yaworsw/euler-manager

---
:id: 262
:name: Mountain Range
:url: https://projecteuler.net/problem=262
:content: "The following equation represents the _continuous_ 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>):\n\n ![p262_formula1.gif]({{ images_dir
  }}/p262_formula1.gif)  \n\nA mosquito intends to fly from A(200,200) to B(1400,1400),
  without leaving the area given by 0&nbsp;≤&nbsp;<var>x</var>,&nbsp;<var>y</var>&nbsp;≤&nbsp;1600.\n\nBecause
  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.\n\nFirst,
  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.  \nThen, find the
  length of the shortest path between A' and B', while flying at that constant elevation
  <var>f<sub>min</sub></var>.\n\nGive that length as your answer, rounded to three
  decimal places.\n\n<font><u>Note</u>: For convenience, the elevation function shown
  above is repeated below, in a form suitable for most programming languages:<br>\nh=(
  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>\n\n"