Cpp 二叉树

Posted 2022-06-14 yejifeng

#include<vector>
#include<iostream>
using namespace std;


//二叉树的一个节点结构 
struct BinaryTreeNode  
    int val;
    BinaryTreeNode *left;
    BinaryTreeNode *right;
    BinaryTreeNode(int x) : val(x), left(NULL), right(NULL) 
;


//使用递归的方法创建二叉树 
struct BinaryTreeNode *CreatBinaryTree()
    int a;
    cin >> a; //有多少叶子就需要输入2倍个 0 才能结束创建进程 
    if(a == 0) return NULL;

    struct BinaryTreeNode *newnode = (struct BinaryTreeNode*)malloc( sizeof(struct BinaryTreeNode) );
    newnode->val = a;
    newnode->left  = CreatBinaryTree();  //递归创建左子树
    newnode->right = CreatBinaryTree();  //递归创建右子树
    return newnode;



//先序遍历
void PreOrderTraverse(struct BinaryTreeNode *root)
    if(root)
        cout << root->val << ' ';
        PreOrderTraverse(root->left);
        PreOrderTraverse(root->right);
    



//中序遍历
void InOrderTraverse(struct BinaryTreeNode *root)  
    if(root)
        InOrderTraverse(root->left);
        cout << root->val << ' ';
        InOrderTraverse(root->right);
    



//后序遍历
void LastOrderTraverse(struct BinaryTreeNode *root)
    if(root)
        LastOrderTraverse(root->left);
        LastOrderTraverse(root->right);
        cout << root->val << ' ';
    



//二叉树节点总数目
int NodeNum(struct BinaryTreeNode *root)
    
    if(root)
        return 1+NodeNum(root->left)+NodeNum(root->right);
    else
        return 0;



//二叉树叶子节点数
int LeafNum(struct BinaryTreeNode *root)
    if(!root)
        return 0;
    else if( (root->left == NULL) && (root->right == NULL) )
        return 1;
    else
        return LeafNum(root->left) + LeafNum(root->right);



//二叉树最大深度
int maxDepth(struct BinaryTreeNode *root)
    if(root == NULL) return 0;
    return max(maxDepth(root->left), maxDepth(root->right)) + 1;



//二叉树最小深度(从根节点到最近叶子节点,注意是叶子)
int minDepth(struct BinaryTreeNode *root)  
    if(root == NULL) return 0;
    if(root->left == NULL) return minDepth(root->right) + 1;
    if(root->right == NULL) return minDepth(root->left) + 1;
    return min(minDepth(root->left), minDepth(root->right)) + 1;



//二叉树所用路径
void dfspath(BinaryTreeNode* node,string path,vector<string> &result)
    path += to_string(node->val);
    //遍历到子节点了，
    if(node->left==NULL && node->right==NULL) result.push_back(path);
    if(node->left!=NULL) dfspath(node->left, path + "->",result);
    if(node->right!=NULL) dfspath(node->right,path + "->",result);
 
vector<string> binaryTreePaths(BinaryTreeNode* root) 
    vector<string> result;
    if(root!=NULL) dfspath(root,"",result);
    return result;



int main()
    struct BinaryTreeNode *root;
    
    root = CreatBinaryTree();
    
    cout<<"二叉树总节点数为："<<NodeNum(root)<<endl;
    
    cout<<"二叉树叶子节点数为："<<LeafNum(root)<<endl;
    
    cout<<"二叉树最大深度(从根节点到最远叶子节点)："<<maxDepth(root)<<endl;
    
    cout<<"二叉树最小深度(从根节点到最近叶子节点)："<<minDepth(root)<<endl;
    
    cout<<"前序遍历结果:";
    PreOrderTraverse(root);
    cout<<endl;
    
    cout<<"中序遍历结果:";
    InOrderTraverse(root);
    cout<<endl;
    
    cout<<"后序遍历结果:";
    LastOrderTraverse(root);
    cout<<endl;
    
    cout<<"二叉树所有路径：\n";
    vector<string> allPaths = binaryTreePaths(root);
    for(auto e:allPaths) cout <<"\t" << e <<endl;
    
    return 0;

/*
测试用例：
3 9 0 0 20 15 0 0 7 0 0

1 2 0 5 0 0 3 0 0
*/