#include <stdio.h>
#include <stdlib.h>
// 定义哈夫曼树的节点结构
typedef struct HuffmanNode {
int weight;
struct HuffmanNode *left;
struct HuffmanNode *right;
} HuffmanNode;
// 创建一个新的哈夫曼树节点
HuffmanNode* createNode(int weight) {
HuffmanNode* newNode = (HuffmanNode*)malloc(sizeof(HuffmanNode));
newNode->weight = weight;
newNode->left = NULL;
newNode->right = NULL;
return newNode;
}
// 优先队列的比较函数,用于排序
int compare(const void* a, const void* b) {
return (*(HuffmanNode**)a)->weight - (*(HuffmanNode**)b)->weight;
}
// 创建哈夫曼树并计算带权路径长度
int createHuffmanTree(int weights[], int n) {
HuffmanNode* nodes[10]; // 哈夫曼树节点数组,最多10个节点
// 将每个权值转换为单独的树节点
for (int i = 0; i < n; i++) {
nodes[i] = createNode(weights[i]);
}
// 循环直到只剩下一棵树
while (n > 1) {
// 排序节点数组,按权值升序
qsort(nodes, n, sizeof(HuffmanNode*), compare);
// 选择权值最小的两个节点
HuffmanNode* left = nodes[0];
HuffmanNode* right = nodes[1];
// 创建一个新节点,其权值为两个子节点权值之和
HuffmanNode* newNode = createNode(left->weight + right->weight);
newNode->left = left;
newNode->right = right;
// 替换节点数组,将新节点放入,并减少节点总数
nodes[0] = newNode;
nodes[1] = nodes[n - 1];
n--;
}
// 计算带权路径长度
int totalWeight = 0;
int currentDepth = 0;
// 递归计算带权路径长度
void calculateWeightedPathLength(HuffmanNode* root, int depth) {
if (root->left == NULL && root->right == NULL) {
totalWeight += root->weight * depth;
return;
}
if (root->left != NULL) {
calculateWeightedPathLength(root->left, depth + 1);
}
if (root->right != NULL) {
calculateWeightedPathLength(root->right, depth + 1);
}
}
calculateWeightedPathLength(nodes[0], currentDepth);
// 释放哈夫曼树节点的内存
void freeTree(HuffmanNode* root)
{
if (root == NULL) return;
freeTree(root->left);
freeTree(root->right);
free(root);
}
freeTree(nodes[0]);
return totalWeight;
}
int main() {
int n;
// 读取正整数的个数
scanf("%d", &n);
int weights[10];
// 读取正整数
for (int i = 0; i < n; i++) {
scanf("%d", &weights[i]);
}
// 创建哈夫曼树并计算带权路径长度
int result = createHuffmanTree(weights, n);
// 输出结果
printf("%d\n", result);
return 0;
}
求节点的哈夫曼的带权路径长度
最新推荐文章于 2025-12-02 15:32:05 发布
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