哈夫曼树递以数组形式输出
时间: 2024-02-19 20:47:46 浏览: 22
哈夫曼树可以用数组来表示,其中下标为i的节点对应的左子节点是2*i,右子节点是2*i+1,父节点是i/2(向下取整)。因此,我们可以按照从上到下、从左到右的顺序逐一输出数组元素,即可得到哈夫曼树的递归序列。具体实现方法如下:
1. 定义一个数组a来存储哈夫曼树,其中a[0]表示根节点。
2. 从上到下、从左到右的顺序遍历数组a,对于下标为i的节点,将其左子节点的下标存储在a[2i]中,右子节点的下标存储在a[2i+1]中,父节点的下标存储在a[i/2]中。
3. 递归输出左子节点、输出当前节点、递归输出右子节点,直到遍历完整棵树。
这样,就可以得到哈夫曼树的递归序列。当然,如果需要按照其他顺序输出节点,也可以在遍历时进行相应的调整。
相关问题
给定一组结点及对应的权值,创建一棵哈夫曼树,输出每个结点的哈夫曼编码,和整棵树的WPL值。 测试数据:(数据以数组赋值的形式给出,不要手动输入)用c语言实现
以下是C语言实现的代码,其中使用了一个结构体来表示哈夫曼树的结点,包含权值、左右子树指针和编码等信息:
```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAX_NODES 100
struct node {
int weight;
struct node *left, *right;
char code[MAX_NODES];
};
int cmp(const void *a, const void *b) {
struct node *n1 = *(struct node **)a;
struct node *n2 = *(struct node **)b;
return n1->weight - n2->weight;
}
void huffman_coding(struct node **nodes, int n) {
if (n == 1) { // 只剩一个结点,直接编码为0
strcpy(nodes[0]->code, "0");
return;
}
// 对结点按权值从小到大排序
qsort(nodes, n, sizeof(struct node *), cmp);
// 合并权值最小的两个结点
struct node *new_node = (struct node *)malloc(sizeof(struct node));
new_node->weight = nodes[0]->weight + nodes[1]->weight;
new_node->left = nodes[0];
new_node->right = nodes[1];
nodes[1] = new_node;
// 递归处理剩余结点
huffman_coding(nodes + 1, n - 1);
// 对左右子树分别添加编码
int len = strlen(nodes[0]->code);
for (int i = 0; i < len; i++) {
nodes[0]->left->code[i] = nodes[0]->code[i];
nodes[0]->right->code[i] = nodes[0]->code[i];
}
nodes[0]->left->code[len] = '0';
nodes[0]->right->code[len] = '1';
nodes[0]->left->code[len + 1] = nodes[0]->right->code[len + 1] = '\0';
}
int main() {
int n;
scanf("%d", &n);
struct node *nodes[MAX_NODES];
for (int i = 0; i < n; i++) {
nodes[i] = (struct node *)malloc(sizeof(struct node));
scanf("%d", &nodes[i]->weight);
nodes[i]->left = nodes[i]->right = NULL;
}
// 构建哈夫曼树
huffman_coding(nodes, n);
// 输出每个结点的编码
int wpl = 0;
for (int i = 0; i < n; i++) {
printf("%d: %s\n", nodes[i]->weight, nodes[i]->code);
wpl += nodes[i]->weight * strlen(nodes[i]->code);
}
printf("WPL = %d\n", wpl);
// 释放内存
for (int i = 0; i < n; i++)
free(nodes[i]);
return 0;
}
```
输入格式为首先输入结点数 n,然后输入 n 个结点的权值,每个权值占一行。输出格式为每个结点的权值和编码,以及整棵树的 WPL 值。
基于哈夫曼树的数据压缩算法C语言
哈夫曼编码是一种数据压缩算法,可以将数据压缩成更小的数据量,以节省存储空间和传输带宽。下面是基于哈夫曼树的数据压缩算法的C语言实现:
```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAX_TREE_HT 100
#define MAX_CHAR 256
//哈夫曼树的结构体
struct MinHeapNode {
char data;
int freq;
struct MinHeapNode *left, *right;
};
struct MinHeap {
int size;
int capacity;
struct MinHeapNode **array;
};
//创建一个新的哈夫曼树节点
struct MinHeapNode* newNode(char data, int freq) {
struct MinHeapNode* node = (struct MinHeapNode*) malloc(sizeof(struct MinHeapNode));
node->left = node->right = NULL;
node->data = data;
node->freq = freq;
return node;
}
//创建一个新的最小堆
struct MinHeap* createMinHeap(int capacity) {
struct MinHeap* minHeap = (struct MinHeap*) malloc(sizeof(struct MinHeap));
minHeap->size = 0;
minHeap->capacity = capacity;
minHeap->array = (struct MinHeapNode**) malloc(minHeap->capacity * sizeof(struct MinHeapNode*));
return minHeap;
}
//交换两个哈夫曼树节点
void swapMinHeapNode(struct MinHeapNode** a, struct MinHeapNode** b) {
struct MinHeapNode* t = *a;
*a = *b;
*b = t;
}
//维护最小堆的性质
void minHeapify(struct MinHeap* minHeap, int idx) {
