Huffman Encoding in DSA C - Execution Trace

Concept Flow - Huffman Encoding

Count frequency of each char

↓

Create leaf nodes for each char

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Build min-heap of leaf nodes

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While more than one node in heap

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Extract two smallest nodes

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Create new internal node with sum freq

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Insert new node back to heap

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Heap has one node -> root of Huffman tree

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Traverse tree to assign codes

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Encode input using codes

The flow shows counting frequencies, building a min-heap, merging nodes to build the tree, then assigning codes.

Execution Sample

DSA C

char input[] = "abbccc";
// Frequencies: a=1, b=2, c=3
// Build tree and assign codes
// a: 10, b: 11, c: 0
// Encode input

This code counts frequencies of characters, builds Huffman tree, assigns codes, and encodes the input string.

Execution Table

Step	Action	Heap Content (freq:char)	New Node Created	Heap After Insertion	Notes
1	Count frequencies	-	-	-	a=1, b=2, c=3
2	Create leaf nodes	1:a, 2:b, 3:c	-	-	Leaf nodes created for each char
3	Build min-heap	1:a, 2:b, 3:c	-	-	Min-heap built with leaf nodes
4	Extract two smallest	1:a, 2:b, 3:c	-	-	Extracted 1:a and 2:b
5	Create internal node	-	3:internal	-	New node freq=1+2=3
6	Insert new node	3:c, 3:internal	-	3:c, 3:internal	Heap now has two nodes with freq=3
7	Extract two smallest	3:c, 3:internal	-	-	Extracted 3:c and 3:internal
8	Create internal node	-	6:root	-	New node freq=3+3=6 root
9	Insert new node	6:root	-	6:root	Heap has one node, tree complete
10	Assign codes	-	-	-	c=0, a=10, b=11
11	Encode input	-	-	-	Input 'abbccc' encoded as 10 11 11 0 0 0
12	End	-	-	-	Encoding complete

💡 Heap reduced to one node, Huffman tree built and encoding done

Variable Tracker

Variable	Start	After Step 3	After Step 6	After Step 9	Final
freq_a	0	1	1	1	1
freq_b	0	2	2	2	2
freq_c	0	3	3	3	3
heap	empty	1:a,2:b,3:c	3:c,3:internal	6:root	6:root
codes	empty	empty	empty	c=0,a=10,b=11	c=0,a=10,b=11
encoded_string	empty	empty	empty	empty	10 11 11 0 0 0

Key Moments - 3 Insights

Why do we combine the two smallest frequency nodes first?

Combining smallest nodes first ensures the tree has minimal weighted path length, as shown in steps 4-8 where nodes with freq 1 and 2 are combined before others.

How do we know when the Huffman tree is complete?

When the heap has only one node left (step 9), that node is the root of the Huffman tree, so the tree is complete.

Why does character 'c' get the shortest code '0'?

Because 'c' has the highest frequency (3), it is placed closer to the root, resulting in a shorter code, as assigned in step 10.

Visual Quiz - 3 Questions

Look at the execution table at step 5, what is the frequency of the new internal node created?

A 3

B 2

C 1

D 6

💡 Hint

Check the 'New Node Created' column at step 5 in the execution_table.

At which step does the heap reduce to a single node?

A Step 6

B Step 9

C Step 4

D Step 11

💡 Hint

Look at the 'Heap After Insertion' column and the notes in the execution_table.

According to the variable_tracker, what is the encoded string after the final step?

A "10 11 11 0 0 0"

B "0 10 11 11 0 0"

C "11 10 0 0 0 11"

D "0 0 0 10 11 11"

💡 Hint

Check the 'encoded_string' row in the variable_tracker at the 'Final' column.

Concept Snapshot

Huffman Encoding builds a binary tree based on character frequencies.
1. Count frequencies.
2. Create leaf nodes and build a min-heap.
3. Merge two smallest nodes repeatedly until one node remains.
4. Assign codes by traversing the tree (left=0, right=1).
5. Encode input using these codes for compression.

Full Transcript

Huffman Encoding starts by counting how often each character appears. Then, each character becomes a leaf node with its frequency. These nodes go into a min-heap to always pick the smallest frequencies. We repeatedly take two smallest nodes, merge them into a new node with combined frequency, and put it back. When only one node remains, it is the root of the Huffman tree. We assign codes by going left (0) or right (1) in the tree. Characters with higher frequency get shorter codes. Finally, we encode the input string using these codes. This process compresses data efficiently.