77 lines
1.4 KiB
C++
77 lines
1.4 KiB
C++
#include <iostream>
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#include <queue>
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#include <vector>
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using namespace std;
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/*
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Huffman 树节点
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在竞赛中一般不需要真的建树，只关心权值
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*/
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struct Node {
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long long w; // 当前节点权值
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Node(long long _w) : w(_w) {}
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};
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/*
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priority_queue 默认是大根堆
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这里通过重载比较函数，使其变为小根堆
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*/
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struct cmp {
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bool operator()(const Node& a, const Node& b) const {
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return a.w > b.w; // 权值小的优先
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}
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};
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int main() {
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ios::sync_with_stdio(false);
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cin.tie(nullptr);
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int n;
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cin >> n;
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/*
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优先队列（小根堆）
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每次可以 O(log n) 取出最小的两个权值
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*/
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priority_queue<Node, vector<Node>, cmp> pq;
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// 读入 n 个权值
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for (int i = 0; i < n; i++) {
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long long x;
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cin >> x;
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pq.push(Node(x));
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}
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/*
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特判：只有一个节点
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WPL = 0（没有边）
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*/
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if (n == 1) {
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cout << 0 << '\n';
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return 0;
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}
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long long WPL = 0;
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/*
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Huffman 树构造过程
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每次取最小的两个合并
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*/
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while (pq.size() > 1) {
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Node a = pq.top(); pq.pop();
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Node b = pq.top(); pq.pop();
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long long mergedWeight = a.w + b.w;
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WPL += mergedWeight;
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pq.push(Node(mergedWeight));
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}
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// 输出带权路径长度
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cout << WPL << '\n';
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return 0;
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}
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