算法1

前缀和优化

include [HTML_REMOVED]

include [HTML_REMOVED]

include [HTML_REMOVED]

using namespace std;

const int N = 100005;

int main() {
int n, m;
cin >> n >> m;

//存储缩放因子和旋转角度的前缀和，使得在处理查询时可以快速获得所需的缩放和旋转值。
vector<double> scale(N, 1.0); // 前缀乘积，初始为1
vector<double> angle(N, 0.0); // 前缀和，初始为0

for (int i = 1; i <= n; i++) {
    int type;
    double value;
    cin >> type >> value;

    if (type == 1) {
        scale[i] = scale[i - 1] * value; // 拉伸
        angle[i] = angle[i - 1]; // 旋转不变
    } else {
        scale[i] = scale[i - 1]; // 拉伸不变
        angle[i] = angle[i - 1] + value; // 累加旋转
    }
}

while (m--) {
    int start, end;
    double x, y;
    cin >> start >> end >> x >> y;

    // 计算最终缩放因子和旋转角度
    double totalScale = scale[end] / scale[start - 1];
    double totalAngle = angle[end] - angle[start - 1];

    // 应用缩放
    x *= totalScale;
    y *= totalScale;

    // 应用旋转
    double xNew = x * cos(totalAngle) - y * sin(totalAngle);
    double yNew = x * sin(totalAngle) + y * cos(totalAngle);

    // 输出结果
    printf("%.5lf %.5lf\n", xNew, yNew);
}

return 0;

}

算法2

(暴力枚举)

include [HTML_REMOVED]

include [HTML_REMOVED]

using namespace std;

const int N = 100005;
int n, m;
double t[N][2];

void trans1(double k, double &x, double &y) {
// 拉伸操作
x = k;
y = k;
}

void trans2(double ce, double &x, double &y) {
// 旋转操作
double newX = x * cos(ce) - y * sin(ce);
double newY = x * sin(ce) + y * cos(ce);
x = newX;
y = newY;
}

int main() {
cin >> n >> m;

// 存储操作类型和参数
for (int i = 1; i <= n; i++) {
    int flag;
    double s;
    cin >> flag >> s;
    t[i][0] = flag; // 操作类型
    t[i][1] = s;    // 操作值
}

while (m--) {
    int start, end;
    double x, y;
    cin >> start >> end >> x >> y;

    // 在查询范围内应用操作
    for (int z = start; z <= end; z++) {
        if (t[z][0] == 1) // 如果是拉伸操作
            trans1(t[z][1], x, y);
        else // 如果是旋转操作
            trans2(t[z][1], x, y);
    }

    // 输出结果
    printf("%.5lf %.5lf\n", x, y);
}

return 0;

}