97.小明逛公园（Floyd）

题目：97. 小明逛公园 (kamacoder.com)

思路：

答案

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();  // 顶点数
        int m = scanner.nextInt();  // 边数

        int[][] grid = new int[n + 1][n + 1];
        final int INF = 10005; // 因为边的最大距离是10^4

        // 初始化图的邻接矩阵
        for (int i = 1; i <= n; i++) {
            Arrays.fill(grid[i], INF);
            grid[i][i] = 0; // 自己到自己的距离为0
        }

        // 读取边的信息并填充邻接矩阵
        for (int i = 0; i < m; i++) {
            int p1 = scanner.nextInt();
            int p2 = scanner.nextInt();
            int val = scanner.nextInt();
            grid[p1][p2] = val;
            grid[p2][p1] = val; // 注意这里是双向图
        }

        // 开始 Floyd-Warshall 算法
        for (int k = 1; k <= n; k++) {
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= n; j++) {
                    grid[i][j] = Math.min(grid[i][j], grid[i][k] + grid[k][j]);
                }
            }
        }

        // 读取查询并输出结果
        int z = scanner.nextInt(); // 查询次数
        while (z-- > 0) {
            int start = scanner.nextInt();
            int end = scanner.nextInt();
            if (grid[start][end] == INF) {
                System.out.println(-1);
            } else {
                System.out.println(grid[start][end]);
            }
        }

        scanner.close();
    }
}

小结

126.骑士的攻击（A*算法）

题目：126. 骑士的攻击 (kamacoder.com)

思路：毫无疑问是最难的一题

答案

import java.util.*;

class Knight implements Comparable<Knight> {
    int x, y, g, h, f;

    public Knight(int x, int y, int g, int h) {
        this.x = x;
        this.y = y;
        this.g = g;
        this.h = h;
        this.f = g + h;
    }

    @Override
    public int compareTo(Knight k) {
        return Integer.compare(this.f, k.f); // 从小到大排序
    }
}

public class Main {
    static int[][] moves = new int[1001][1001];
    static int[][] dir = {
            {-2, -1}, {-2, 1}, {-1, 2}, {1, 2},
            {2, 1}, {2, -1}, {1, -2}, {-1, -2}
    };
    static int b1, b2;
    static PriorityQueue<Knight> que = new PriorityQueue<>();

    public static int heuristic(Knight k) {
        return (k.x - b1) * (k.x - b1) + (k.y - b2) * (k.y - b2); // 统一不开根号，这样可以提高精度
    }

    public static void astar(Knight start) {
        que.add(start);
        while (!que.isEmpty()) {
            Knight cur = que.poll();
            if (cur.x == b1 && cur.y == b2)
                break;
            for (int i = 0; i < 8; i++) {
                int nextX = cur.x + dir[i][0];
                int nextY = cur.y + dir[i][1];
                if (nextX < 1 || nextX > 1000 || nextY < 1 || nextY > 1000)
                    continue;
                if (moves[nextX][nextY] == 0) {
                    moves[nextX][nextY] = moves[cur.x][cur.y] + 1;
                    int nextG = cur.g + 5; // 马走日，1 * 1 + 2 * 2 = 5
                    int nextH = heuristic(new Knight(nextX, nextY, 0, 0));
                    que.add(new Knight(nextX, nextY, nextG, nextH));
                }
            }
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        while (n-- > 0) {
            int a1 = scanner.nextInt();
            int a2 = scanner.nextInt();
            b1 = scanner.nextInt();
            b2 = scanner.nextInt();
            for (int[] row : moves) Arrays.fill(row, 0);
            Knight start = new Knight(a1, a2, 0, heuristic(new Knight(a1, a2, 0, 0)));
            astar(start);
            que.clear(); // 清空队列
            System.out.println(moves[b1][b2]);
        }
        scanner.close();
    }
}