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id	title	challengeType	forumTopicId	dashedName
5900f4731000cf542c50ff85	Problem 262: Mountain Range	5	301911	problem-262-mountain-range

--description--

The following equation represents the continuous topography of a mountainous region, giving the elevation h at any point (x,y):

h = \left(5000 - \frac{x^2 + y^2 + xy}{200} + \frac{25(x + y)}{2}\right) \times e^{-\left|\frac{x^2 + y^2}{1\\,000\\,000} - \frac{3(x + y)}{2000} + \frac{7}{10}\right|}

A mosquito intends to fly from A(200,200) to B(1400,1400), without leaving the area given by 0 ≤ x, y ≤ 1600.

Because of the intervening mountains, it first rises straight up to a point A', having elevation f. Then, while remaining at the same elevation f, it flies around any obstacles until it arrives at a point B' directly above B.

First, determine f_{min} which is the minimum constant elevation allowing such a trip from A to B, while remaining in the specified area. Then, find the length of the shortest path between A' and B', while flying at that constant elevation f_{min}.

Give that length as your answer, rounded to three decimal places.

Note: For convenience, the elevation function shown above is repeated below, in a form suitable for most programming languages: h=( 5000-0.005*(x*x+y*y+x*y)+12.5*(x+y) )* exp( -abs(0.000001*(x*x+y*y)-0.0015*(x+y)+0.7) ).

--hints--

mountainRange() should return 2531.205.

assert.strictEqual(mountainRange(), 2531.205);

--seed--

--seed-contents--

function mountainRange() {

  return true;
}

mountainRange();

--solutions--

// solution required

1.6 KiB Raw Blame History