【PTA数据结构 | C语言版】创建哈夫曼树

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文章目录

• • 题目
  • 代码

题目

请编写程序，根据给定的权重值序列，构建哈夫曼树，并计算带权路径长度。

输入格式：

输入首先给出一个不超 20 的正整数 n，随后一行给出 n 个权重值。其中权重值都是不超过 100 的正整数。

输出格式：

在一行中输出哈夫曼树的带权路径长度。

输入样例：

5

1 2 3 4 5

输出样例：

33

代码

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

typedef struct HuffmanNode {
    int weight;
    struct HuffmanNode *left, *right;
} HuffmanNode;

typedef struct {
    HuffmanNode **array;
    int size;
    int capacity;
} MinHeap;

// 创建新节点
HuffmanNode* newNode(int weight) {
    HuffmanNode* node = (HuffmanNode*)malloc(sizeof(HuffmanNode));
    node->weight = weight;
    node->left = node->right = NULL;
    return node;
}

// 创建最小堆
MinHeap* createMinHeap(int capacity) {
    MinHeap* minHeap = (MinHeap*)malloc(sizeof(MinHeap));
    minHeap->size = 0;
    minHeap->capacity = capacity;
    minHeap->array = (HuffmanNode**)malloc(capacity * sizeof(HuffmanNode*));
    return minHeap;
}

// 交换两个节点
void swapHuffmanNode(HuffmanNode** a, HuffmanNode** b) {
    HuffmanNode* t = *a;
    *a = *b;
    *b = t;
}

// 最小堆化
void minHeapify(MinHeap* minHeap, int idx) {
    int smallest = idx;
    int left = 2 * idx + 1;
    int right = 2 * idx + 2;

    if (left < minHeap->size && minHeap->array[left]->weight < minHeap->array[smallest]->weight)
        smallest = left;

    if (right < minHeap->size && minHeap->array[right]->weight < minHeap->array[smallest]->weight)
        smallest = right;

    if (smallest != idx) {
        swapHuffmanNode(&minHeap->array[smallest], &minHeap->array[idx]);
        minHeapify(minHeap, smallest);
    }
}

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

// 提取最小值
HuffmanNode* extractMin(MinHeap* minHeap) {
    HuffmanNode* temp = minHeap->array[0];
    minHeap->array[0] = minHeap->array[minHeap->size - 1];
    --minHeap->size;
    minHeapify(minHeap, 0);
    return temp;
}

// 插入新节点
void insertMinHeap(MinHeap* minHeap, HuffmanNode* node) {
    ++minHeap->size;
    int i = minHeap->size - 1;
    while (i && node->weight < minHeap->array[(i - 1) / 2]->weight) {
        minHeap->array[i] = minHeap->array[(i - 1) / 2];
        i = (i - 1) / 2;
    }
    minHeap->array[i] = node;
}

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

// 判断是否是叶子节点
int isLeaf(HuffmanNode* root) {
    return !(root->left) && !(root->right);
}

// 创建并构建最小堆
MinHeap* createAndBuildMinHeap(int weights[], int size) {
    MinHeap* minHeap = createMinHeap(size);
    for (int i = 0; i < size; ++i)
        minHeap->array[i] = newNode(weights[i]);
    minHeap->size = size;
    buildMinHeap(minHeap);
    return minHeap;
}

// 构建哈夫曼树
HuffmanNode* buildHuffmanTree(int weights[], int size) {
    HuffmanNode *left, *right, *top;
    MinHeap* minHeap = createAndBuildMinHeap(weights, size);

    while (!isSizeOne(minHeap)) {
        left = extractMin(minHeap);
        right = extractMin(minHeap);
        top = newNode(left->weight + right->weight);
        top->left = left;
        top->right = right;
        insertMinHeap(minHeap, top);
    }
    return extractMin(minHeap);
}

// 计算带权路径长度
int calculateWPL(HuffmanNode* root, int depth) {
    if (root == NULL) return 0;
    if (isLeaf(root)) return root->weight * depth;
    return calculateWPL(root->left, depth + 1) + calculateWPL(root->right, depth + 1);
}

int main() {
    int n;
    scanf("%d", &n);
    int weights[20];
    for (int i = 0; i < n; i++) {
        scanf("%d", &weights[i]);
    }

    HuffmanNode* root = buildHuffmanTree(weights, n);
    int wpl = calculateWPL(root, 0);
    printf("%d\n", wpl);
    
    return 0;
}