用c语言编写费诺编码

Fano编码是一种用于数据压缩的无损编码方法，它利用了字符集中某些字符出现频率较高的特性。在C语言中编写Fano编码的基本步骤包括：

1. **预处理阶段**：
- 创建一个字符频率表，统计给定文本中每个字符的出现次数。

   #include <stdio.h>
   int freq[256] = {0}; // 初始化一个大小为ASCII码范围的数组

2. **构建Fano树**：
- 对于最常见的字符，创建叶子节点；对于其他字符，根据其频率将其插入到适当位置，形成Fano树结构。
- C语言可以递归地遍历字符数组并更新Fano树。

3. **编码过程**：
- 比较当前字符和前一个字符的频率，根据Fano树的关系生成二进制编码。

   for (int i = 0; i < strlen(text); ++i) {
       if (freq[text[i]] == freq[text[i - 1]]) continue;
       // 根据Fano树规则生成编码
   }

4. **解码过程**：
- 接收编码后的二进制串，并根据Fano树规则回溯到原始字符。

请注意，实际的Fano编码算法需要考虑如何存储树结构以及优化编码长度。这里给出的是一个简化的示例，完整的实现会更复杂一些。在编码过程中，你需要根据字符频率动态调整编码规则。

相关问题

用C语言分别利用香农-费诺编码、霍夫曼编码、LZ编码、算术编码实现数据压缩

以下是分别利用C语言实现数据压缩的示例代码：

1. 香农-费诺编码

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef struct node {
    char ch;
    int freq;
    struct node *left, *right;
} Node;

typedef struct heap {
    int size;
    int capacity;
    Node **arr;
} Heap;

Node* new_node(char ch, int freq) {
    Node* temp = (Node*) malloc(sizeof(Node));
    temp->ch = ch;
    temp->freq = freq;
    temp->left = temp->right = NULL;
    return temp;
}

Heap* create_heap(int capacity) {
    Heap* heap = (Heap*) malloc(sizeof(Heap));
    heap->size = 0;
    heap->capacity = capacity;
    heap->arr = (Node**) malloc(capacity * sizeof(Node*));
    return heap;
}

void swap_node(Node **a, Node **b) {
    Node* temp = *a;
    *a = *b;
    *b = temp;
}

void min_heapify(Heap *heap, int idx) {
    int smallest = idx;
    int left = 2 * idx + 1;
    int right = 2 * idx + 2;
    if (left < heap->size && heap->arr[left]->freq < heap->arr[smallest]->freq) {
        smallest = left;
    }
    if (right < heap->size && heap->arr[right]->freq < heap->arr[smallest]->freq) {
        smallest = right;
    }
    if (smallest != idx) {
        swap_node(&heap->arr[idx], &heap->arr[smallest]);
        min_heapify(heap, smallest);
    }
}

int is_leaf_node(Node* node) {
    return !(node->left) && !(node->right);
}

Heap* build_heap(char *str, int *freq) {
    Heap* heap = create_heap(strlen(str));
    for (int i = 0; i < strlen(str); i++) {
        heap->arr[i] = new_node(str[i], freq[i]);
        heap->size++;
    }
    for (int i = heap->size / 2 - 1; i >= 0; i--) {
        min_heapify(heap, i);
    }
    return heap;
}

Node* build_huffman_tree(char *str, int *freq) {
    Heap* heap = build_heap(str, freq);
    while (heap->size != 1) {
        Node *left = heap->arr[0];
        swap_node(&heap->arr[0], &heap->arr[heap->size - 1]);
        heap->size--;
        min_heapify(heap, 0);
        Node *right = heap->arr[0];
        swap_node(&heap->arr[0], &heap->arr[heap->size - 1]);
        heap->size--;
        min_heapify(heap, 0);
        Node *parent = new_node('#', left->freq + right->freq);
        parent->left = left;
        parent->right = right;
        heap->arr[heap->size] = parent;
        heap->size++;
        min_heapify(heap, heap->size - 1);
    }
    return heap->arr[0];
}

void print_codes(Node *root, int arr[], int top) {
    if (root->left) {
        arr[top] = 0;
        print_codes(root->left, arr, top + 1);
    }
    if (root->right) {
        arr[top] = 1;
        print_codes(root->right, arr, top + 1);
    }
    if (is_leaf_node(root)) {
        printf("%c: ", root->ch);
        for (int i = 0; i < top; i++) {
            printf("%d", arr[i]);
        }
        printf("\n");
    }
}

void huffman_encoding(char *str, int *freq) {
    Node *root = build_huffman_tree(str, freq);
    int arr[100], top = 0;
    print_codes(root, arr, top);
}

int main() {
    char str[] = "Hello, World!";
    int freq[256] = {0};
    for (int i = 0; i < strlen(str); i++) {
        freq[(int) str[i]]++;
    }
    huffman_encoding(str, freq);
    return 0;
}

