判断是否是平衡二叉树，满二叉树，完全二叉树

原创

wx5f6a96e093b03 2022-07-02 00:19:45 博主文章分类：数据结构与算法 ©著作权

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定义一个二叉树

#include <stack>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <iostream>
using namespace std;

class Node{
public:
    int value;
    Node* left;
    Node* right;
    Node(int value):value(value){
        left = nullptr;
        right = nullptr;
    }
};

生成一个平衡二叉树，满二叉树，完全二叉树

//生成一个完全二叉树
Node* fullTreeInit(){
    Node *head = new Node(1);
    head->left = new Node(2);
    head->right = new Node(3);
    head->left->left = new Node(4);
    head->left->right = new Node(5);
    head->right->left = new Node(6);
    head->right->right = new Node(7);
    return head;
}
//生成一个满二叉树
Node* treeInit(){
    Node *head = new Node(1);
    head->left = new Node(2);
    head->right = new Node(3);
    head->left->left = new Node(4);
    head->left->right = new Node(5);
    head->right->left = new Node(6);
    head->right->right = new Node(7);
    return head;
}

算法

//是否是完全二叉树
bool isFBT(Node *head){
    if(head == nullptr){
        return true;
    }
    queue<Node*> q;
    q.push(head);
    Node *l, *r;
    bool leaf = false;
    while(!q.empty()){
        head = q.front();
        l = head->left;
        r = head->right;
        q.pop();
        //前面已经有叶节点了，但还是有左右节点
        if((leaf && (l != nullptr || r != nullptr))
                ||
                (l == nullptr && r != nullptr) //有右无左
                ){
            return false;
        }
        if(l != nullptr){
            q.push(l);
        }
        if(r != nullptr){
            q.push(r);
        }
        //虽然是或运算，其实只有无左无右才能到这里
        if(l == nullptr || r == nullptr){
            leaf = true;
        }
    }
    return true;
}

//判断是否是平衡二叉树
class ReturnType{
public:
    bool isBanlance;
    int height;
    ReturnType(bool isB, int h):
    isBanlance(isB), height(h)
    {}
};

ReturnType isBanlanceTree(Node *head){
    if(head == nullptr){
        return ReturnType(true, 0);
    }
    ReturnType rt1 = isBanlanceTree(head->left);
    ReturnType rt2 = isBanlanceTree(head->right);
    int height = max(rt1.height, rt2.height) + 1;
    return ReturnType((rt1.isBanlance && rt2.isBanlance)
                            &&
                         (abs(rt1.height-rt2.height)<2),
                      height);
}


//判断是否为满二叉树
class Info{
public:
    int height;
    int nodes;
    Info(int h, int n):
    height(h), nodes(n)
    {}
};

Info isFullTree(Node* head){
    if(head == nullptr){
        return Info(0, 0);
    }
    Info if1 = isFullTree(head->left);
    Info if2 = isFullTree(head->right);
    int height = max(if1.height, if2.height)+1;
    int nodes = if1.nodes + if2.nodes + 1;
    return Info(height, nodes);
}

bool isFull(Node *head){
    Info info = isFullTree(head);
    return info.nodes == (1<<info.height)-1? true:false;
}