C++优先队列解决哈夫曼(Huffmam)编码问题 (STL priority_queue)

Huffman树和Huffman编码的概念在此不再赘述了。

实现Huffman树的难点在于如何从节点集合中找到两个权最小的节点并将其合并。
STL中的priority_queue基于小顶堆实现，能满足较快找到权重最小两节点的要求。

1.priority_queue的基本用法

首先对priority_queue的基本用法做简要介绍

#include <iostream>#include <queue>using namespace std;struct Node{    int n;    Node(int _n):n(_n){}};//自定义比较类struct cmp{    bool operator() (const Node &a, const Node &b)    {        return a.n > b.n;    }};int main(){    //声明一个优先队列pq    priority_queue<Node, vector<Node>, cmp> pq;    Node n1(9);    Node n2(1);    Node n3(5);    Node n4(2);    //将元素依次插入优先队列pq    pq.push(n1);    pq.push(n2);    pq.push(n3);    pq.push(n4);    //输出队首元素,输出结果为1    cout << pq.top().n << endl;    //取出队首元素    pq.pop();    return 0;}

2.实现Huffman编码

#include<iostream>#include<cstdio>#include<queue>#include<deque>using namespace std;//字符结构体struct Hcode{    char ch;//字符    deque<int> huffcode;//字符的哈夫曼编码};//Huffman树节点struct Hnode{    int weight = 0;    Hnode *parent = NULL;    Hnode *Lchild = NULL;    Hnode *Rchild = NULL;};struct cmp{    bool operator() (const Hnode *a, const Hnode *b)    {        return a->weight > b->weight;    }};//Huffman树构造函数void huff_init(priority_queue<Hnode*, vector<Hnode*>, cmp>& pq, int n){    for(int i=0; i<n-1; i++)    {        if(pq.size() == 1)            break;        Hnode *Pnode = new Hnode();        Hnode *Lnode = pq.top();        pq.pop();        Hnode *Rnode = pq.top();        pq.pop();        Pnode->weight = Lnode->weight + Rnode->weight;        Pnode->Lchild = Lnode;        Pnode->Rchild = Rnode;        Lnode->parent = Pnode;        Rnode->parent = Pnode;        pq.push(Pnode);    }}//Huffman编码获取函数/*获取Huffman编码的基本思想是从Huffman树的叶子节点出发，自底向上 * 若当前结点为父节点的左子树则在huffcode头部插入编码1，为左子树 * 则在huffcode头部插入编码0（01顺序不影响最优编码长度），直到根 * 节点，Huffman编码获取完成，从huffcode中顺序输出即可*/void huff_code(Hnode *node, Hcode *code, int n){    for(int i=0; i<n; i++)    {        Hnode *currNode = &node[i];        for(;;)        {            if(currNode->parent == NULL)                break;            else            {                if(currNode->parent->Rchild == currNode)                {                    code[i].huffcode.push_front(1);                }                else                {                    code[i].huffcode.push_front(0);                }            }            currNode = currNode->parent;        }    }}//Huffman编码输出函数void huff_print(Hcode *code, int n){    for(int i=0; i<n; i++)    {        printf("%c 's Huffman code is:",code[i].ch);        deque<int>::iterator it;        for(it = code[i].huffcode.begin(); it != code[i].huffcode.end(); it++)            cout << *it;        cout << endl;    }}int main(){    int n;//字符数    scanf("%d",&n);    Hcode code[n];    Hnode node[n];    //依次读入字符频率    for(int i=0; i<n; i++)        scanf("%d",&node[i].weight);    fflush(stdin);    //依次读入字符    for(int i=0; i<n; i++)        scanf("%c",&code[i].ch);    //构造优先队列并初始化    priority_queue<Hnode*, vector<Hnode*>, cmp> pq;    for(int i=0; i<n; i++)        pq.push(node+i);    //构造Huffman树    huff_init(pq, n);    //获得Huffman编码    huff_code(node, code, n);    //输出Huffman编码    huff_print(code, n);    return 0;}

3.输入输出样例

input:

6
45 13 12 16 9 5
ABCDEF

output:

A 's Huffman code is:0
B 's Huffman code is:101
C 's Huffman code is:100
D 's Huffman code is:111
E 's Huffman code is:1101
F 's Huffman code is:1100