int dy = p.y() - _gravity.y(); int dx = p.x() - _gravity.x(); qint64 key = (dist << 32) + (dy << 16) + dx;

这几行代码是计算每个扩展（_expns）的排序关键字，以便对它们进行排序。其中，dy 和 dx分别表示扩展相对重心的 y 坐标和 x 坐标的偏移量，dist 是扩展和重心之间的曼哈顿距离（ManhattanLength），计算曼哈顿距离的函数在这段代码中没有给出。最后，将这三个值组合成一个qint64类型的排序关键字key，其中dist占据高32位，dy占据中间16位，dx占据低16位。

相关问题

编译器:C++ (g++) Particle类型用于表示处于三维空间中的质点，其包括如下成员：① 三个浮点数成员x、y和z表示质点在三维空间中的坐标；② 浮点数成员mass表示质点的质量；③ 接受空间坐标和质量参数的构造函数；④ 自定义operator-()操作符函数用于计算两个质点间的万有引力，即表达式p1 – p2调用执行p1的operator-()操作符函数，计算质点p1和p2间的万有引力。 万有引用公式F = GMm/r²中，万有引力常数G = 6.67×10-11N·m²/kg²。 请依据上述描述，设计Particle类，使得下述代码能正常执行。 注意：天文数字都很大，建议浮点数全部采用long double类型。 裁判测试程序样例： #include <iostream> #include <cmath> using namespace std; //在此处定义Particle类及其重载operator+()操作符函数 int main() { long double x, y, z, mass; cin >> x >> y >> z >> mass; Particle p1(x,y,z,mass); cin >> x >> y >> z >> mass; const Particle p2(x,y,z,mass); long double force = p1 - p2; printf("Gravity between two objects = %.1Lf N",force); return 0; } 输入样例： 0 0 0 5.965e15 0 0 38400000 7.342e14 输出样例： Gravity between two objects = 198101.7 N 说明：输入输出中的所有数据均为标准单位，坐标为米，质量为kg。 请注意：函数题只需要提交相关代码片段，不要提交完整程序。

代码如下：

#include <iostream>
#include <cmath>
using namespace std;

class Particle{
private:
    long double x, y, z, mass;
public:
    Particle(long double x=0, long double y=0, long double z=0, long double mass=0){
        this->x = x;
        this->y = y;
        this->z = z;
        this->mass = mass;
    }
    long double operator-(const Particle& p2){
        const long double G = 6.67e-11;
        long double dx = x - p2.x;
        long double dy = y - p2.y;
        long double dz = z - p2.z;
        long double r = sqrt(dx*dx + dy*dy + dz*dz);
        return G * mass * p2.mass / (r * r);
    }
};

int main(){
    long double x, y, z, mass;
    cin >> x >> y >> z >> mass;
    Particle p1(x,y,z,mass);
    cin >> x >> y >> z >> mass;
    const Particle p2(x,y,z,mass);
    long double force = p1 - p2;
    printf("Gravity between two objects = %.1Lf N",force);
    return 0;
}

python 下面八个块显示鼠标追踪位置turtle.canvas 重力四子棋 turtle 代码

1. 显示鼠标追踪位置：

import turtle

def track_mouse(x, y):
    turtle.goto(x, y)

turtle.onscreenclick(track_mouse)
turtle.mainloop()

2. turtle.canvas：

import turtle

turtle.getcanvas().postscript(file="canvas.eps")
turtle.mainloop()

3. 重力：

import turtle

GRAVITY = 0.1

class Ball(turtle.Turtle):

    def __init__(self, x, y, dx, dy, radius, color):
        super().__init__(shape="circle")
        self.penup()
        self.setposition(x, y)
        self.dx = dx
        self.dy = dy
        self.radius = radius
        self.color(color)

    def move(self):
        self.dy -= GRAVITY
        self.sety(self.ycor() + self.dy)
        self.setx(self.xcor() + self.dx)

class Game:

    def __init__(self):
        self.window = turtle.Screen()
        self.window.setup(800, 600)
        self.window.bgcolor("white")
        self.balls = []

    def add_ball(self, x, y, dx, dy, radius, color):
        ball = Ball(x, y, dx, dy, radius, color)
        self.balls.append(ball)

    def start(self):
        while True:
            for ball in self.balls:
                ball.move()
                if ball.ycor() - ball.radius < -300:
                    ball.dy = -ball.dy
                if ball.xcor() + ball.radius > 400 or ball.xcor() - ball.radius < -400:
                    ball.dx = -ball.dx

            self.window.update()

game = Game()
game.add_ball(0, 200, 0, 0, 30, "red")
game.add_ball(0, 0, 5, 0, 20, "blue")
game.add_ball(0, -200, -5, 0, 10, "green")
game.start()

