49 lines
1.4 KiB
Markdown
49 lines
1.4 KiB
Markdown
---
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id: 5900f4731000cf542c50ff85
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title: 'Problem 262: Mountain Range'
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challengeType: 5
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forumTopicId: 301911
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dashedName: problem-262-mountain-range
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---
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# --description--
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The following equation represents the continuous topography of a mountainous region, giving the elevation h at any point (x,y):
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A mosquito intends to fly from A(200,200) to B(1400,1400), without leaving the area given by 0 ≤ x, y ≤ 1600.
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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.
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First, determine fmin 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 fmin.
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Give that length as your answer, rounded to three decimal places.
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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) )
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# --hints--
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`euler262()` should return 2531.205.
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```js
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assert.strictEqual(euler262(), 2531.205);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler262() {
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return true;
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}
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euler262();
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```
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# --solutions--
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```js
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// solution required
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```
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