Huffman coding

最新推荐文章于 2025-03-09 23:08:29 发布

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最新推荐文章于 2025-03-09 23:08:29 发布

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本文介绍了一种使用哈夫曼编码进行数据压缩的方法，并通过一个具体的编码实例详细展示了如何构建哈夫曼树并计算编码效率。

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In computer science and information theory, a Huffman code is an optimal prefix code algorithm.

In this exercise, please use Huffman coding to encode a given data.

You should output the number of bits, denoted asB(T), to encode the data:

B(T)=∑f(c)d_T(c),

wheref(c) is the frequency of character c, and d_T(c) is be the depth of characterc's leaf in the tree T.

Input

The first line is the number of characters n.

The following n lines, each line gives the character c and its frequencyf(c).

Output

Output a single number B(T).

Sample Input

Copy sample input to clipboard

Sample Output

Hint

0: 01

1: 00

2: 11

3: 100

4: 101

这道题是哈夫曼编码，主要是优先队列没用好，数据类型的指针变量应该这么传参才能小根堆，如果是普通变量可以直接在结构体里重载 < 即可，其余没什么

#include <iostream>
#include <queue>
#include <map>

using namespace std;

struct huffman{
    char c;
    int num;
};

struct tree{
    huffman h;
    tree* left;
    tree* right;
    
}; 
struct cmp{
	bool operator() (tree const*a, tree const*b){
		return a->h.num > b->h.num;
	}
};//小根堆比较 
map <char,int> mm;

void deal(tree* t,int n){
    if(t->left==NULL&&t->right==NULL){
        mm[t->h.c]=n;
    }
    else {
        deal(t->left,n+1);
        deal(t->right,n+1);
    }
}//计算树的深度，用于计算字符长度 
int main()
{
    int n;
    cin >> n;
    priority_queue <tree*, vector<tree*>, cmp> pq;
    huffman hu[1001];
    for(int i=0; i < n; ++i){
        cin >> hu[i].c >> hu[i].num;
        tree *tmp=new tree;
        tmp->h=hu[i];
        tmp->left=NULL;
        tmp->right=NULL;
        pq.push(tmp);
    }//将字符存进优先队列 
    /*tree* t=pq.top();
	cout << t->h.c << endl; */
    while(pq.size() > 1){
        tree* t1=pq.top();
        //cout << t1->h.c << "   "<<t1->h.num << endl;
        pq.pop();
        tree* t2=pq.top();
        //cout << t2->h.c << "   "<< t2->h.num << endl;
        pq.pop();
        tree *tmp=new tree;
        tmp->h.c='.';
        tmp->h.num=t1->h.num+t2->h.num;
        tmp->left=t1;
        tmp->right=t2;
        pq.push(tmp);
        //cout << endl;
    }//建立哈夫曼编码树 
    tree* res=pq.top();
    //cout << res->h.num << endl;
    deal(res,0);
    int resu=0;
	for(int i=0; i < n; ++i){
		//cout << hu[i].num << "   "  << mm[hu[i].c] << endl;
		resu+=(hu[i].num*(mm[hu[i].c]));	
	}
	cout << resu << endl;
}