longest line in image hough - performance

Question

I'm going to find lines in an image, so I use hough transform to do it.
But now I'm trying to find the longest line in the image(there must exist a longest line in my image), is there any method to do it without sacrifice the computation speed?
using namespace std;
using namespace cv;
int main()
{
VideoCapture cap("D:\\DataBox\\v0.avi");
if (!cap.isOpened())
cout << "fail to open!" << endl; //return -1;
else
cout << "Video Load Succeed" << endl;
while (true)
{
cout << "----------------------------------------------------" << endl;
Mat src;
cap >> src;
pyrDown(src, src, Size(src.cols / 2, src.rows / 2));
pyrDown(src, src, Size(src.cols / 2, src.rows / 2));
cvtColor(src, src, CV_BGR2GRAY);
Mat tsrc;
threshold(src, tsrc, 90, 255, THRESH_BINARY_INV);
Mat grad_x, grad_y;
Mat abs_grad_x, abs_grad_y;
Mat sobel;
int scale = 1;
int delta = 0;
int ddepth = CV_16S;
Sobel(tsrc, grad_x, ddepth, 1, 0, 3, scale, delta, BORDER_DEFAULT);
convertScaleAbs(grad_x, abs_grad_x);
Sobel(tsrc, grad_y, ddepth, 0, 1, 3, scale, delta, BORDER_DEFAULT);
convertScaleAbs(grad_y, abs_grad_y);
addWeighted(abs_grad_x, 0.5, abs_grad_y, 0.5, 0, sobel);
vector<Vec2f> lines;
int threshold = 250;
HoughLines(sobel , lines, 1, CV_PI / 180, threshold, 0, 0);
Mat cdst;
cvtColor(sobel, cdst, CV_GRAY2BGR);
for (size_t i = 0; i < lines.size(); i++)
{
float rho = lines[i][0], theta = lines[i][1];
Point pt1, pt2;
double a = cos(theta), b = sin(theta);
double x0 = a*rho, y0 = b*rho;
pt1.x = cvRound(x0 + 1000 * (-b));
pt1.y = cvRound(y0 + 1000 * (a));
pt2.x = cvRound(x0 - 1000 * (-b));
pt2.y = cvRound(y0 - 1000 * (a));
line(cdst, pt1, pt2, Scalar(0, 0, 255), 3, CV_AA);
}
imshow("Video", cdst);
waitKey(30);
}
}