Problem 1456. Beads on a Necklace (Convex Hulls)

Created by Ned Gulley

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We may describe a <a href = "http://en.wikipedia.org/wiki/Convex_hull">convex hull</a> as a rubber band stretched around a list of points. Some of the points will be inside the rubber band, and some will define vertices of (or lie along the edge of) a <a href = "http://en.wikipedia.org/wiki/Convex_and_concave_polygons">convex polygon</a>.Given an n-by-2 list of points xy where each row describes a point, your job is to determine if all the points belong to the convex hull for those points. In the matrix xy, the x coordinate is the first column and the y coordinate is the second column.So, for example, the points below form a single convex hull.<pre> * *</pre><pre> * * </pre>In contrast, the points below do not, since the convex hull is a triangle that includes an interior point. Any polygon that includes all the points must necessarily be concave.<pre> *
 * 
 * *</pre>Thus if<pre> xy = [1 1;1 2;2 2;2 1]</pre>then<pre> allConvex(xy) => true</pre>Whereas<pre> xy = [1 1;3 1;2 2;2 3]
 allConvex(xy) => false</pre>

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Problem 1456. Beads on a Necklace (Convex Hulls)

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