Update README.md

trees_and_graphs/README.md

@@ -135,6 +135,17 @@ def postorder(self, root):
   	3. two items with an equal priority are dequeued based on their order in the queue   
  
 
+<br>
+
+----
+
+### n-ary tree
+
+<br>
+
+* if a tree is a rooted tree in which each node has no more than N children, it's called N-ary tree.
+
+
 <br>
 
 ----
@@ -143,14 +154,35 @@ def postorder(self, root):
 
 <br>
 
-* a variant of n-ary tree in which characters are stored in each node
+* tries, also called prefix tree, are a variant of n-ary tree in which characters are stored in each node.
-* each path down the tree represents a word
+* each trie node represents a string (a prefix) and each path down the tree represents a word. note that not all the strings represented by trie nodes are meaningful.
-* the * nodes (null nodes) are often used to indicate complete words (usually represented by a special type of child) or a boolean flag that terminates the parent node
+* the root is associated with the empty string.
-* a node can have anywhere from 1 through alphabet_size + 1 child
+* the * nodes (null nodes) are often used to indicate complete words (usually represented by a special type of child) or a boolean flag that terminates the parent node.
-* can be used to store the entire english language for quick prefix lookup (O(k), where k is the length of the string)
+* a node can have anywhere from 1 through alphabet_size + 1 child.
+* can be used to store the entire english language for quick prefix lookup (O(k), where k is the length of the string). they are also widely used on autocompletes, spell checkers, etc.
+* tries structures can be represented by arrays and maps or trees.
 
 <br>
 
+#### insertion
+
+<br>
+
+* similar to a bst, when we insert a value to a trie, we need to decide which path to go depending on the target value we insert.
+* the root node needs to be initialized before you insert strings.
+
+<br>
+
+#### search
+
+<br>
+
+* all the descendants of a node have a common prefix of the string associated with that node, so it should be easy to search if there are any words in the trie that starts with the given prefix.
+* we go down the tree depending on the given prefix, once we cannot find the child node, the search fails.
+* we can also search for a specific word rather than a prefix, treating this word as a prefix and searching in the same way as above.
+* if the search succeeds, we need to check if the target word is only a prefix of words in the trie or if it's exactly a word (for example, by adding a boolean flag).
+
+<br>
 
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