基础算法——二叉树

/*************************************************************************
    > File Name: binary_tree.cpp
    > Author: xinyang
    > Mail: xuechen.xy@gmail.com 
    > Created Time: Fri 02 Oct 2015 05:24:25 PM CST
 ************************************************************************/
#include <iostream>
#include <stack>
#include <queue>
using namespace std;

/*
 * 二叉树节点
 */
struct Node {
    int value;
    Node *lchild, *rchild;
    Node *next;

    Node (int x) {
        value = x;
        lchild = NULL;
        rchild = NULL;
        next = NULL;
    }
};

/*
 * 往二叉树中插入节点
 */
Node *insert(Node *T, int x) {
    if (T == NULL) {
        T = new Node(x);
    } else if (T->value > x) {
        T->lchild = insert(T->lchild, x);
    } else if (T->value < x) {
        T->rchild = insert(T->rchild, x);
    }

    return T;
}

/*
 * 前序遍历（递归）
 */
void pre_order_recur(Node *T) {
    cout << T->value << ' ';
    if (T->lchild != NULL) {
        pre_order_recur(T->lchild);
    } 
    if (T->rchild != NULL) {
        pre_order_recur(T->rchild);
    }
}

/*
 * 前序遍历（非递归）
 */
void pre_order_iter(Node *T) {
    if (T == NULL) {
        return;
    }

    Node *tmp = T;
    stack<Node *> S;
    while (tmp != NULL || !S.empty()) {
        while (tmp != NULL) {
            S.push(tmp);
            cout << tmp->value << ' ';
            tmp = tmp->lchild;
        }
        if (!S.empty()) {
            tmp = S.top();
            S.pop();
            tmp = tmp->rchild;
        }
    }
}

/*
 * 中序遍历（递归）
 */
void in_order_recur(Node *T) {
    if (T->lchild != NULL) {
        in_order_recur(T->lchild);
    }
    cout << T->value << ' ';
    if (T->rchild != NULL) {
        in_order_recur(T->rchild);
    }
}

/*
 * 中序遍历（非递归）
 */
void in_order_iter(Node *T) {
    if (T == NULL) {
        return ;
    }

    Node *tmp = T;
    stack<Node *> S;
    while (tmp != NULL || !S.empty()) {
        while (tmp != NULL) {
            S.push(tmp);
            tmp = tmp->lchild;
        }
        if (!S.empty()) {
            tmp = S.top();
            S.pop();
            cout << tmp->value << ' ';
            tmp = tmp->rchild;
        }
    }
}

/*
 * 后序遍历（递归）
 */
void post_order_recur(Node *T) {
    if (T->lchild != NULL) {
        post_order_recur(T->lchild);
    }
    if (T->rchild != NULL) {
        post_order_recur(T->rchild);
    }
    cout << T->value << ' ';
}
/*
 * 后序遍历（非递归）
 */
void post_order_iter(Node *T) {
    if (T == NULL) {
        return;
    }

    Node *pre = NULL, *cur = NULL;
    stack<Node *> S;
    S.push(T);
    while (!S.empty()) {
        cur = S.top();
        if ((cur->lchild == NULL && cur->rchild == NULL)
                || (pre != NULL && (pre == cur->lchild || pre == cur->rchild))) {
            cout << cur->value << ' ';
            S.pop();
            pre = cur;
        } else {
            if (cur->rchild != NULL) {
                S.push(cur->rchild);
            }
            if (cur->lchild != NULL) {
                S.push(cur->lchild);
            }
        }
    }
}

/*
 * 层次遍历
 */
void level_order(Node *T) {
    if (T == NULL) {
        return;
    }

    Node *tmp = T;
    queue<Node *> Q;
    Q.push(tmp);
    while (!Q.empty()) {
        tmp = Q.front();
        Q.pop();
        cout << tmp->value << ' ';
        if (tmp->lchild != NULL) {
            Q.push(tmp->lchild);
        }
        if (tmp->rchild != NULL) {
            Q.push(tmp->rchild);
        }
    }
}

