title: determine if a given point is inside the polygon
body: <p>Given a convex polygon as a counter-clockwise list of n vertices, give O(lgn) algorithm to determine if a given point is inside the polygon. Assume the basic operations take O(1).</p>
  
  <p>I am think a direction that: if a point is inside a convex polygon, what is the special relationship among the points and all the vertecies or edges? Also, I am guessing the trick here is the convex polygon which makes the algorithm lgn. </p>