哈夫曼树(最优二叉树)与哈夫曼编码

huffmanNode.h

#ifndef __HUFFMANNODE_H__
#define __HUFFMANNODE_H__

class huffmanNode
{
public:
	int weight;
	int lchild, rchild, parent;
};

#endif

huffmanTree.cpp

#include 
#include "huffmanNode.h"
using namespace std;

void selectMinWeight(huffmanNode *_huffmanTree, int _num, int &_minIndex1, int &_minIndex2)
{
	int i = 0, minWeight = 0;

	for (i = 0; i < _num; i++)
		if (_huffmanTree[i].parent == -1)
		{
			minWeight = i;
			break;
		}
	for (i = 0; i < _num; i++)
		if (_huffmanTree[i].parent == -1)
			if (_huffmanTree[i].weight < _huffmanTree[minWeight].weight)
				minWeight = i;
	_minIndex1 = minWeight;

	for (i = 0; i < _num; i++)
		if (_huffmanTree[i].parent == -1 && i != _minIndex1)
		{
			minWeight = i;
			break;
		}
	for (i = 0; i < _num; i++)
		if (_huffmanTree[i].parent == -1 && i != _minIndex1)
			if (_huffmanTree[i].weight < _huffmanTree[minWeight].weight)
				minWeight = i;
	_minIndex2 = minWeight;
}

//构造哈夫曼树
void HuffmanTree(huffmanNode *_huffmanTree, int _weight[], int _num)
{
	int i = 0;
	int minIndex1 = -1, minIndex2 = -1;

	for (i = 0; i < 2 * _num - 1; i++)
	{
		
		_huffmanTree[i].parent = -1;
		_huffmanTree[i].lchild = -1;
		_huffmanTree[i].rchild = -1;
	}

	for (i = 0; i < _num; i++)
		_huffmanTree[i].weight = _weight[i];

	//合并节点，构建哈夫曼树
	for (i = _num; i < 2 * _num - 1; i++)
	{
		selectMinWeight(_huffmanTree, i, minIndex1, minIndex2);
		_huffmanTree[minIndex1].parent = i;
		_huffmanTree[minIndex2].parent = i;
		_huffmanTree[i].lchild = minIndex1;
		_huffmanTree[i].rchild = minIndex2;
		_huffmanTree[i].weight = _huffmanTree[minIndex1].weight + _huffmanTree[minIndex2].weight;

		cout << _huffmanTree[i].weight << "(" << _huffmanTree[minIndex1].weight << "," << _huffmanTree[minIndex2].weight << ")" << endl;
	}
}

//求哈夫曼树的哈夫曼编码
void HuffmanCode(huffmanNode *_huffmanTree, int _num)
{
	int parentIndex = -1, j = 0;
	vector<int> code;
	vector<int> nodeCode;

	for (int i = 0; i < _num; i++)
	{
		j = i;
		while(_huffmanTree[j].parent != -1)
		{
			parentIndex = _huffmanTree[j].parent;

			if (j == _huffmanTree[parentIndex].lchild)
				nodeCode.insert(nodeCode.begin(), 0);
			else
				nodeCode.insert(nodeCode.begin(), 1);

			j = parentIndex;
		}
		code.insert(code.end(), nodeCode.begin(), nodeCode.end());
		nodeCode.clear();
	}
	for (unsigned int i = 0; i < code.size(); i++)
		cout << code.at(i);
	cout << endl;
}

int main()
{
	huffmanNode huffmanTree[2 * 5 - 1];
	int weight[] = { 35, 25, 15, 15, 10 };

	HuffmanTree(huffmanTree, weight, sizeof(weight) / sizeof(4));
	HuffmanCode(huffmanTree, sizeof(weight) / sizeof(4));

	return 0;
}

输出

5(2,3)
9(4,5)
14(5,9)

即：
_________________________________________
坐标： 0  1  2  3   4   5   6   7   8   9
权重：(2)(4)(5)(3)(-1)(-1)(-1)(-1)(-1)(-1)

                    ||
                    ||
                    \/
                    
                   4(5)
                  /    \
                0(2)   3(3)       
                     
                    ||
                    ||
                    \/
                    
           4(5)           5(9)
          /    \         /    \
        0(2)   3(3)   1(4)    2(5)
                             
                    ||
                    ||
                    \/
                
                  6(14)
                /       \
            4(5)         5(9)
           /   \        /    \
        0(2)   3(3)   1(4)    2(5)

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