/*
 * 按行打印（换行）
 */
void level_order_line(Node *T) {
    if (T == NULL) {
        return;
    }

    int cur = 0, last = 0;
    Node *tmp = T;
    queue<Node *> Q;
    Q.push(tmp);
    cur = 1;
    while (!Q.empty()) {
        last = cur;
        while (last--) {
            tmp = Q.front();
            Q.pop();
            cout << tmp->value << ' ';
            if (tmp->lchild != NULL) {
                Q.push(tmp->lchild);
            } 
            if (tmp->rchild != NULL) {
                Q.push(tmp->rchild);
            }
        }
        cur = Q.size();
        cout << endl;
    }
}

/*
 * 按行打印（之字形）
 */
void level_order_s(Node *T) {
    if (T == NULL) {
        return;
    }

    stack<Node *> levels[2];
    int current = 0, next = 1;
    Node *tmp = T;
    levels[current].push(tmp);
    while (!levels[current].empty() || !levels[next].empty()) {
        tmp = levels[current].top();
        levels[current].pop();
        cout << tmp->value << ' ';

        if (current == 0) {
            if (tmp->lchild != NULL) {
                levels[next].push(tmp->lchild);
            }
            if (tmp->rchild != NULL) {
                levels[next].push(tmp->rchild);
            }
        } else {
            if (tmp->rchild != NULL) {
                levels[next].push(tmp->rchild);
            }
            if (tmp->lchild != NULL) {
                levels[next].push(tmp->lchild);
            }
        }

        if (levels[current].empty()) {
            cout << endl;
            current = 1 - current;
            next = 1 - next;
        }
    }
}
/*
 * 高度（递归）
 */
int height_recur(Node *T) {
    if (T == NULL) {
        return 0;
    }

    int left = height_recur(T->lchild);
    int right = height_recur(T->rchild);
    return left > right ? (left + 1) : (right + 1);
}
/*
 * 高度（非递归）
 */
int height_iter(Node *T) {
    if (T == NULL) {
        return 0;
    }

    Node *tmp = T;
    queue<Node *> Q;
    Q.push(tmp);
    while (!Q.empty()) {
        tmp = Q.front();
        Q.pop();
        if (tmp->lchild != NULL) {
            Q.push(tmp->lchild);
        }
        if (tmp->rchild != NULL) {
            Q.push(tmp->rchild);
        }
    }

    Node *m = tmp, *n = T;
    int h = 0;
    while (m != n) {
        Q.push(n);
        while (!Q.empty()) {
            tmp = Q.front();
            Q.pop();
            if (tmp->lchild == m || tmp->rchild == m) {
                ++h;
                m = tmp;
                break;
            }
            if (tmp->lchild != NULL) {
                Q.push(tmp->lchild);
            }
            if (tmp->rchild != NULL) {
                Q.push(tmp->rchild);
            }
        }
    }
    return h + 1;
}
/*
 * 宽度
 */
int width(Node *T) {
    if (T == NULL) {
        return 0;
    }

    Node *tmp = T;
    queue<Node *> Q;
    Q.push(tmp);
    int last_width = 1, last_width_tmp = 1;
    int width = 1, cur_width = 1;
    while (!Q.empty()) {
        last_width_tmp = last_width;
        while (last_width_tmp--) {
            tmp = Q.front();
            Q.pop();
            if (tmp->lchild != NULL) {
                Q.push(tmp->lchild);
            }
            if (tmp->rchild != NULL) {
                Q.push(tmp->rchild);
            }
        }
        cur_width = Q.size();
        width = cur_width > width ? cur_width : width;
        last_width = cur_width;
    }
    return width;
}

