algorithm B manipulations 1/99

step by step for the Huffman algorithm in C++, writing down every action on each data structure and labeling it as Insert / Update / Remove / Combine / Traverse. This will show exactly how manipulations map to steps in the algorithm.

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Huffman Algorithm: Step-by-Step Data Actions

Step	Data Structure	Action	Manipulation Type	Purpose
Count character frequencies	unordered_map<char,int>	freqMap[c]++	Insert / Update	Add new character or increment frequency
Create leaf nodes	priority_queue<HuffmanNode*>	pq.push(new HuffmanNode(c,freq))	Insert	Add leaf nodes for all characters
Build Huffman tree	priority_queue<HuffmanNode*>	left = pq.top(); pq.pop()	Remove / Read	Retrieve smallest frequency node
Build Huffman tree	priority_queue<HuffmanNode*>	right = pq.top(); pq.pop()	Remove / Read	Retrieve second smallest node
Build Huffman tree	HuffmanNode* merged = new HuffmanNode('\0', left->freq + right->freq)	Combine / Insert	Create new parent node combining left & right
Build Huffman tree	merged->left = left; merged->right = right	Update / Combine	Connect children to new node
Build Huffman tree	pq.push(merged)	Insert	Add merged node back to priority queue
Generate Huffman codes	HuffmanNode*	Recursive call generateCodes(root->left, code + "0", huffmanCode)	Traverse / Read	Go down left subtree
Generate Huffman codes	HuffmanNode*	Recursive call generateCodes(root->right, code + "1", huffmanCode)	Traverse / Read	Go down right subtree
Generate Huffman codes	unordered_map<char,string>	huffmanCode[root->ch] = code	Insert / Update	Assign Huffman code to leaf node
Encode string	unordered_map<char,string>	encoded += huffmanCode[c]	Read	Convert input character to Huffman code

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Observations

1. Insert occurs when creating new entries (map, queue, tree leaf, or code map).
2. Update occurs when modifying existing data (frequency increment, updating tree pointers, updating code map).
3. Remove occurs when popping nodes from the priority queue.
4. Combine occurs when merging two nodes into one parent.
5. Traverse occurs during recursion in code generation.

By explicitly labeling every action, you can see why each manipulation is needed, not just what data structure to use.

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