2023-08-03 14:48:10 +08:00
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/**
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* File: array_binary_tree.c
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* Created Time: 2023-07-29
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* Author: Gonglja (glj0@outlook.com)
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*/
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#include "../utils/common.h"
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2023-10-29 00:09:54 +08:00
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/* 数组表示下的二叉树结构体 */
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2023-10-18 02:16:26 +08:00
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typedef struct {
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2023-10-27 23:26:48 +08:00
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int *tree;
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int size;
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} ArrayBinaryTree;
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2023-08-03 14:48:10 +08:00
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2023-10-29 00:09:54 +08:00
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/* 构造函数 */
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2023-10-27 23:26:48 +08:00
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ArrayBinaryTree *createArrayBinaryTree(int *arr, int arrSize) {
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ArrayBinaryTree *abt = (ArrayBinaryTree *)malloc(sizeof(ArrayBinaryTree));
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abt->tree = malloc(sizeof(int) * arrSize);
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memcpy(abt->tree, arr, sizeof(int) * arrSize);
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abt->size = arrSize;
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return abt;
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2023-08-03 14:48:10 +08:00
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}
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/* 节点数量 */
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int size(ArrayBinaryTree *abt) {
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return abt->size;
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}
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/* 获取索引为 i 节点的值 */
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int val(ArrayBinaryTree *abt, int i) {
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// 若索引越界,则返回 INT_MAX ,代表空位
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if (i < 0 || i >= size(abt))
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return INT_MAX;
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return abt->tree[i];
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}
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/* 获取索引为 i 节点的左子节点的索引 */
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int left(int i) {
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return 2 * i + 1;
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}
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/* 获取索引为 i 节点的右子节点的索引 */
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int right(int i) {
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return 2 * i + 2;
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}
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/* 获取索引为 i 节点的父节点的索引 */
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int parent(int i) {
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return (i - 1) / 2;
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}
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2023-10-27 23:26:48 +08:00
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/* 层序遍历 */
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int *levelOrder(ArrayBinaryTree *abt, int *returnSize) {
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int *res = (int *)malloc(sizeof(int) * size(abt));
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int index = 0;
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// 直接遍历数组
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for (int i = 0; i < size(abt); i++) {
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if (val(abt, i) != INT_MAX)
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res[index++] = val(abt, i);
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}
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*returnSize = index;
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return res;
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}
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/* 深度优先遍历 */
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void dfs(ArrayBinaryTree *abt, int i, char *order, int *res, int *index) {
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// 若为空位,则返回
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if (val(abt, i) == INT_MAX)
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return;
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// 前序遍历
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if (strcmp(order, "pre") == 0)
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res[(*index)++] = val(abt, i);
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dfs(abt, left(i), order, res, index);
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// 中序遍历
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if (strcmp(order, "in") == 0)
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res[(*index)++] = val(abt, i);
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dfs(abt, right(i), order, res, index);
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// 后序遍历
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if (strcmp(order, "post") == 0)
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res[(*index)++] = val(abt, i);
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}
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/* 前序遍历 */
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int *preOrder(ArrayBinaryTree *abt, int *returnSize) {
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int *res = (int *)malloc(sizeof(int) * size(abt));
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int index = 0;
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dfs(abt, 0, "pre", res, &index);
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*returnSize = index;
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2023-08-03 14:48:10 +08:00
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return res;
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}
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/* 中序遍历 */
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int *inOrder(ArrayBinaryTree *abt, int *returnSize) {
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int *res = (int *)malloc(sizeof(int) * size(abt));
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int index = 0;
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dfs(abt, 0, "in", res, &index);
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*returnSize = index;
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return res;
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}
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/* 后序遍历 */
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int *postOrder(ArrayBinaryTree *abt, int *returnSize) {
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int *res = (int *)malloc(sizeof(int) * size(abt));
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int index = 0;
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dfs(abt, 0, "post", res, &index);
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*returnSize = index;
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return res;
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}
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/* Driver Code */
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int main() {
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// 初始化二叉树
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// 使用 INT_MAX 代表空位 NULL
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int arr[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};
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int arrSize = sizeof(arr) / sizeof(arr[0]);
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TreeNode *root = arrayToTree(arr, arrSize);
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printf("\n初始化二叉树\n");
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printf("二叉树的数组表示:\n");
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printArray(arr, arrSize);
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printf("二叉树的链表表示:\n");
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printTree(root);
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ArrayBinaryTree *abt = createArrayBinaryTree(arr, arrSize);
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// 访问节点
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int i = 1;
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int l = left(i), r = right(i), p = parent(i);
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printf("\n当前节点的索引为 %d,值为 %d\n", i, val(abt, i));
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printf("其左子节点的索引为 %d,值为 %d\n", l, l < arrSize ? val(abt, l) : INT_MAX);
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printf("其右子节点的索引为 %d,值为 %d\n", r, r < arrSize ? val(abt, r) : INT_MAX);
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printf("其父节点的索引为 %d,值为 %d\n", p, p < arrSize ? val(abt, p) : INT_MAX);
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// 遍历树
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int returnSize;
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int *res;
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res = levelOrder(abt, &returnSize);
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printf("\n层序遍历为: ");
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printArray(res, returnSize);
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free(res);
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res = preOrder(abt, &returnSize);
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printf("前序遍历为: ");
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printArray(res, returnSize);
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free(res);
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res = inOrder(abt, &returnSize);
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printf("中序遍历为: ");
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printArray(res, returnSize);
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free(res);
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res = postOrder(abt, &returnSize);
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printf("后序遍历为: ");
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printArray(res, returnSize);
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free(res);
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// 释放内存
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freeMemoryTree(root);
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free(abt);
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2023-08-03 14:48:10 +08:00
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return 0;
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}
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