/*
 * 平衡二叉树判断1
 */
bool is_balanced1(Node *T) {
    if (T == NULL) {
        return true;
    }

    int left = height_recur(T->lchild);
    int right = height_recur(T->rchild);
    int diff = left - right;
    if (diff > 1 || diff < -1) {
        return false;
    } else {
        return is_balanced1(T->lchild)
            && is_balanced1(T->rchild);
    }
}
/*
 * 最小高度
 */
int min_depth(Node *T) {
    if (T == NULL) {
        return 0;
    }

    return 1 + min(min_depth(T->lchild), 
            min_depth(T->rchild));
}
/*
 * 最大高度
 */
int max_depth(Node *T) {
    if (T == NULL) {
        return 0;
    }

    return 1 + max(max_depth(T->lchild), 
            max_depth(T->rchild));
}

/*
 * 平衡二叉树判断2
 */
bool is_balanced2(Node *T) {
    if (T == NULL) {
        return true;
    }

    int min_h = min_depth(T);
    int max_h = max_depth(T);
    return max_h - min_h <= 1;
}

/*
 * 判断两棵二叉树是否相等
 */
bool is_equal(Node *T1, Node *T2) {
    if (T1 == NULL && T2 == NULL) {
        return true;
    }

    if (T1 == NULL || T2 == NULL) {
        return false;
    }

    if (T1->value == T2->value) {
        return is_equal(T1->lchild, T2->lchild)
            && is_equal(T1->rchild, T2->rchild);
    } else {
        return false;
    }
}

/*
 * 判断两棵二叉树是否对称
 */
bool is_symmetrical(Node *T1, Node *T2) {
    if (T1 == NULL && T2 == NULL) {
        return true;
    }

    if (T1 == NULL || T2 == NULL) {
        return false;
    }

    if (T1->value == T2->value) {
        return is_symmetrical(T1->lchild, T2->rchild)
            && is_symmetrical(T1->rchild, T2->lchild);
    } else {
        return false;
    }
}

bool is_symmetrical(Node *T) {
    if (T == NULL) {
        return true;
    }

    return is_symmetrical(T, T);
}

/*
 * 求一棵二叉树的镜像
 */
Node *mirror(Node *T) {
    if (T == NULL) {
        return NULL;
    }

    if (T->lchild == NULL && T->rchild == NULL) {
        return T;
    }

    Node *tmp = T->lchild;
    T->lchild = T->rchild;
    T->rchild = tmp;
    if (T->lchild != NULL) {
        T->lchild = mirror(T->lchild);
    }
    if (T->rchild != NULL) {
        T->rchild = mirror(T->rchild);
    }
    return T;
}

/*
 * 二叉树1与2有相同的根节点，判断1是否包含2
 */
bool does_1_has_2(Node *T1, Node *T2) {
    if (T2 == NULL) {
        return true;
    }

    if (T1 == NULL) {
        return false;
    }

    if (T1->value == T2->value) {
        return does_1_has_2(T1->lchild, T2->lchild)
            && does_1_has_2(T1->rchild, T2->rchild);
    } else {
        return false;
    }
}

/*
 * 判断二叉树1中是否包含二叉树2
 */
bool has_subtree(Node *T1, Node *T2) {
    bool result = false;
    if (T2 == NULL) {
        return true;
    }

    if (T1 == NULL) {
        return false;
    }

    if (T1->value == T2->value) {
        result = does_1_has_2(T1, T2);
    }

    if (false == result) {
        result = has_subtree(T1->lchild, T2);
    }

    if (false == result) {
        result = has_subtree(T1->rchild, T2);
    }

    return result;
}

/*
 * 判断一棵完美二叉树
 */
bool is_perfect_tree(Node *T) {
    if (T == NULL) {
        return true;
    }

    queue<Node *> Q;
    Node *tmp = T;
    Q.push(tmp);
    while (!Q.empty()) {
        tmp = Q.front();
        Q.pop();
        if ((tmp->lchild != NULL && tmp->rchild == NULL) 
                || (tmp->lchild == NULL && tmp->rchild != NULL)) {
            return false;
        }
        if (tmp->lchild != NULL) {
            Q.push(tmp->lchild);
        }
        if (tmp->rchild != NULL) {
            Q.push(tmp->rchild);
        }
    }
    return true;
}

