86 lines
5.6 KiB
HTML
86 lines
5.6 KiB
HTML
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<h2>Mountain Range.</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 262</h3><span style="width:300px;color:#666;">Published on Friday, 30th October 2009, 09:00 pm; Solved by 473</span></div>
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<p>The following equation represents the <i>continuous</i> topography of a mountainous region, giving the <dfn title="height above sea level">elevation</dfn> <var>h</var> at any point (<var>x</var>,<var>y</var>):</p>
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<p>A mosquito intends to fly from A(200,200) to B(1400,1400), without leaving the area given by 0 ≤ <var>x</var>, <var>y</var> ≤ 1600.</p>
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<p>Because of the intervening mountains, it first rises straight up to a point A', having elevation <var>f</var>. Then, while remaining at the same elevation <var>f</var>, it flies around any obstacles until it arrives at a point B' directly above B.</p>
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<p>First, determine <var>f<sub>min</sub></var> which is the minimum constant elevation allowing such a trip from A to B, while remaining in the specified area.<br />
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Then, find the length of the shortest path between A' and B', while flying at that constant elevation <var>f<sub>min</sub></var>.</p>
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<p>Give that length as your answer, rounded to three decimal places.</p>
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<p><font "size=2"><u>Note</u>: For convenience, the elevation function shown above is repeated below, in a form suitable for most programming languages:<br />
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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) )</font></p>
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