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/**
* Worg
*/
#include <deque>
#include <vector>
#include <fstream>
#include <algorithm>
struct Node {
public:
int left_child_id;
int right_child_id;
long long subtree_weight;
static const long long MAX_WEIGHT = 1e15;
static const int NULL_ID = -1;
Node() {}
Node(const int& _left_child_id, const int& _right_child_id, const long long& _subtree_weight) :
left_child_id(_left_child_id),
right_child_id(_right_child_id),
subtree_weight(_subtree_weight) {
}
};
class HuffmanCoder {
private:
int num_symbols;
int root_id;
std::vector<Node> nodes;
std::vector<long long> encodings;
std::deque<int> symbol_node_ids;
std::deque<int> inner_node_ids;
std::vector<char> encoding_lengths;
void dfs(int node_id, char crt_length, long long crt_value) {
if (node_id < num_symbols) {
encodings[node_id] = crt_value;
encoding_lengths[node_id] = crt_length;
} else {
dfs(nodes[node_id].left_child_id, crt_length + 1, crt_value * 2);
dfs(nodes[node_id].right_child_id, crt_length + 1, crt_value * 2 + 1);
}
}
public:
HuffmanCoder(const int& _num_symbols) : num_symbols(_num_symbols), root_id(Node::NULL_ID) {
nodes = std::vector<Node>();
nodes.reserve(num_symbols * 2 + 2);
encodings = std::vector<long long>(num_symbols);
encoding_lengths = std::vector<char>(num_symbols);
}
void add_symbol(const int symbol_weight) {
Node symbol_node(Node::NULL_ID, Node::NULL_ID, symbol_weight);
nodes.push_back(symbol_node);
symbol_node_ids.push_back((int)nodes.size() - 1);
}
int dequeue_min_weight_node() {
long long min_subtree_weight = Node::MAX_WEIGHT;
std::deque<int>* deque_ptr;
if (!symbol_node_ids.empty()) {
min_subtree_weight = nodes[symbol_node_ids.front()].subtree_weight;
deque_ptr = &symbol_node_ids;
}
if (!inner_node_ids.empty() && nodes[inner_node_ids.front()].subtree_weight < min_subtree_weight) {
min_subtree_weight = nodes[inner_node_ids.front()].subtree_weight;
deque_ptr = &inner_node_ids;
}
int min_weight_node_id = deque_ptr->front();
deque_ptr->pop_front();
return min_weight_node_id;
}
void build_prefix_code_tree() {
// Recursively merge nodes until we only have one left (the root)
while (symbol_node_ids.size() + inner_node_ids.size() > 1) {
int left_child_id = dequeue_min_weight_node();
int right_child_id = dequeue_min_weight_node();
Node inner_node(left_child_id, right_child_id, nodes[left_child_id].subtree_weight + nodes[right_child_id].subtree_weight);
nodes.push_back(inner_node);
inner_node_ids.push_back((int)nodes.size() - 1);
root_id = (int)nodes.size() - 1;
}
if (!symbol_node_ids.empty()) {
int left_child_id = symbol_node_ids.front();
nodes.push_back(Node(left_child_id, root_id, nodes[left_child_id].subtree_weight + nodes[root_id].subtree_weight));
root_id = (int)nodes.size() - 1;
}
}
void build_and_print_encodings() {
dfs(root_id, 0, 0);
std::ofstream fout("huffman.out");
// Compute the total length
long long text_encoded_length = 0;
for (int i = 0; i < num_symbols; i++) {
text_encoded_length += nodes[i].subtree_weight * encoding_lengths[i];
}
fout << text_encoded_length << "\n";
for (int i = 0; i < num_symbols; i++) {
fout << (int)encoding_lengths[i] << " " << encodings[i] << '\n';
}
fout.close();
}
};
int main() {
std::ifstream fin("huffman.in");
int num_symbols;
fin >> num_symbols;
HuffmanCoder huffman_coder(num_symbols);
for (int symbol_id = 0; symbol_id < num_symbols; symbol_id++) {
int symbol_weight;
fin >> symbol_weight;
huffman_coder.add_symbol(symbol_weight);
}
fin.close();
huffman_coder.build_prefix_code_tree();
huffman_coder.build_and_print_encodings();
return 0;
}