【问题描述】
使用贪心算法编程,求解霍夫曼编码问题
【输入形式】
输入一个字符串
【输出形式】
输出该字符串建成哈夫曼树的最小权重
【样例输入】
ABCBDAB
【样例输出】
13
【样例说明】
该字符串中B的频数为3,A的频数为2,C、D的频数为1,建成哈夫曼树后最小权重为3×1+2×2+1×3+1×3=13
c++代码
#include<iostream>
#include<stdlib.h>
#include<string.h>
#include<stdio.h>
#include<algorithm>
using namespace std;
typedef struct Node
{
char typeChar;
int rate;
Node *leftChild;
Node *rightChild;
}charNode;
//存放输入的字符种类
char *inputStr;
//存放字符节点的数组
Node nodes[200 + 199];
//总的节点数
int total;
//记录当前所处的深度
int depth;
//统计数量
int getNum(char *in, char c)
{
int num = 0;
for (int i = 0; i <= strlen(in); i++)
{
if (*(in + i) == c) num++;
}
return num;
}
//统计输入的字符种类(当时写的这方法不好,个人推荐使用hash存储的方式统计)
int getTypeChar(char *in)
{
inputStr = (char *)malloc(sizeof(char)*200);
memset(inputStr, '\0', sizeof(inputStr));
int p = 0;
bool isAdded;
//cout<<strlen(in)<<endl;
for (int i = 0; i<strlen(in); i++)
{
isAdded = false;
if (p == 0)
{
*inputStr = *in;
nodes[p].typeChar = *inputStr;
nodes[p].rate = getNum(in, *in);
nodes[p].leftChild = NULL; //叶节点
nodes[p].rightChild = NULL; //叶节点
p++;
continue;
}
for (int j = 0; j<p; j++)
{
if (*(inputStr + j) == *(in + i))
{
isAdded = true;
break;
}
}
if (!isAdded)
{
inputStr[p] = *(in + i);
nodes[p].typeChar = *(inputStr + p);
nodes[p].rate = getNum(in, *(in + i));
nodes[p].leftChild = NULL; //叶节点
nodes[p].rightChild = NULL; //叶节点
p++;
}
}
return p;
}
//给排序函数使用的比较函数
bool compNode(const Node & node1, const Node & node2)
{
if (node1.rate <= node2.rate)
{
return true;
}
else
{
return false;
}
}
//哈夫曼编码
void huf(int startIndex, int endIndex, int length)
{
sort(nodes + startIndex, nodes + startIndex + length, compNode);
nodes[endIndex + 1].rate =
nodes[startIndex].rate + nodes[startIndex+1].rate;
nodes[endIndex + 1].leftChild = &nodes[startIndex];
nodes[endIndex + 1].rightChild = &nodes[startIndex+1];
if (endIndex + 1 != total)
{
huf(startIndex + 2, endIndex + 1, length - 1);
}
}
int depthFirst(charNode *);
//遍历哈夫曼树,计算出编编码长度
int getCodeLength(int lastIndex)
{
charNode *root = &nodes[lastIndex];
depth = -1;
return depthFirst(root);
}
//递归遍历
int depthFirst(charNode *node)
{
depth++;
if (node->leftChild == NULL && node->rightChild == NULL)
{
return node->rate * depth;
}
else
{
int leftSize = depthFirst(node->leftChild);
depth--;
int rightSize = depthFirst(node->rightChild);
depth--;
return leftSize + rightSize;
}
}
int main()
{
char *in;
int num; //不同字符的数量
in = (char *)malloc(sizeof(char) * 1000);
while(scanf("%s", in) != EOF)
{
num = getTypeChar(in);
if(num == 1)
{
cout<<strlen(in)<<endl;
continue;
}
total = num * 2 - 1;
huf(0, num - 1, num);
cout<<getCodeLength(total-1)<<endl;
}
return 0;
}