
|
|
|
|
ans[i][j] = (int) (Math.random() * value);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return ans;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// 为了测试
|
|
|
|
|
public static void printMap(int[][] map) {
|
|
|
|
|
for (int i = 0; i < map.length; i++) {
|
|
|
|
|
for (int j = 0; j < map[0].length; j++) {
|
|
|
|
|
System.out.print((map[i][j] == 0 ? "X" : map[i][j]) + " ");
|
|
|
|
|
}
|
|
|
|
|
System.out.println();
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
public static void main(String[] args) {
|
|
|
|
|
int len = 100;
|
|
|
|
|
int value = 50;
|
|
|
|
|
int testTime = 10000;
|
|
|
|
|
System.out.println("功能测试开始");
|
|
|
|
|
for (int i = 0; i < testTime; i++) {
|
|
|
|
|
int n = (int) (Math.random() * len) + 2;
|
|
|
|
|
int[][] map = randomMap(n, value);
|
|
|
|
|
int startX = (int) (Math.random() * n);
|
|
|
|
|
int startY = (int) (Math.random() * n);
|
|
|
|
|
int targetX = (int) (Math.random() * n);
|
|
|
|
|
int targetY = (int) (Math.random() * n);
|
|
|
|
|
int ans1 = minDistance1(map, startX, startY, targetX, targetY);
|
|
|
|
|
int ans2 = minDistance2(map, startX, startY, targetX, targetY);
|
|
|
|
|
if (ans1 != ans2) {
|
|
|
|
|
System.out.println("出错了!");
|
|
|
|
|
printMap(map);
|
|
|
|
|
System.out.println(startX + "," + startY);
|
|
|
|
|
System.out.println(targetX + "," + targetY);
|
|
|
|
|
System.out.println(ans1);
|
|
|
|
|
System.out.println(ans2);
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
System.out.println("功能测试结束");
|
|
|
|
|
|
|
|
|
|
int[][] map = new int[4000][4000];
|
|
|
|
|
for (int i = 0; i < map.length; i++) {
|
|
|
|
|
for (int j = 0; j < map[0].length; j++) {
|
|
|
|
|
map[i][j] = (int) (Math.random() * 10);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
int startX = 0;
|
|
|
|
|
int startY = 0;
|
|
|
|
|
int targetX = 3456;
|
|
|
|
|
int targetY = 3728;
|
|
|
|
|
|
|
|
|
|
long start = System.currentTimeMillis();
|
|
|
|
|
minDistance2(map, startX, startY, targetX, targetY);
|
|
|
|
|
long end = System.currentTimeMillis();
|
|
|
|
|
System.out.println("运行时间(毫秒) : " + (end - start));
|
|
|
|
|
|
|
|
|
|
// System.out.println("性能测试开始");
|
|
|
|
|
// int n = 10000;
|
|
|
|
|
// int v = 500;
|
|
|
|
|
// int[][] map = randomMap(n, v);
|
|
|
|
|
// int startX = 0;
|
|
|
|
|
// int startY = 0;
|
|
|
|
|
// int targetX = n - 1;
|
|
|
|
|
// int targetY = n - 1;
|
|
|
|
|
// System.out.println("数据规模 : " + n + " * " + n);
|
|
|
|
|
// long start = System.currentTimeMillis();
|
|
|
|
|
// minDistance2(map, startX, startY, targetX, targetY);
|
|
|
|
|
// long end = System.currentTimeMillis();
|
|
|
|
|
// System.out.println("运行时间(毫秒) : " + (end - start));
|
|
|
|
|
// System.out.println("性能测试结束");
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
}
|