树和二叉树

Posted 2020-10-10

二叉树的定义如下：树要么为空，要么由根结点、左子树、右子树组成，而左子树和右子树分别是一颗二叉树。注意，在计算机中，树一般是“倒置”的，即根在上，叶子在下。

而树的定义比二叉树区别在于有很多的子树。

但是不管是二叉树还是树，每个非根结点都有一个父节点。

简单的二叉树实现代码（C++）

struct Tree {
    int data;
    struct Tree *left;
    struct Tree *right;
};

 

二叉树深度的求法可以用简单的递归就可以实现

int maxDepth(Tree *root) {
    if(!root) return 0;
    int leftDepth = maxDepth(root -> left) + 1;
    int rightDepth = maxDepth(root -> right) + 1;
    return leftDepth >= rightDepth?leftDepth:rightDepth;
}

 

二叉树的三种遍历方式：

前序、中序、后序

前序遍历：根节点->左子树->右子树

中序遍历：左子树->根节点->右子树

后序遍历：左子树->右子树->根节点

递归实现如下

void preorder_print(Tree *tree) {
    if(tree){
        std::cout << tree -> data;
        preorder_dev(tree -> left);
        preorder_dev(tree -> right);
    }
}

void inorder_print(Tree * tree) {
    if(tree) {
        print_inorder(tree->left);
        std::cout << tree -> data;
        print_inorder(tree->right);
    }
}

void postorder_print(Tree * tree) {
    if(tree) {
        print_postorder(tree->left);
        print_postorder(tree->right);
        std::cout << tree -> data;
    }
}

非递归，栈的方法实现

void preorder_stack(Tree *tree){
    std::stack<Tree> stack;
    Tree *p = tree;
    while (p || !stack.empty()) {
        if(p != NULL) {
            stack.push(*p);
            printf("%d ",p->data);
            p = p -> left;
        } else {
            p = &stack.top();
            stack.pop();
            p = p -> right;
        }
    }
}

void inorder_stack(Tree *tree){
    std::stack<Tree> stack;
    Tree *p = tree;
    while(p || !stack.empty()){
        if(p != NULL){
            stack.push(*p);
            p = p -> left;
        } else {
            p = &stack.top();
            printf("%d ",p -> data);
            stack.pop();
            p = p -> right;
        }
    }
}

//后续遍历需要标示是否已经达到根结点，1为左 2为右
struct PostTree {
    Tree *tree;
    int IsChecked = 0;
};
typedef PostTree PostTree;

void postorder_stack(Tree *tree){
    std::stack<PostTree> stack;
    Tree *p = tree;
    PostTree *post;
    
    while (p || !stack.empty()) {
        //遍历左节点
        while(p != NULL){
            post = (PostTree *)malloc(sizeof(PostTree));
            post ->tree = p;
            post ->IsChecked = 1;
            stack.push(*post);
            p = p -> left;
        }
        //遍历右结点
        while(!stack.empty()){
            post = &stack.top();
            post -> IsChecked = 2;
            p = post->tree;
            p = p -> right;
        }
        //访问根结点
        while (!stack.empty() && (stack.top()).IsChecked == 2) {
            post = &stack.top();
            stack.pop();
            printf("%d ",post -> tree -> data);
        }
    }//end while
}