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 ## searching
 
+<br>
+
+
+### binary search
+
+<br>
+
+* a binary search operates on a contiguous sequence with a specified left and right index. this is called the search space.
+* binary searching is composed of 3 sections:
+    * pre-processing: sort if collection is unsorted
+    * binary search: using a loop or recursion to divide search sapce in half after each comparison
+    * post-processing: determine viable candidates in the remaining space
+
+* there are 3 "templates" when writing a binary search:
+    * `while left < right`, with `left = mid + 1` and `right = mid - 1`
+    * `while left < right`, with `left = mid + 1` and `right = mid`, and `left` is returned
+    * `while left + 1 < right`, with `left = 1` and `right = mid`, and `left` and `right` are returned