/**
	 * If a vertex named name exists in the the array vertices between positions begin and end (inclusive), then
	 * returns the position where this vertex is, i.e., i such that vertices[i].word.compareTo(name) == 0
	 * 
	 * If such a vertex does not exist, returns -(1 + the first position in the array that is greater than name),
	 * i.e., i such that vertices[-(i+1)].word.compareTo(name)>0, but vertices[-(i+2)].word.compareTo(name) < 0,
	 * or, in other words -(1+insertion point of name).
	 * 
	 * For example, if vertices contains {"b", "d", "f"}, begin is 0, and end is 2 then it will return:
	 * 0 on input "b"
	 * 1 on input "d"
	 * 2 on input "f"
	 * -1 on input "a" (because the first position in the array that is greater than "a" is 0)
	 * -2 on input "c"
	 * -3 on input "e"
	 * -4 on input "g" and above
	 * 
	 * In particular, the vertex has been found if and only if the return value is >=0, and
	 * the vertices in locations Math.abs(return_value  + 1) and above are exactly the vertices that are greater than name,
	 * regardless of whether the vertex has been found
	 * 
	 * This behaviour is the same as Java's Arrays.binarySearch method
	 * 
	 * If end<begin, returns -(begin+1)
	 * 
	 * Both begin and end are assumed to be nonnegative and below size 
	 * 
	 * @param name the name of the vertex we are looking for
	 * @param begin beginning location (inclusive) of the array where to search; assumed >=0 and <size
	 * @param end end location (inclusive) of the array where to search; assumed >=0 and <size
	 * @return the position in the vertices array if found; -(1+insertion point) if not 
	 */
	private int find (char[] name, int begin, int end) {