Competitive Programming Solutions

abc183_b - Billards

04 Jan 2021 — Tags: math,geometry — URL

With a bit of geo, we can define the following two equations for the $x$-coordinate of the incident point, $A_x$.

\[A_x = S_x + S_y \frac{\cos{\alpha}}{\sin{\alpha}}\] \[A_x = G_x - G_y \frac{\cos{\alpha}}{\sin{\alpha}}\]

We can solve for $\alpha$ and then replace it on one of those equations to get the answer.

Time complexity: $O(1)$

Memory complexity: $O(1)$

Click to show code.

 

using namespace std;
using ll = long long;
using ii = pair<int, int>;
using vi = vector<int>;
int main(void)
{
    ios::sync_with_stdio(false), cin.tie(NULL);
    int x1, y1, x2, y2;
    cin >> x1 >> y1 >> x2 >> y2;
    double alpha = atan(double(y1 + y2) / double(x2 - x1));
    cout << setprecision(12) << fixed << x1 + y1 * cos(alpha) / sin(alpha)
         << endl;
    return 0;
}

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