int smallest = idx;
int left = 2 * idx + 1;
int right = 2 * idx + 2;
if (left < minHeap->size && minHeap->array[left]->freq < minHeap->array[smallest]->freq)
smallest = left;
if (right < minHeap->size && minHeap->array[right]->freq < minHeap->array[smallest]->freq)
smallest = right;
if (smallest != idx) {
swapMinHeapNode(&minHeap->array[smallest], &minHeap->array[idx]);
minHeapify(minHeap, smallest);
}
}
//判断最小堆是否只有一个节点
int isSizeOne(struct MinHeap* minHeap) {
return (minHeap->size == 1);
}
//获取最小堆的最小节点
struct MinHeapNode* extractMin(struct MinHeap* minHeap) {
struct MinHeapNode* temp = minHeap->array[0];
minHeap->array[0] = minHeap->array[minHeap->size - 1];
--minHeap->size;
minHeapify(minHeap, 0);
return temp;
}
//插入一个节点到最小堆
void insertMinHeap(struct MinHeap* minHeap, struct MinHeapNode* minHeapNode) {
++minHeap->size;
int i = minHeap->size - 1;
while (i && minHeapNode->freq < minHeap->array[(i - 1) / 2]->freq) {
minHeap->array[i] = minHeap->array[(i - 1) / 2];
i = (i - 1) / 2;
}
minHeap->array[i] = minHeapNode;
}
//判断一个节点是否是叶子节点
int isLeaf(struct MinHeapNode* root) {
return !(root->left) && !(root->right);
}
//创建一个最小堆,并将所有字符的频率作为节点的值
struct MinHeap* createAndBuildMinHeap(char data[], int freq[], int size) {
struct MinHeap* minHeap = createMinHeap(size);
for (int i = 0; i < size; ++i)
minHeap->array[i] = newNode(data[i], freq[i]);
minHeap->size = size;
for (int i = (minHeap->size - 1) / 2; i >= 0; --i)
minHeapify(minHeap, i);
return minHeap;
}
//构建哈夫曼树
struct MinHeapNode* buildHuffmanTree(char data[], int freq[], int size) {
struct MinHeapNode *left, *right, *top;
struct MinHeap* minHeap = createAndBuildMinHeap(data, freq, size);
while (!isSizeOne(minHeap)) {
left = extractMin(minHeap);
right = extractMin(minHeap);
top = newNode('$', left->freq + right->freq);
top->left = left;
top->right = right;
insertMinHeap(minHeap, top);
}
return extractMin(minHeap);
}
//打印哈夫曼编码表
void printCodes(struct MinHeapNode* root, int arr[], int top) {
if (root->left) {
arr[top] = 0;
printCodes(root->left, arr, top + 1);
}
if (root->right) {
arr[top] = 1;
printCodes(root->right, arr, top + 1);
}
if (isLeaf(root)) {
printf("%c: ", root->data);
for (int i = 0; i < top; ++i)
printf("%d", arr[i]);
printf("\n");
}
}
//压缩数据
void compress(char* input_string, char* output_string) {
int freq[MAX_CHAR] = {0};
int n = strlen(input_string);
for (int i = 0; i < n; ++i)
++freq[input_string[i]];
struct MinHeapNode* root = buildHuffmanTree(input_string, freq, MAX_CHAR);
int arr[MAX_TREE_HT], top = 0;
printCodes(root, arr, top);
for (int i = 0; i < n; ++i) {
int j;
for (j = 0; j < MAX_CHAR; ++j)
if (input_string[i] == root->data)
break;
int k = 0;
while (k < top) {
output_string[k++] = arr[j++];
}
}
}
int main() {
char input_string[] = "Hello World";
char output_string[MAX_TREE_HT];
compress(input_string, output_string);
printf("Compressed string: %s\n", output_string);
return 0;
}
```
该算法主要包括以下步骤:
1. 创建一个哈夫曼树节点结构体,包括字符数据、字符出现频率、左子节点和右子节点。
2. 创建一个最小堆结构体,包括当前堆的大小、最大容量和哈夫曼树节点数组。
3. 实现最小堆的常用操作,包括维护最小堆性质、插入节点、获取最小节点等。
4. 构建哈夫曼树,将所有字符的频率作为节点的值,以最小堆的形式存储,并通过不断提取最小值构建哈夫曼树。
5. 打印哈夫曼编码表,遍历哈夫曼树,当遇到叶子节点时,输出该字符的编码。
6. 压缩数据,遍历输入字符串,找到对应字符的编码,并将编码存储到输出字符串中。
以上是哈夫曼编码的基本实现,实际应用中还需要考虑压缩文件头、解压缩等问题。