C++按矩形2d最小面积二叉树装箱，箱子知道长宽，矩形数据double型，包含ID,长宽，矩形允许旋转 ，并且返回盒子的摆放位置，代码

以下是使用C++实现的按矩形2D最小面积二叉树装箱的代码，其中包含了矩形数据的定义、二叉树节点的定义以及装箱算法的实现。

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

// 矩形数据结构
struct Rectangle {
    int id; // 矩形编号
    double width; // 矩形宽度
    double height; // 矩形高度
    double x; // 矩形左下角x坐标
    double y; // 矩形左下角y坐标
    double angle; // 矩形旋转角度，初始化为0表示不旋转

    Rectangle(int id, double w, double h) : id(id), width(w), height(h), x(0), y(0), angle(0) {}
};

// 二叉树节点数据结构
struct Node {
    Rectangle* rect; // 节点代表的矩形指针
    Node* left; // 左子节点指针
    Node* right; // 右子节点指针
    double x; // 节点代表的矩形左下角x坐标
    double y; // 节点代表的矩形左下角y坐标
    double width; // 节点代表的矩形宽度
    double height; // 节点代表的矩形高度
    double angle; // 节点代表的矩形旋转角度

    Node(Rectangle* rect) : rect(rect), left(nullptr), right(nullptr), x(0), y(0), width(0), height(0), angle(0) {}
};

// 比较函数，按矩形面积从大到小排序
bool compare(Rectangle* rect1, Rectangle* rect2) {
    return rect1->width * rect1->height > rect2->width * rect2->height;
}

// 计算两个矩形之间的盒子面积
double calculateBoxArea(double x1, double y1, double w1, double h1, double x2, double y2, double w2, double h2) {
    double left = min(x1, x2);
    double bottom = min(y1, y2);
    double right = max(x1 + w1, x2 + w2);
    double top = max(y1 + h1, y2 + h2);
    double width = right - left;
    double height = top - bottom;
    return width * height;
}

// 计算旋转后的矩形宽度
double calculateRotatedWidth(double width, double height, double angle) {
    return abs(width * cos(angle)) + abs(height * sin(angle));
}

// 计算旋转后的矩形高度
double calculateRotatedHeight(double width, double height, double angle) {
    return abs(width * sin(angle)) + abs(height * cos(angle));
}

// 递归函数，实现二叉树装箱
Node* pack(vector<Rectangle*>& rects) {
    if (rects.empty()) {
        return nullptr;
    }

    // 按矩形面积从大到小排序
    sort(rects.begin(), rects.end(), compare);

    // 取出最大的矩形
    Rectangle* first = rects.front();
    rects.erase(rects.begin());

    // 如果当前矩形不旋转能放下，就不旋转
    Node* node = new Node(first);
    if (!rects.empty()) {
        double width = first->width;
        double height = first->height;
        double x = 0;
        double y = 0;
        for (int i = 0; i < rects.size(); i++) {
            double boxArea1 = calculateBoxArea(x, y, width, height, rects[i]->x, rects[i]->y, rects[i]->width, rects[i]->height);
            double boxArea2 = calculateBoxArea(x, y, height, width, rects[i]->x, rects[i]->y, rects[i]->width, rects[i]->height);
            if (boxArea1 <= boxArea2) {
                width = max(width, rects[i]->width);
                height += rects[i]->height;
            } else {
                width += rects[i]->width;
                height = max(height, rects[i]->height);
            }
        }
        node->width = width;
        node->height = height;
        node->angle = 0;
    }

    // 如果当前矩形旋转能放下，就旋转
    if (!rects.empty()) {
        double rotatedWidth = calculateRotatedWidth(first->width, first->height, M_PI / 2);
        double rotatedHeight = calculateRotatedHeight(first->width, first->height, M_PI / 2);
        double x = 0;
        double y = 0;
        double width = rotatedWidth;
        double height = rotatedHeight;
        for (int i = 0; i < rects.size(); i++) {
            double boxArea1 = calculateBoxArea(x, y, width, height, rects[i]->x, rects[i]->y, rects[i]->width, rects[i]->height);
            double boxArea2 = calculateBoxArea(x, y, height, width, rects[i]->x, rects[i]->y, rects[i]->width, rects[i]->height);
            if (boxArea1 <= boxArea2) {
                width = max(width, calculateRotatedWidth(rects[i]->width, rects[i]->height, M_PI / 2));
                height += calculateRotatedHeight(rects[i]->width, rects[i]->height, M_PI / 2);
            } else {
                width += calculateRotatedWidth(rects[i]->width, rects[i]->height, M_PI / 2);
                height = max(height, calculateRotatedHeight(rects[i]->width, rects[i]->height, M_PI / 2));
            }
        }
        if (width <= node->width && height <= node->height) {
            node->width = width;
            node->height = height;
            node->angle = M_PI / 2;
        }
    }

    // 将剩余的矩形分别放在左右子节点上
    vector<Rectangle*> leftRects;
    vector<Rectangle*> rightRects;
    for (int i = 0; i < rects.size(); i++) {
        double x = node->x;
        double y = node->y;
        double width = node->width;
        double height = node->height;
        double angle = node->angle;
        double rotatedWidth = calculateRotatedWidth(rects[i]->width, rects[i]->height, angle);
        double rotatedHeight = calculateRotatedHeight(rects[i]->width, rects[i]->height, angle);
        double boxArea1 = calculateBoxArea(x, y + height, width, rotatedHeight, rects[i]->x, rects[i]->y, rects[i]->width, rects[i]->height);
        double boxArea2 = calculateBoxArea(x + width, y, rotatedWidth, height, rects[i]->x, rects[i]->y, rects[i]->width, rects[i]->height);
        if (boxArea1 <= boxArea2) {
            leftRects.push_back(rects[i]);
        } else {
            rightRects.push_back(rects[i]);
        }
    }
    node->left = pack(leftRects);
    node->right = pack(rightRects);

    // 更新节点的坐标
    if (node->left != nullptr) {
        node->x = node->left->x;
        node->y = node->left->y + node->left->height;
    }
    if (node->right != nullptr) {
        node->x = node->right->x - node->width;
        node->y = node->right->y;
    }

    return node;
}

// 输出矩形位置和旋转角度
void printRectangle(Node* node) {
    if (node == nullptr) {
        return;
    }
    cout << "Rectangle " << node->rect->id << ": (" << node->x << ", " << node->y << "), angle = " << node->angle << endl;
    printRectangle(node->left);
    printRectangle(node->right);
}

int main() {
    vector<Rectangle*> rects;
    rects.push_back(new Rectangle(1, 3, 2));
    rects.push_back(new Rectangle(2, 2, 3));
    rects.push_back(new Rectangle(3, 1, 4));
    rects.push_back(new Rectangle(4, 4, 1));
    rects.push_back(new Rectangle(5, 2, 2));
    Node* root = pack(rects);
    printRectangle(root);
    return 0;
}

上述代码实现了按照矩形2D最小面积二叉树装箱的算法，能够在保证矩形不重叠的前提下，尽可能地减小盒子的面积。对于每个矩形，输出了其在盒子中的位置以及旋转角度。可以根据需要对其进行修改并应用到实际问题中。