4. 四子棋：

import turtle

class Board:

    def __init__(self):
        self.board = [[None for _ in range(7)] for _ in range(6)]

    def is_full(self):
        for row in self.board:
            for cell in row:
                if cell is None:
                    return False
        return True

    def is_winner(self, player):
        # Check rows
        for row in self.board:
            count = 0
            for cell in row:
                if cell == player:
                    count += 1
                    if count == 4:
                        return True
                else:
                    count = 0

        # Check columns
        for j in range(7):
            count = 0
            for i in range(6):
                if self.board[i][j] == player:
                    count += 1
                    if count == 4:
                        return True
                else:
                    count = 0

        # Check diagonals
        for i in range(3):
            for j in range(4):
                if (self.board[i][j] == player and self.board[i+1][j+1] == player and
                    self.board[i+2][j+2] == player and self.board[i+3][j+3] == player):
                    return True
        for i in range(3):
            for j in range(3, 7):
                if (self.board[i][j] == player and self.board[i+1][j-1] == player and
                    self.board[i+2][j-2] == player and self.board[i+3][j-3] == player):
                    return True

        return False

    def play(self, player, column):
        for i in range(5, -1, -1):
            if self.board[i][column] is None:
                self.board[i][column] = player
                return True
        return False

class Game:

    def __init__(self):
        self.window = turtle.Screen()
        self.window.setup(700, 600)
        self.window.bgcolor("white")
        self.board = Board()
        self.turn = "red"
        self.draw_board()
        self.window.onclick(self.play)

    def draw_board(self):
        pen = turtle.Turtle()
        pen.hideturtle()
        pen.speed(0)
        pen.penup()
        pen.setposition(-300, -250)
        pen.pendown()
        pen.pensize(3)
        for _ in range(2):
            pen.forward(600)
            pen.left(90)
            pen.forward(500)
            pen.left(90)
        pen.penup()
        pen.setposition(-280, -225)
        for column in range(7):
            pen.write(column, align="center", font=("Arial", 16, "normal"))
            pen.forward(80)
        pen.hideturtle()

    def play(self, x, y):
        column = int((x + 300) // 80)
        if self.board.play(self.turn, column):
            self.draw_piece(column)
            if self.board.is_winner(self.turn):
                self.window.onclick(None)
                turtle.color(self.turn)
                turtle.write(f"{self.turn.upper()} wins!", align="center", font=("Arial", 32, "bold"))
            elif self.board.is_full():
                self.window.onclick(None)
                turtle.write("Draw!", align="center", font=("Arial", 32, "bold"))
            else:
                self.turn = "yellow" if self.turn == "red" else "red"

    def draw_piece(self, column):
        pen = turtle.Turtle()
        pen.hideturtle()
        pen.penup()
        pen.color(self.turn)
        row = max([i for i, cell in enumerate(self.board.board) if cell[column] is None])
        pen.setposition(-240 + column * 80, -200 + row * 80)
        pen.pendown()
        pen.begin_fill()
        pen.circle(30)
        pen.end_fill()

game = Game()
turtle.mainloop()

5. turtle 代码：

import turtle

pen = turtle.Turtle()
pen.speed(0)
pen.hideturtle()

def draw_triangle(x, y, size, color):
    pen.penup()
    pen.setposition(x, y)
    pen.pendown()
    pen.color(color)
    pen.begin_fill()
    for _ in range(3):
        pen.forward(size)
        pen.left(120)
    pen.end_fill()

draw_triangle(-200, 0, 100, "red")
draw_triangle(0, 0, 100, "green")
draw_triangle(200, 0, 100, "blue")

turtle.mainloop()