/*
 * 判断一棵完全二叉树
 */
bool is_complete_tree(Node *T) {
    if (T == NULL) {
        return true;
    }

    queue<Node *> Q;
    Node *tmp = T;
    Q.push(tmp);
    while (!Q.empty()) {
        tmp = Q.front();
        Q.pop();
        if (tmp == NULL) {
            break;
        }
        Q.push(tmp->lchild);
        Q.push(tmp->rchild);
    }

    while (!Q.empty()) {
        tmp = Q.front();
        Q.pop();
        if (tmp != NULL) {
            return false;
        }
    }
    return true;
}

/*
 * 由前序遍历以及中序遍历序列构建二叉树
 */
int pre[] = {3, 1, 2, 8, 7, 5, 4, 6, 9};
int in[] = {1, 2, 3, 4, 5, 6, 7, 8, 9};
Node *build_tree(int s1, int e1, int s2, int e2) {
    Node *ret = new Node(pre[s1]);
    int rootIdx;
    int i;
    for (i = s2; i <= e2; ++i) {
        if (in[i] == pre[s1]) {
            rootIdx = i;
            break;
        }
    }

    if (i == e2 + 1) {
        return NULL;
    }

    if (rootIdx != s2) {
        ret->lchild = build_tree(s1 + 1, s1 + rootIdx - s2, 
                s2, rootIdx - 1);
    }

    if (rootIdx != e2) {
        ret->rchild = build_tree(s1 + rootIdx - s2 + 1, 
                e1, rootIdx + 1, e2);
    }

    return ret;
}

/*
 * 判断是否是BST的后序序列
 */
bool verify_sequence_of_BST(int A[], int n) {
    if (A == NULL || n <= 0) {
        return true;
    }

    int root = A[n - 1];
    int i = 0;
    for (; i < n - 1; ++i) {
        if (A[i] > root) {
            break;
        }
    }

    int j = i;
    for (; j < n - 1; ++j) {
        if (A[j] < root) {
            return false;
        }
    }

    bool left = true;
    if (i > 0) {
        left = verify_sequence_of_BST(A, i);
    }
    bool right = true;
    if (i < n - 1) {
        right = verify_sequence_of_BST(A + i, n - i - 1);
    }
    return left && right;
}

/*
 * 从二叉树中查找和为定值的路径
 */
void find_path(Node *T, int sum, vector<int> &path, int cur_sum) {
    cur_sum += T->value;
    path.push_back(T->value);
    bool is_leaf = T->lchild == NULL && T->rchild == NULL;
    if (is_leaf == true && cur_sum == sum) {
        for (int i = 0; i < path.size(); ++i) {
            cout << path[i] << ' ';
        }
        cout << endl;
    }

    if (T->lchild != NULL) {
        find_path(T->lchild, sum, path, cur_sum);
    }

    if (T->rchild != NULL) {
        find_path(T->rchild, sum, path, cur_sum);
    }
    path.pop_back();
}

void find_path(Node *T, int sum) {
    if (T == NULL) {
        return;
    }

    int cur_sum = 0;
    vector<int> path;
    find_path(T, sum, path, cur_sum);
}

/*
 * 将二叉搜索树转换为双向链表
 */
void convert_node(Node *T, Node **last_node) {
    if (T == NULL) {
        return ;
    }

    if (T->lchild != NULL) {
        convert_node(T->lchild, last_node);
    }

    T->lchild = *last_node;
    if (*last_node != NULL) {
        (*last_node)->rchild = T;
    }
    *last_node = T;

    if (T->rchild != NULL) {
        convert_node(T->rchild, last_node);
    }
}    

Node *convert(Node *T) {
    Node *last_node = NULL;
    convert_node(T, &last_node);
    Node *head = last_node;
    while (head != NULL && head->lchild != NULL) {
        head = head->lchild;
    }
    return head;
}

