Create Hashing_CheatSheet.md

DSA/Hashing_CheatSheet.md

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+# Hashing:  
+	Short Intro -> Finding exact value in a faster way for present or future use.
+
+	-> Direct Address Table Hashing: Simply it uses the array indices to match the value asked and check whether it is hit or not.
+	   ~ Disadvantage: This technique fails for the larger value, floating-point values, string ,and other non-integer values.
+
+
+	-> Hashing Using Hash Function: We use a hash function that maps the universe of the key with some finite length table using some hash function.
+
+	~ Few points to be kept in mind while selecting hash function :
+
+		1. It should always map a large Key to some small key.
+		2. It should generate value from 0 to n-1, where n is the size of the table.
+		3. It should make the operations like insert, delete and search faster, O(1) for integers and O(size) for a string of length 'size' on an average.
+		4. It should uniformly distribute the keys into the Hash Table Slots. (MOST IMPORTANT)
+
+	~ Few Hash Functions:
+
+		1. Using Modulo Property that modulo with any number M generates a number from 0 to M-1.
+			-> H(large_key) = large_key % M, where M is a prime number greater than hash table size.
+
+		2. We use weighted sum for the hash function of string.
+			-> str="abcd" => H(str) = str[0]*x^0 + str[1]*x^1 + str[2]*x^2 +str[3]*x^3.
+
+		3. Universal Hashing - It's a mixture of several hash functions.
+
+
+# Since the hashtable size is smaller than the set of universal, the collision of keys will take place.
+
+	:) Following are the techniques to tackle collision problems:-
+
+		~ If the keys are known in advance we can use a technique called Perfect Hashing. (Wikipedia says:  In computer science, a perfect hash function for a set S is a hash function that maps distinct elements in S to a set of integers, with no collisions).
+
+		~ But if we do not know the keys in advance then the following are the techniques which will help us :) 
+
+# Chaining 
+	Short Intro -> It links the keys with same hash value as chain which can be implemented using a dynamic array or LinkedList or even using self-balancing BST.
+
+		       Keys = { 21, 58, 17, 54, 50, 102, 8, 159, 205,506, 711, 544, 989 }
+		       H(key) = key%5
+			    ------
+		       0   |  50  | -> 205
+			    ------
+		       1   |  21  | -> 506 -> 711
+			    ------
+		       2   |  17  | -> 102
+			    ------
+		       3   |  58  | -> 8
+			    ------
+		       4   |  54  | -> 159 -> 544 -> 989
+			    ------
+
+# Open Addressing 
+
+		Short Intro -> When there is a collision it uses the next free slot of the Hash table for insertion.   
+		Condition for Open addressing :	- Number of slots in the hash table must be greater than or equal to the number of keys to be inserted.   
+		Advantage: i) Cache Friendly, since it uses the hash table only.
+
+		       Keys = { 50, 51, 49, 16, 56, 15, 19 }
+		       H(key) = key%7
+			    ------
+		       0   |  49  | 
+			    ------
+		       1   |  50  | 
+			    ------
+		       2   |  51  | 
+			    ------
+		       3   |  16  | 
+			    ------
+		       4   |  56  | 
+			    ------
+		       0   |  15  | 
+			    ------
+		       1   |  19  |
+			    ------
+
+		   Types of Open Addressing Based on Efficiency:   
+		   i. Linear Probing - It searches linearly from the next empty slot when a collision happens.
+
+					H(key,i)=[H(key)+i]%M , where H(key) is a hash function.
+
+		     -> Disadvantage: i) When there is a large number of collision clustering takes place which makes the searching costly.
+
+		   ii. Quadratic Probing - It searches in a Quadratic manner for The next empty slot when a collision happens.
+
+				       H(key,i)=[H(key)+i^2]%M , where H(key) is a hash function.
+
+		     -> Disadvantage: i) Clustering is reduced to some extent as secondary clustering takes place instead of primary.		       
+				     ii) It may fail to find an empty slot even when the empty slot present.			   
+					- This problem can be removed by making the number of slots in the hash table more than twice of the number of keys to be inserted and taking M as a
+					   prime number.
+
+# Double Hashing 
+
+		Short Intro-> To avoid primary and secondary clustering we use two hash functions instead of one.
+
+		H(key,i)=[H1(key)+i*H2(key)]%M , where H1(key)and H2(key) are the hash function.	
+
+
+For Detailed Info: https://www.geeksforgeeks.org/hashing-data-structure/
+