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POTriangle fit inside another triangle
 

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  1. POTriangle fit inside another triangle
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    <p>Given the lengths of the sides of 2 triangles. Determine if the second triangle can fit inside the first triangle?</p> <p>For more detailed info read the full problem statement below:</p> <p><a href="http://acm.timus.ru/problem.aspx?space=1&amp;num=1566&amp;locale=en" rel="nofollow noreferrer">http://acm.timus.ru/problem.aspx?space=1&amp;num=1566&amp;locale=en</a></p> <p>My implementation below tries all the (3!)^2 possible combinations of aligning the bases of the triangles. It then tries to shift the second triangle inside the first triangle while checking that the base of the second triangle doesn't exceed the base of the first triangle.</p> <p>But I keep getting Wrong Answer(WA) #16. </p> <p><img src="https://i.stack.imgur.com/JB1L4.jpg" alt="enter image description here"></p> <p>The case I gave is the second image. It is obvious that if you rotate PQR to align the sides of length 2.77 and 3.0 the third vertex will not be inside triangle ABC. The side of length 4.2 can only be aligned along the side of len 5. Thus this case is satisfied only in the configuration show in the second image.</p> <p>Can you help me find the bug, suggest some test cases where my algorithm breaks down. Alternative algorithms are also welcome.</p> <pre><code>#include &lt;cmath&gt; #include &lt;iostream&gt; using namespace std; const double PI = atan(1.0)* 4; // Traingle ABC (Envelope) double xa, ya, xb, yb, xc, yc; // Traingle PQR (Postcard) double xp, yp, xq, yq, xr, yr; // Angle between sides AB and AC double theta; double signWrtLine(double x1, double y1, double x2, double y2, double x, double y) { double A = y2 - y1; double B = x1 - x2; double C = -(A * x1 + B * y1); return (A * x + B * y + C); } bool fit() { if ((xr &gt; xc) || (yq &gt; yb)) return false; if (signWrtLine(xa, ya, xb, yb, xq, yq) &lt; 0) { double d = (yq / tan(theta)) - xq; return (xr + d &lt;= xc); } return (signWrtLine(xa, ya, xb, yb, xq, yq) &gt;= 0 &amp;&amp; signWrtLine(xb, yb, xc, yc, xq, yq) &gt;= 0 &amp;&amp; signWrtLine(xc, yc, xa, ya, xq, yq) &gt;= 0); } bool fit(double a[], double b[]) { // generate the 3! permutations of the envelope // loops i,k for (int i = 0; i &lt; 3; i++) { double angle; double u = a[i], v = a[(i + 1) % 3], w = a[(i + 2) % 3]; for (int k = 0; k &lt; 2; k++) { switch (k) { case 0: xa = 0, ya = 0; angle = theta = acos((u * u + v * v - w * w) / (2 * u * v)); xb = v * cos(angle), yb = v * sin(angle); xc = u, yc = 0; break; case 1: // reflect envelope swap(v, w); angle = theta = acos((u * u + v * v - w * w) / (2 * u * v)); xb = v * cos(angle), yb = v * sin(angle); break; } // generate the 3! permutations of the postcard // loops j,k for (int j = 0; j &lt; 3; j++) { double angle; double u = b[j], v = b[(j + 1) % 3], w = b[(j + 2) % 3]; for (int k = 0; k &lt; 2; k++) { switch (k) { case 0: xp = 0, yp = 0; angle = acos((u * u + v * v - w * w) / (2 * u * v)); xq = v * cos(angle), yq = v * sin(angle); xr = u, yr = 0; break; case 1: // reflect postcard swap(v, w); angle = acos((u * u + v * v - w * w) / (2 * u * v)); xq = v * cos(angle), yq = v * sin(angle); break; } if (fit()) return true; } } } } return false; } int main() { double a[3], b[3]; for (int i = 0; i &lt; 3; i++) cin &gt;&gt; a[i]; for (int i = 0; i &lt; 3; i++) cin &gt;&gt; b[i]; if(fit(a, b)) cout &lt;&lt; "YES" &lt;&lt; endl; else cout &lt;&lt; "NO" &lt;&lt; endl; return 0; } </code></pre>
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    1. PO
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      1. PTAnswer
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    1. PTQuestion
    1. USiCodez
    1. USNaximus
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    1. This table or related slice is empty.
    1. This table or related slice is empty.
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    1. PO
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    1. VO
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      1. POTriangle fit inside another triangle
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
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      1. POTriangle fit inside another triangle
      1. This table or related slice is empty.
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    3. VO
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      1. VTUpMod
    1. COAligning the orientation of the bases probably isn't the only way to get one triangle to fit inside the other. The image at that link hints at a different orientation.
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      1. POTriangle fit inside another triangle
      1. USOliver Charlesworth
    2. COSeems a rather complicated way of doing this. Why not use some geometry and calculate the height of the triangles and the various angles. Then move the second ones longest side along the longes side of the first triangle until its heigth will fit. Compare angles and ensure that the first triangles longest edge has enough room for the second one (i might have explained that better).
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      1. POTriangle fit inside another triangle
      1. USEd Heal
    3. COCan you clarify which angles to compare?
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      1. POTriangle fit inside another triangle
      1. USNaximus
 

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