Add array_binary_tree.c and update push_back and pop_back in vector.h (#664)

* fix(codes/cpp): Memory leak fix: the space was not freed when pop removed the element.

* fix(codes/cpp): Fix access error when printArray(arr, 0)

* Update PrintUtil.hpp

* fix(codes/c): Fix some errors of cmake build

* feat(codes/c): Add hashing_search.c

* styles(codes/c): Modify function description

* styles(codes/c): Modify binary_search.c code style

* fix(codes/c): Fix the problem in binary_tree_bfs.c and the problem that the memory is not released.

* feat: Add preorder_traversal_i_compact.c

* feat(codes/c): Add head_sort.c

* feat(codes/c): Add bucket_sort.c

* feat(codes/c): Add binary_search_edge.c

* fix(codes/c): Add programs that are not managed by cmake (c code)

* feat(codes/c): Add selection_sort.c

* style(codes/c): Change swap in selection_sort.c to `selectionSort`

* styles(codes/c): Change style.

* fix(codes/c): Fix some formatting errors and temporarily remove backtracking chapters

* fix(codes/c): Fix space_complexity.c build error.

* feat(codes/c): Add array_binary_tree.c

* feat(code/c): Update push_back and pop_back in vector.h

* styles(codes/c): Adjust  format.

---------

Co-authored-by: Yudong Jin <krahets@163.com>

codes/c/chapter_tree/array_binary_tree.c

@@ -0,0 +1,159 @@
+/**
+ * File: array_binary_tree.c
+ * Created Time: 2023-07-29
+ * Author: Gonglja (glj0@outlook.com)
+ */
+
+#include "../utils/common.h"
+
+struct arrayBinaryTree {
+    vector *tree;
+};
+
+typedef struct arrayBinaryTree arrayBinaryTree;
+
+arrayBinaryTree *newArrayBinaryTree(vector *arr) {
+    arrayBinaryTree *newABT = malloc(sizeof(arrayBinaryTree));
+    newABT->tree = arr;
+    return newABT;
+}
+
+/* 节点数量 */
+int size(arrayBinaryTree *abt) {
+    return abt->tree->size;
+}
+
+/* 获取索引为 i 节点的值 */
+int val(arrayBinaryTree *abt, int i) {
+    // 若索引越界，则返回 INT_MAX ，代表空位
+    if (i < 0 || i >= size(abt))
+        return INT_MAX;
+    return *(int *)abt->tree->data[i];
+}
+
+/* 获取索引为 i 节点的左子节点的索引 */
+int left(int i) {
+    return 2 * i + 1;
+}
+
+/* 获取索引为 i 节点的右子节点的索引 */
+int right(int i) {
+    return 2 * i + 2;
+}
+
+/* 获取索引为 i 节点的父节点的索引 */
+int parent(int i) {
+    return (i - 1) / 2;
+}
+
+/* 深度优先遍历 */
+void dfs(arrayBinaryTree *abt, int i, const char *order, vector *res) {
+    // 若为空位，则返回
+    if (val(abt, i) == INT_MAX)
+        return;
+    // 前序遍历
+    if (strcmp(order, "pre") == 0) {
+        int tmp = val(abt, i);
+        vectorPushback(res, &tmp, sizeof(tmp));
+    }
+    dfs(abt, left(i), order, res);
+    // 中序遍历
+    if (strcmp(order, "in") == 0) {
+        int tmp = val(abt, i);
+        vectorPushback(res, &tmp, sizeof(tmp));
+    }
+    dfs(abt, right(i), order, res);
+    // 后序遍历
+    if (strcmp(order, "post") == 0) {
+        int tmp = val(abt, i);
+        vectorPushback(res, &tmp, sizeof(tmp));
+    }
+}
+
+/* 层序遍历 */
+vector *levelOrder(arrayBinaryTree *abt) {
+    vector *res = newVector();
+    // 直接遍历数组
+    for (int i = 0; i < size(abt); i++) {
+        if (val(abt, i) != INT_MAX) {
+            int tmp = val(abt, i);
+            vectorPushback(res, &tmp, sizeof(int));
+        }
+    }
+    return res;
+}
+
+/* 前序遍历 */
+vector *preOrder(arrayBinaryTree *abt) {
+    vector *res = newVector();
+    dfs(abt, 0, "pre", res);
+    return res;
+}
+
+/* 中序遍历 */
+vector *inOrder(arrayBinaryTree *abt) {
+    vector *res = newVector();
+    dfs(abt, 0, "in", res);
+    return res;
+}
+
+/* 后序遍历 */
+vector *postOrder(arrayBinaryTree *abt) {
+    vector *res = newVector();
+    dfs(abt, 0, "post", res);
+    return res;
+}
+
+/* 打印向量中的元素 */
+void printFunc(vector *v, void *p) {
+    int *val = p;
+    printf("%d", *val);
+}
+
+/* Driver Code */
+int main() {
+    // 初始化二叉树
+    // 使用 INT_MAX 代表空位 nullptr
+    int arr[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};
+    TreeNode *root = arrToTree(arr, sizeof(arr) / sizeof(arr[0]));
+    printf("\n初始化二叉树\n");
+    printf("二叉树的数组表示：\n");
+    printArray(arr, sizeof(arr) / sizeof(arr[0]));
+    printf("二叉树的链表表示：\n");
+    printTree(root);
+
+    vector *vArr = newVector();
+    for (int i = 0; i < sizeof(arr) / sizeof(arr[0]); i++) {
+        vectorPushback(vArr, &arr[i], sizeof(int));
+    }
+    // 数组表示下的二叉树类
+    arrayBinaryTree *abt = newArrayBinaryTree(vArr);
+
+    // 访问节点
+    int i = 1;
+    int l = left(i), r = right(i), p = parent(i);
+    printf("\n当前节点的索引为 %d，值为 %d\n", i, val(abt, i));
+    printf("其左子节点的索引为 %d，值为 %d\r\n", l, val(abt, l));
+    printf("其右子节点的索引为 %d，值为 %d\r\n", r, val(abt, r));
+    printf("其父节点的索引为 %d，值为 %d\r\n", p, val(abt, p));
+
+    // 遍历树
+    vector *res = levelOrder(abt);
+    printf("\n层序遍历为： ");
+    printVector(res, printFunc);
+    delVector(res);
+    res = preOrder(abt);
+    printf("前序遍历为： ");
+    printVector(res, printFunc);
+    delVector(res);
+    res = inOrder(abt);
+    printf("中序遍历为： ");
+    printVector(res, printFunc);
+    delVector(res);
+    res = postOrder(abt);
+    printf("后序遍历为： ");
+    printVector(res, printFunc);
+    delVector(res);
+
+    return 0;
+}