2. 霍夫曼编码

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define MAX_TREE_HT 100

typedef struct node {
    char ch;
    int freq;
    struct node *left, *right;
} Node;

typedef struct heap {
    int size;
    int capacity;
    Node **arr;
} Heap;

Node* new_node(char ch, int freq) {
    Node* temp = (Node*) malloc(sizeof(Node));
    temp->ch = ch;
    temp->freq = freq;
    temp->left = temp->right = NULL;
    return temp;
}

Heap* create_heap(int capacity) {
    Heap* heap = (Heap*) malloc(sizeof(Heap));
    heap->size = 0;
    heap->capacity = capacity;
    heap->arr = (Node**) malloc(capacity * sizeof(Node*));
    return heap;
}

void swap_node(Node **a, Node **b) {
    Node* temp = *a;
    *a = *b;
    *b = temp;
}

void min_heapify(Heap *heap, int idx) {
    int smallest = idx;
    int left = 2 * idx + 1;
    int right = 2 * idx + 2;
    if (left < heap->size && heap->arr[left]->freq < heap->arr[smallest]->freq) {
        smallest = left;
    }
    if (right < heap->size && heap->arr[right]->freq < heap->arr[smallest]->freq) {
        smallest = right;
    }
    if (smallest != idx) {
        swap_node(&heap->arr[idx], &heap->arr[smallest]);
        min_heapify(heap, smallest);
    }
}

int is_leaf_node(Node* node) {
    return !(node->left) && !(node->right);
}

Heap* build_heap(char *str, int *freq) {
    Heap* heap = create_heap(strlen(str));
    for (int i = 0; i < strlen(str); i++) {
        heap->arr[i] = new_node(str[i], freq[i]);
        heap->size++;
    }
    for (int i = heap->size / 2 - 1; i >= 0; i--) {
        min_heapify(heap, i);
    }
    return heap;
}

Node* build_huffman_tree(char *str, int *freq) {
    Heap* heap = build_heap(str, freq);
    while (heap->size != 1) {
        Node *left = heap->arr[0];
        swap_node(&heap->arr[0], &heap->arr[heap->size - 1]);
        heap->size--;
        min_heapify(heap, 0);
        Node *right = heap->arr[0];
        swap_node(&heap->arr[0], &heap->arr[heap->size - 1]);
        heap->size--;
        min_heapify(heap, 0);
        Node *parent = new_node('#', left->freq + right->freq);
        parent->left = left;
        parent->right = right;
        heap->arr[heap->size] = parent;
        heap->size++;
        min_heapify(heap, heap->size - 1);
    }
    return heap->arr[0];
}

void print_codes(Node *root, int arr[], int top) {
    if (root->left) {
        arr[top] = 0;
        print_codes(root->left, arr, top + 1);
    }
    if (root->right) {
        arr[top] = 1;
        print_codes(root->right, arr, top + 1);
    }
    if (is_leaf_node(root)) {
        printf("%c: ", root->ch);
        for (int i = 0; i < top; i++) {
            printf("%d", arr[i]);
        }
        printf("\n");
    }
}

void huffman_encoding(char *str, int *freq) {
    Node *root = build_huffman_tree(str, freq);
    int arr[MAX_TREE_HT], top = 0;
    print_codes(root, arr, top);
}

void huffman_decoding(Node *root, char *str) {
    FILE *output_file = fopen("output.txt", "w");
    Node *curr = root;
    for (int i = 0; i < strlen(str); i++) {
        if (str[i] == '0') {
            curr = curr->left;
        } else {
            curr = curr->right;
        }
        if (is_leaf_node(curr)) {
            fprintf(output_file, "%c", curr->ch);
            curr = root;
        }
    }
    fclose(output_file);
}

int main() {
    char str[] = "Hello, World!";
    int freq[256] = {0};
    for (int i = 0; i < strlen(str); i++) {
        freq[(int) str[i]]++;
    }
    Node *root = build_huffman_tree(str, freq);
    huffman_encoding(str, freq);
    FILE *input_file = fopen("output.txt", "r");
    fseek(input_file, 0, SEEK_END);
    long input_file_size = ftell(input_file);
    rewind(input_file);
    char *input_str = (char*) malloc((input_file_size + 1) * sizeof(char));
    fread(input_str, sizeof(char), input_file_size, input_file);
    input_str[input_file_size] = '\0';
    fclose(input_file);
    huffman_decoding(root, input_str);
    free(input_str);
    return 0;
}

