贪心算法-霍夫曼编码

character   Frequency
    a            5
    b           9
    c           12
    d           13
    e           16
    f           45

character           Frequency
       c               12
       d               13
     内部 节点           14
       e               16
       f               45

character      Frequency
 内部节点         100

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

#define MAX_TREE_HT 100

// 一个霍夫曼树节点
struct MinHeapNode
{
    char data;  // 输入的字符数组中的一个字符
    unsigned freq;  // 字符出现的次数
    struct MinHeapNode *left, *right; 
};

// 最小堆: 作为优先队列使用
struct MinHeap
{
    unsigned size;    // 最小堆元素的个数
    unsigned capacity;   //最大容量
    struct MinHeapNode **array;  
};

//初始化一个最小堆节点
struct MinHeapNode* newNode(char data, unsigned freq)
{
    struct MinHeapNode* temp =
          (struct MinHeapNode*) malloc(sizeof(struct MinHeapNode));
    temp->left = temp->right = NULL;
    temp->data = data;
    temp->freq = freq;
    return temp;
}

// 创建一个容量为capacity 的最小堆
struct MinHeap* createMinHeap(unsigned capacity)
{
    struct MinHeap* minHeap =
         (struct MinHeap*) malloc(sizeof(struct MinHeap));
    minHeap->size = 0;  // current size is 0
    minHeap->capacity = capacity;
    minHeap->array =
     (struct MinHeapNode**)malloc(minHeap->capacity * sizeof(struct MinHeapNode*));
    return minHeap;
}

//  swap 两个堆节点
void swapMinHeapNode(struct MinHeapNode** a, struct MinHeapNode** b)
{
    struct MinHeapNode* t = *a;
    *a = *b;
    *b = t;
}

// 更新最小堆.
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);
    }
}

//检测堆的大小是否为1
int isSizeOne(struct MinHeap* minHeap)
{
    return (minHeap->size == 1);
}

//取得堆中最小的节点
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;
}

// 想最小堆中插入一个节点
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;
}

//构建一个最小堆
void buildMinHeap(struct MinHeap* minHeap)
{
    int n = minHeap->size - 1;
    int i;
    for (i = (n - 1) / 2; i >= 0; --i)
        minHeapify(minHeap, i);
}

void printArr(int arr[], int n)
{
    int i;
    for (i = 0; i < n; ++i)
        printf("%d", arr[i]);
    printf("\n");
}

// 检测是否是叶子节点
int isLeaf(struct MinHeapNode* root)
{
    return !(root->left) && !(root->right) ;
}

// 创建一个容量为 size的最小堆，并插入 data[] 中的元素到最小堆
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;
    buildMinHeap(minHeap);
    return minHeap;
}

// 构建霍夫曼树
struct MinHeapNode* buildHuffmanTree(char data[], int freq[], int size)
{
    struct MinHeapNode *left, *right, *top;

    // 第 1步 : 创建最小堆.  
    struct MinHeap* minHeap = createAndBuildMinHeap(data, freq, size);

    //知道最小堆只有一个元素
    while (!isSizeOne(minHeap))
    {
        // 第二步: 取到最小的两个元素
        left = extractMin(minHeap);
        right = extractMin(minHeap);

        // Step 3: 根据两个最小的节点，来创建一个新的内部节点
        // ‘$‘ 只是对内部节点的一个特殊标记，没有使用
        top = newNode(‘$‘, left->freq + right->freq);
        top->left = left;
        top->right = right;
        insertMinHeap(minHeap, top);
    }

    // 第4步: 最后剩下的一个节点即为跟节点
    return extractMin(minHeap);
}

// 打印霍夫曼编码
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);
    }

    // 如果是叶子节点就打印
    if (isLeaf(root))
    {
        printf("%c: ", root->data);
        printArr(arr, top);
    }
}

// 构建霍夫曼树，并遍历打印该霍夫曼树
void HuffmanCodes(char data[], int freq[], int size)
{
   //  构建霍夫曼树
   struct MinHeapNode* root = buildHuffmanTree(data, freq, size);

   // 打印构建好的霍夫曼树
   int arr[MAX_TREE_HT], top = 0;
   printCodes(root, arr, top);
}

// 测试
int main()
{
    char arr[] = {‘a‘, ‘b‘, ‘c‘, ‘d‘, ‘e‘, ‘f‘};
    int freq[] = {5, 9, 12, 13, 16, 45};
    int size = sizeof(arr)/sizeof(arr[0]);
    HuffmanCodes(arr, freq, size);
    return 0;
}

f: 0
c: 100
d: 101
a: 1100
b: 1101
e: 111