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\section{Pseudocode}  We'll first assume that we have access to the following constant time subroutines:  \begin{verbatim}  /*  * Finds the minimum angle needed for a ray originating in O to intersect  * a circle C. To be consistent with max_intersection_angle(), the angle of  * a ray originating in O and passing through the center of C is defined to  * lie in the interval [0, 2pi]. This means that the value returned by this  * function may be negative, but never greater than 2pi.  */  function min_intersection_angle(O, C)  /*  * Finds the maximum angle needed for a ray originating in O to intersect  * a circle C. To be consistent with min_intersection_angle(), the angle of  * a ray originating in O and passing through the center of C is defined to  * lie in the interval [0, 2pi]. This means that the value returned by this  * function may be greater then 2pi, but never negative.  */  function max_intersection_angle(O, C)  \end{verbatim}  \subsection{Abstract pseudocode}  \begin{verbatim}  function min_rays_intersecting(origin, circles) begin  find a ray R which doesn't intersect any of the circles  let Q be a priority queue of angles intervals ordered by the angle at which they end  convert circles into a set of intervals beginning at angle(R) and add them to Q  while Q not empty loop  let I = delete_min(Q)  if I is not intersected then  add ray at end of I  end if  end loop  return number of rays  end  \end{verbatim}  \subsection{More detailed version}  \begin{verbatim}  function min_rays_intersecting(origin, circles) begin  find a ray R which doesn't intersect any of the circles  let Q be a priority queue of angles intervals ordered by the angle at which they end  for each C in circles loop  let A_min = (min_intersection_angle(origin, C) - angle(R)) mod 2pi  let A_max = (max_intersection_angle(origin, C) - angle(R)) mod 2pi  add [A_min, A_max] to Q  end loop  let P = R  let N_R = 0  while Q not empty loop  let I = delete_min(Q)  if starting_angle(I) > P then  increment N_R  P = ending_angle(I)  end if  end loop  return N_R  end  \end{verbatim}