3. LZ编码

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef struct {
    int id;
    int offset;
    int length;
} Tuple;

int find_match(char *str, int i, int j) {
    int k = 0;
    while (str[i + k] == str[j + k] && str[i + k] != '\0' && str[j + k] != '\0' && k < 255) {
        k++;
    }
    return k;
}

Tuple* lz_encoding(char *str) {
    Tuple *result = (Tuple*) malloc(strlen(str) * sizeof(Tuple));
    int result_idx = 0, i = 0;
    while (i < strlen(str)) {
        int max_length = 0, max_offset = 0;
        for (int j = i - 1; j >= 0 && j >= i - 255; j--) {
            int length = find_match(str, i, j);
            if (length > max_length) {
                max_length = length;
                max_offset = i - j - length;
            }
        }
        if (max_length > 0) {
            result[result_idx].id = -1;
            result[result_idx].offset = max_offset;
            result[result_idx].length = max_length;
            result_idx++;
            i += max_length;
        } else {
            result[result_idx].id = (int) str[i];
            result[result_idx].offset = -1;
            result[result_idx].length = -1;
            result_idx++;
            i++;
        }
    }
    result[result_idx].id = -2;
    result[result_idx].offset = -2;
    result[result_idx].length = -2;
    return result;
}

void lz_decoding(Tuple *result) {
    FILE *output_file = fopen("output.txt", "w");
    int i = 0;
    while (result[i].id != -2) {
        if (result[i].id == -1) {
            int j = 0;
            while (j < result[i].length) {
                char ch = fgetc(output_file - result[i].offset - 1);
                fprintf(output_file, "%c", ch);
                j++;
            }
        } else {
            fprintf(output_file, "%c", (char) result[i].id);
        }
        i++;
    }
    fclose(output_file);
}

int main() {
    char str[] = "Hello, World!";
    Tuple *result = lz_encoding(str);
    lz_decoding(result);
    free(result);
    return 0;
}

4. 算术编码

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef struct {
    int start;
    int end;
} Range;

Range new_range(int start, int end) {
    Range r;
    r.start = start;
    r.end = end;
    return r;
}

void arithmetic_encoding(char *str, int *freq) {
    int total_freq = 0;
    for (int i = 0; i < 256; i++) {
        total_freq += freq[i];
    }
    Range r = new_range(0, total_freq);
    for (int i = 0; i < strlen(str); i++) {
        int ch = (int) str[i];
        int freq_sum = 0;
        for (int j = 0; j < ch; j++) {
            freq_sum += freq[j];
        }
        Range new_r = new_range(r.start + freq_sum * (r.end - r.start) / total_freq, r.start + (freq_sum + freq[ch]) * (r.end - r.start) / total_freq);
        r = new_r;
    }
    int code = (r.start + r.end) / 2;
    printf("Arithmetic code: %d\n", code);
}

void arithmetic_decoding(int code, char *str, int *freq) {
    int total_freq = 0;
    for (int i = 0; i < 256; i++) {
        total_freq += freq[i];
    }
    Range r = new_range(0, total_freq);
    for (int i = strlen(str) - 1; i >= 0; i--) {
        int ch = (int) str[i];
        int freq_sum = 0;
        for (int j = 0; j < ch; j++) {
            freq_sum += freq[j];
        }
        Range new_r = new_range(r.start + freq_sum * (r.end - r.start) / total_freq, r.start + (freq_sum + freq[ch]) * (r.end - r.start) / total_freq);
        if (code >= new_r.start && code < new_r.end) {
            printf("%c", (char) ch);
            r = new_r;
            code = (code - r.start) * total_freq / (r.end - r.start);
        }
    }
}

int main() {
    char str[] = "Hello, World!";
    int freq[256] = {0};
    for (int i = 0; i < strlen(str); i++) {
        freq[(int) str[i]]++;
    }
    arithmetic_encoding(str, freq);
    arithmetic_decoding(2192935, str, freq);
    return 0;
}

费诺编码matlab

以下是用Matlab实现的费诺编码代码：

function [code, dict] = huffmanenco(source, prob)
% source: 待编码的源信号
% prob: 源信号中每个符号出现的概率

[~, dict] = huffmandict(1:length(prob), prob); % 生成哈夫曼码字典
code = huffmanenco(source, dict); % 对源信号进行编码

使用示例：

source = [1 2 3 4 5 6];
prob = [0.1 0.2 0.15 0.05 0.3 0.2];
[code, dict] = huffmanenco(source, prob);

其中，source是待编码的源信号，prob是源信号中每个符号出现的概率。函数返回的code是编码后的结果，dict是生成的哈夫曼码字典。