Trie Book analysis added

Author: bhavinjawade

Trie_Data_Structure.md

@@ -1,8 +1,38 @@
 # Trie Data Structure
 
-Trie is an efficient information reTrieval data structure. Using Trie, search complexities can be brought to optimal limit (key length). If we store keys in binary search tree, a well balanced BST will need time proportional to M * log N, where M is maximum string length and N is number of keys in tree. Using Trie, we can search the key in O(M) time. However the penalty is on Trie storage requirements.
+Trie is an efficient information reTrieval data structure. Trie also called digital tree, radix tree or prefix tree is a kind of search tree—an ordered tree data structure used to store a dynamic set or associative array where the keys are usually strings. Using Trie, search complexities can be brought to optimal limit (key length). If we store keys in binary search tree, a well balanced BST will need time proportional to M * log N, where M is maximum string length and N is number of keys in tree. Using Trie, we can search the key in O(M) time. However the penalty is on Trie storage requirements.
 <br>
 
+## Efficiency of Trie
+
+The complexity of creating a trie is O(W*L), where W is the number of words, and L is an average length of the word: you need to perform L lookups on the average for each of the W words in the set.
+<br>
+In the associated [code](Trie_Data_Structure.py), I have used a text file with more than 7 million words (A file created by concatinating text from Books like - [Gone with the wind](http://biblioteka.kijowski.pl/mitchell%20margaret/gone%20with%20the%20wind.pdf) and few others). Creating the Trie Data structure takes O(m*n) time complexity. 
+But searching takes only O(L) complexity where L is the length of word you are going to search.
+<br>
+
+### Analysis
+
+If you run the associated [code](Trie_Data_Structure.py) , you must get something like:
+
+```python
+
+Reading the File
+Calculating the number of words
+No of words: 7171744
+>>TIME: 1.359375
+
+Creating Trie Data Structure
+Trie Successfully Created
+>>TIME: 24.203125
+
+enter the word to search: the
+{'No of times word occurs': 407360, 'The word exists': True}
+>>TIME: 0.0
+
+```
+where the time is in **fractional seconds** and measured using **time.process_time()** in python.
+
 ## Advantages of Tries
 
 <br>

Trie_Data_Structure.py

@@ -41,23 +41,26 @@ def search(word,root):
     current = node
   return {"The word exists" : current.endofword,"No of times word occurs" : current.count}
 
- 
+start = time.process_time()
 print("Reading the File")
 store = open("store_for_trie.txt","r",encoding="utf8")
 text = store.read()
 words = text.split()
 print("Calculating the number of words")
 print("No of words: " + str(len(words)))
- 
+print(">>TIME: "+str(time.process_time() - start))
+
+starts = time.process_time()
 print("Creating Trie Data Structure")
 for word in words:
       insert(word)
 print("Trie Successfully Created")
+print(">>TIME: "+str(time.process_time() - starts))
 
+startss = time.process_time()
 tosearch = input("enter the word to search: ")
 print(search(tosearch,root))
-
-# to simply try the trie data structure uncomment below lines
+print(">>TIME: "+str(time.process_time() - startss))
 
 # insert("HelloBhavin")
 # insert("Hell")