二叉树的题目

树的题目

　　判断是否为满二叉树

　　判断是否为平衡二叉树

　　判断是否为搜索二叉树

　　判断是否为完全二叉树

　　找最低公共祖先结点

 

树的结点

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

 

判断是否为满二叉树

class Info
{
public:
    Info(int n,int h):nodes(n),height(h){}
    int nodes;
    int height;
};

Info process(Node *head)
{
    if (head == NULL)
    {
        return Info(0, 0);
    }
    Info leftInfo = process(head->left);
    Info rightInfo = process(head->right);
    int nodes = leftInfo.nodes + rightInfo.nodes + 1;
    int height = (leftInfo.height > rightInfo.height ? leftInfo.height : rightInfo.height) + 1;
    return Info(nodes, height);
}

bool isFull(Node *head)
{
    Info info = process(head);
    int N = info.nodes;
    int H = info.height;
    return N == (1 << H) - 1;
}

 

判断是否为平衡二叉树

class Info
{
public:
    Info(int h,bool is):height(h),isBalance(is){}
    int height;
    bool isBalance;
};

Info process(Node *head)
{
    if (head == NULL)
    {
        return Info(0, true);
    }
    Info leftInfo = process(head->left);
    Info rightInfo = process(head->right);
    int height = max(leftInfo.height, rightInfo.height) + 1;
    bool isBalance = leftInfo.isBalance&&rightInfo.isBalance && (abs(leftInfo.height - rightInfo.height) < 2);
    return Info(height, isBalance);
}

bool isBalance(Node *head)
{
    Info info = process(head);
    return info.isBalance;
}

 

判断是否为搜索二叉树

class Info
{
public:
    Info(bool is, int ma, int mi) :isBST(is), max(ma), min(mi) {}
    bool isBST;
    int max;
    int min;
};

Info process(Node *x)
{
    if (x == NULL)
    {
        return Info(false, 0, 0);
    }
    Info leftData = process(x->left);
    Info rightData = process(x->right);

    int max = x->value;
    int min = x->value;

    if (x->left != NULL)
    {
        max = x->left->value > max ? x->left->value : max;
        min = x->left->value < min ? x->left->value : min;
    }
    if (x->right != NULL)
    {
        max = x->right->value > max ? x->right->value : max;
        min = x->right->value < min ? x->right->value : min;
    }
    bool isBST = false;
    if (((x->left != NULL) ? (leftData.isBST && leftData.max < x->value) : true)
        &&
        ((x->right!=NULL)?(rightData.isBST&&rightData.min>x->value):true))
    {
        isBST = true;
    }
    return Info(isBST, min, max);
}

bool isBSTTest(Node *head)
{
    Info info = process(head);
    return info.isBST;
}

 

判断是否为完全二叉树

bool isCBT(Node *head)
{
    if (head == NULL)
    {
        return true;
    }
    queue<Node*>queue;
    queue.push(head);
    bool leaf = false;
    Node *L = NULL;
    Node *R = NULL;
    while (!queue.empty())
    {
        head = queue.front();
        queue.pop();
        L = head->left;
        R = head->right;
        if (leaf && (L != NULL && R != NULL) || (L == NULL && R != NULL))
        {
            return false;
        }
        if (L != NULL)
        {
            queue.push(L);
        }
        if (R != NULL)
        {
            queue.push(R);
        }
        if (L == NULL && R == NULL)
        {
            leaf = true;
        }
    }
    return true;
}

 

找最低公共祖先结点

class Info
{
public:
    Info(bool f1,bool f2,Node* f):findO1(f1),findO2(f2),findAns(f){}
    bool findO1;
    bool findO2;
    Node *findAns;
};

Info process(Node *x, Node *o1, Node *o2)
{
    if (x == NULL)
    {
        return Info(false, false, NULL);
    }
    Info leftInfo = process(x->left, o1, o2);
    Info rightInfo = process(x->right, o1, o2);
    
    if (leftInfo.findAns != NULL)
    {
        return Info(true, true, leftInfo.findAns);
    }
    if (rightInfo.findAns != NULL)
    {
        return Info(true, true, rightInfo.findAns);
    }
    if (leftInfo.findO1 && rightInfo.findO2)
    {
        return Info(true, true, x);
    }
    if (leftInfo.findO2 && rightInfo.findO1)
    {
        return Info(true, true, x);
    }

    bool findO1 = x == o1;
    bool findO2 = x == o2;

    if (leftInfo.findO1 || rightInfo.findO2)
    {
        if (findO2) {
            return Info(true, true, x);
        }
        else {
            return Info(true, false, NULL);
        }
    }
    if (leftInfo.findO2 || rightInfo.findO1)
    {
        if (findO1)
        {
            return Info(true, true, x);
        }
        else
        {
            return Info(false, true, NULL);
        }
    }
    return Info(findO1, findO2, NULL);
}

Node* lowestCommon(Node *head, Node *o1, Node *o2)
{
    Info info = process(head, o1, o2);
    return info.findAns;
}