Hash function concept in Data Structures Theory - Step-by-Step Execution

Concept Flow - Hash function concept

Input Data

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Apply Hash Function

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Generate Hash Code (Number)

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Use Hash Code to Index Storage

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Store or Retrieve Data

A hash function takes input data and converts it into a fixed-size number called a hash code, which is then used to find where data is stored or retrieved.

Execution Sample

Data Structures Theory

Input: "apple"
Hash function: sum of ASCII codes % 10
Output: hash code = ?

This example shows how the word "apple" is converted into a hash code by summing ASCII values and taking remainder by 10.

Analysis Table

Step	Character	ASCII Code	Running Sum	Hash Code (sum % 10)
1	"a"	97	97	7
2	"p"	112	209	9
3	"p"	112	321	1
4	"l"	108	429	9
5	"e"	101	530	0
6	End of input	-	-	0

💡 All characters processed; final hash code is 0 (530 % 10)

State Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	Final
Running Sum	0	97	209	321	429	530	530
Hash Code	-	7	9	1	9	0	0

Key Insights - 3 Insights

Why does the hash code change with each character processed?

Because the hash function adds each character's ASCII code to a running sum, the hash code updates step-by-step as shown in the execution_table rows 1 to 5.

Why do we use modulo (%) operation in the hash function?

Modulo limits the hash code to a fixed range (0-9 here), which helps map the hash code to a fixed-size storage like an array index, as seen in the final hash code calculation.

Can different inputs produce the same hash code?

Yes, different inputs can have the same hash code (called collisions). This example doesn't show collisions but it's a common hash function property.

Visual Quiz - 3 Questions

Look at the execution_table, what is the running sum after processing the second character?

A 321

B 97

C 209

D 112

💡 Hint

Check the 'Running Sum' column at Step 2 in the execution_table.

At which step does the hash code become 1?

A Step 2

B Step 3

C Step 5

D Step 4

💡 Hint

Look at the 'Hash Code' column in the execution_table for when it equals 1.

If the modulo was changed from 10 to 5, what would be the final hash code for "apple"?

A 0

B 4

C 3

D 1

💡 Hint

Calculate 530 % 5 and compare with the final hash code in variable_tracker.

Concept Snapshot

Hash function:
- Takes input data
- Converts to a number (hash code)
- Uses modulo to limit range
- Maps data to storage index
- Collisions can happen

Full Transcript

A hash function converts input data into a fixed-size number called a hash code. This code helps find where data is stored or retrieved. For example, the word 'apple' is processed character by character. Each character's ASCII code is added to a running sum. After all characters, the sum is taken modulo 10 to get the final hash code. This process is shown step-by-step in the execution table. The hash code changes as each character is processed. Modulo operation limits the hash code to a fixed range, useful for indexing storage. Different inputs can sometimes produce the same hash code, known as collisions. Understanding these steps helps grasp how hash functions work in data structures.