/*
 * 找出BST中第k个节点
 */
Node *kth_node_core(Node *T, int &k) {
    Node *target = NULL;
    if (T->lchild != NULL) {
        target = kth_node_core(T->lchild, k);
    }

    if (target == NULL) {
        if (k == 1) {
            target = T;
        }
        --k;
    }

    if (target == NULL && T->rchild != NULL) {
        target = kth_node_core(T->rchild, k);
    }
    return target;
}

Node *kth_node(Node *T, int k) {
    if (T == NULL || k <= 0) {
        return NULL;
    }

    return kth_node_core(T, k);
}

/*
 * 获取二叉树中两个节点的最大距离（边个数）
 */
struct RESULT {
    int max_distance;
    int max_depth;
};

RESULT get_max_distance(Node *T) {
    if (T == NULL) {
        RESULT empty = {0, -1};
        return empty;
    }
    
    RESULT lhs = get_max_distance(T->lchild);
    RESULT rhs = get_max_distance(T->rchild);
    RESULT ret;
    ret.max_depth = max(lhs.max_depth + 1, rhs.max_depth + 1);
    ret.max_distance = max(max(lhs.max_distance, rhs.max_distance),
            lhs.max_depth + rhs.max_depth + 2);
    return ret;
}

/*
 * 获取两个节点的最低公共祖先（递归）
 */
Node *common_parent1(Node *T, Node *node1, Node *node2) {
    if (T == NULL) {
        return NULL;
    }

    if (node1 == T || node2 == T) {
        return T;
    }

    Node *left = common_parent1(T->lchild, node1, node2);
    Node *right = common_parent1(T->rchild, node1, node2);
    if (left == NULL) {
        return right;
    } else if (right == NULL) {
        return left;
    } else {
        return T;
    }
}

/*
 * 获取两个节点的最低公共祖先（迭代）
 */
bool find_node(Node *T, Node *node, vector<Node *> &path) {
    if (T == NULL) {
        return false;
    }

    path.push_back(T);
    if (T == node) {
        return true;
    }

    bool found = false;
    found = find_node(T->lchild, node, path);
    if (false == found) {
        found = find_node(T->rchild, node, path);
    }
    if (false == found) {
        path.pop_back();
    }
    return found;
}

Node *common_parent2(Node *T, Node *node1, Node *node2) {
    Node *ret = NULL;
    vector<Node *> path1;
    vector<Node *> path2;
    bool has_node1 = find_node(T, node1, path1);
    bool has_node2 = find_node(T, node2, path2);
    if (false == has_node1 || false == has_node2) {
        return T;
    }

    int L1 = path1.size();
    int L2 = path2.size();
    for (int i = 0, j = 0; i != L1 && j != L2; ++i, ++j) {
        if (path1[i] != path2[j]) {
            break;
        }
        ret= path1[i];
    }
    return ret;
}

/*
 * 判断一个节点是否是叶节点，如果是，求出根节点到该节点的路径
 */
bool find_leaf_node(Node *T, Node *node, vector<Node *> &path) {
    if (T == NULL) {
        return false;
    }

    path.push_back(T);
    bool is_leaf = T->lchild == NULL && T->rchild == NULL;
    if (true == is_leaf && T == node) {
        return true;
    }

    bool found = false;
    found = find_leaf_node(T->lchild, node, path);
    if (false == found) {
        found = find_leaf_node(T->rchild, node, path);
    }
    if (false == found) {
        path.pop_back();
    }
    return found;
}

/*
 * 在一棵完全二叉树中使用next指针链接旁边的节点
 */
void connect_complete_tree(Node *T) {
    if (T == NULL) {
        return ;
    }

    Node *tmp = T;
    Node *first = NULL;
    while (tmp != NULL) {
        if (first == NULL) {
            first = tmp->lchild;
        }
        if (tmp->lchild != NULL) {
            tmp->lchild->next = tmp->rchild;
        } else {
            break;
        }
        if (tmp->next != NULL) {
            tmp->rchild->next = tmp->next->lchild;
            tmp = tmp->next;
            continue;
        } else {
            tmp = first;
            first = NULL;
        }
    }
}

