个人练习-PAT甲级-1123 Is It a Complete AVL Tree

题目链接https://pintia.cn/problem-sets/994805342720868352/problems/994805351302414336

题目大意：给出N个数字，建AVL树。然后输出层序遍历。最后判断是否是完全二叉树。

正常的左旋右旋左右旋右左旋代码书上都有，不赘述了。层序遍历用个queue就行。在层序遍历时判断是否是完全二叉树，我们给每个结点加一个属性pos，根的pos==1，那么左儿子的pos等于父亲的2倍，右儿子的pos等于父亲的两倍+1。如果一棵树是完全二叉树，那么其pos应该刚好为从1到N，出现大于N的pos时，直接置isComp为false就行。

void lvlOrder(Node* root) {
    queue<Node*> q;
    q.push(root);
    q.front()->pos = 1;
    while (!q.empty()) {
        if (q.front()->left) {
            q.push(q.front()->left);
            q.front()->left->pos = q.front()->pos * 2;
        }

        if (q.front()->right) {
            q.push(q.front()->right);
            q.front()->right->pos = q.front()->pos * 2 + 1;
        }

        if (q.front() == root)
            printf("%d", q.front()->val);
        else
            printf(" %d", q.front()->val);

        if (q.front()->pos > N)
            isComp = false;

        q.pop();
    }
    printf("\n");
}

一开始做的时候，测试点2、3一直过不去，感觉也没问题了。检查半天才发现，结点的高度（height）是可能变化的，而我一开始仅在插入时计算其高度，并将高度作为结点的一个属性了。实际上由于AVL树会调整结构，所以高度也有可能变化，每次需要高度时应该用函数getHeight()重新计算才行。

完整代码

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 


using namespace std;


class Node{
public:
    int val, pos;
    Node *left, *right;
    Node() {
        left = right = nullptr;
    }
    Node(int num) {
        val = num;
        left = right = nullptr;
    }
};


int N;
Node* tree = nullptr;
bool isComp = true;


int getHeight(Node* node) {
    if (node == nullptr)
        return -1;
    else
        return max(getHeight(node->left), getHeight(node->right)) + 1;
}


Node* leftSingleRot(Node* root) {
    Node* mid = root->left;
    root->left = mid->right;
    mid->right = root;
    return mid;
}


Node* rightSingleRot(Node* root) {
    Node* mid = root->right;
    root->right = mid->left;
    mid->left = root;
    return mid;
}


Node* leftDoubleRot(Node* root) {
    root->left = rightSingleRot(root->left);
    return leftSingleRot(root);
}


Node* rightDoubleRot(Node* root) {
    root->right = leftSingleRot(root->right);
    return rightSingleRot(root);
}


Node* insert(Node* node, int num) {
    if (node == nullptr) {
        node = new Node(num);
        return node;
    }
    if (num > node->val) {
        node->right = insert(node->right, num);
        if (getHeight(node->right) - getHeight(node->left) == 2) {
            if (num > node->right->val)
                node = rightSingleRot(node);
            else
                node = rightDoubleRot(node);
        }
    }
    else {
        node->left = insert(node->left, num);
        if (getHeight(node->left) - getHeight(node->right) == 2) {
            if (num < node->left->val)
                node = leftSingleRot(node);
            else
                node = leftDoubleRot(node);
        }
    }

    return node;
}


void lvlOrder(Node* root) {
    queue<Node*> q;
    q.push(root);
    q.front()->pos = 1;
    while (!q.empty()) {
        if (q.front()->left) {
            q.push(q.front()->left);
            q.front()->left->pos = q.front()->pos * 2;
        }

        if (q.front()->right) {
            q.push(q.front()->right);
            q.front()->right->pos = q.front()->pos * 2 + 1;
        }

        if (q.front() == root)
            printf("%d", q.front()->val);
        else
            printf(" %d", q.front()->val);

        if (q.front()->pos > N)
            isComp = false;

        q.pop();
    }
    printf("\n");
}


int main() {
    scanf("%d", &N);
    for (int i = 0; i < N; i++) {
        int num;
        scanf("%d", &num);
        tree = insert(tree, num);
    }

    lvlOrder(tree);

    if (isComp)
        printf("YES");
    else
        printf("NO");

    return 0;
}