import heapq

from collections import defaultdict

class HuffmanNode:

def $\_\_$init$\_\_($self$,$ char, freq$)$:

self.char $=$ char

self.freq $=$ freq

self.left $=$ None

self.right $=$ None

# Comparator for the priority queue

def $\_\_$lt$\_\_($self$,$ other$)$:

return self.freq $$ other.freq

def calculate$\_$huffman$\_$codes$($frequencies$)$:

# Priority queue for building the tree

heap $=[$HuffmanNode$($char$,$ freq$)$ for char, freq in frequencies.items$()]$

heapq.heapify$($heap$)$

print$("$

Step$-$by$-$step Tree Building:"$)$

while len$($heap$)>1$:

# Pop the two smallest nodes

left $=$ heapq.heappop$($heap$)$

right $=$ heapq.heappop$($heap$)$

# Combine these two nodes into a new parent node

merged $=$ HuffmanNode$($None$,$ left.freq $+$ right.freq$)$

merged.left $=$ left

merged.right $=$ right

# Push the parent node back into the priority queue

heapq.heappush$($heap$,$ merged$)$

print$($f$"$Combined nodes with frequencies $\{$left$.$freq$\}$ and $\{$right$.$freq$\}$ into $\{$merged$.$freq$\}")$

# The root of the tree

root $=$ heap$[0]$

# Recursively assign codes

codes $=\{\}$

def assign$\_$codes$($node$,$ code$="")$:

if node is not None:

if node.char is not None:

codes$[$node$.$char$]=$ code

assign$\_$codes$($node$.$left, code $+"0")$

assign$\_$codes$($node$.$right, code $+"1")$

assign$\_$codes$($root$)$

print$("$

Final Huffman Codes:"$)$

for char, code in codes.items$()$:

print$($f$"\{$char$\}$: $\{$code$\}")$

return codes

# Input frequencies

frequencies $=\{$

$\text{'}$a$\text{'}$: $10,$

$\text{'}$b$\text{'}$: $2,$

$\text{'}$c$\text{'}$: $4,$

$\text{'}$d$\text{'}$: $5,$

$\text{'}$e$\text{'}$: $15,$

$\text{'}$f$\text{'}$: $9,$

$\text{'}$g$\text{'}$: $6,$

$\text{'}$h$\text{'}$: $8,$

$\text{'}$i$\text{'}$: $12,$

$\text{'}$j$\text{'}$: $1$

$\}$

# Run the Huffman coding algorithm

codes $=$ calculate$\_$huffman$\_$codes$($frequencies$)$