/*
 * 在一棵普通二叉树中使用next指针链接旁边的节点
 */
void connext_normal_tree(Node *T) {
    if (T == NULL) {
        return ;
    }

    Node *tmp = T;
    Node *first = NULL, *last = NULL;
    while (tmp != NULL) {
        if (first == NULL) {
            if (tmp->lchild != NULL) {
                first = tmp->lchild;
            } else if (tmp->rchild != NULL) {
                first = tmp->rchild;
            }
            if (tmp->lchild != NULL) {
                if (last != NULL) {
                    last->next = tmp->lchild;
                }
                last = tmp->next;
            }
            if (tmp->rchild != NULL) {
                
                if (last != NULL) {
                    last->next = tmp->rchild;
                } 
                last = tmp->next;
            }
            if (tmp->next != NULL) {
                tmp = tmp->next;
            } else {
                tmp = first;
                first = NULL;
                last = NULL;
            }
        }
    }
}

/*
 * 将一个排过序的链表转成一棵BST
 */
struct ListNode {
    int value;
    ListNode *next;
    ListNode(int x) {
        value = x;
        next = NULL;
    }
};

Node *build_from_list(ListNode *start, ListNode *end) {
    if (start == end) {
        return NULL;
    }

    ListNode *fast = start, *slow = start;
    while (fast != end && fast->next != end) {
        slow = slow->next;
        fast = fast->next->next;
    }

    Node *ret = new Node(slow->value);
    
    ret->lchild = build_from_list(start, slow);
    ret->rchild = build_from_list(slow->next, end);

    return ret;
}

Node *sorted_list_to_BST(ListNode *head) {
    return build_from_list(head, NULL);
}

/*
 * 将一个排过序的数组转换成一棵BST
 */
Node *build_from_array(const vector<int> &num, int start, int end) {
    if (start >= end) {
        return NULL;
    }

    int mid = (start + end) / 2;
    Node *ret = new Node(num[mid]);

    ret->lchild = build_from_array(num, start, mid);
    ret->rchild = build_from_array(num, mid + 1, end);

    return ret;
}

Node *sort_array_to_BST(const vector<int> &num) {
    return build_from_array(num, 0, num.size());
}

/*
 * 将一颗二叉树磨平
 */
void flatten(Node *T) {
    if (T == NULL) {
        return;
    }

    stack<Node *> S;
    Node *p = new Node (0);
    Node *ret = p;

    S.push(T);
    while (!S.empty()) {
        Node *tmp = S.top();
        S.pop();

        p->rchild = tmp;
        p = tmp;

        if (tmp->rchild != NULL) {
            S.push(tmp->rchild);
            tmp->rchild = NULL;
        }
        if (tmp->lchild != NULL) {
            S.push(tmp->lchild);
            tmp->lchild = NULL;
        }
    }
}

/*
 * 判断一棵二叉树是否是BST
 */
#define MIN 0x80000000
#define MAX 0x7fffffff
bool is_valid_BST_core(Node *T, int min, int max) {
    if (T == NULL) {
        return true;
    }

    if (T->value < min || T->value > max) {
        return false;
    }

    return is_valid_BST_core(T->lchild, min, T->value)
        && is_valid_BST_core(T->rchild, T->value, max);

}

bool is_valid_BST(Node *T) {
    return is_valid_BST_core(T, MIN, MAX);
}

int main() {
    int A[] = {3, 8, 7, 1, 2, 5, 6, 4, 9};
    Node *T = NULL;
    for (int i = 0; i < 9; ++i) {
        T = insert(T, A[i]);
    }

    cout << "pre_order_recur" << endl;
    pre_order_recur(T);
    cout << endl;
    cout << "pre_order_iter" << endl;
    pre_order_iter(T);
    cout << endl << endl;

    cout << "in_order_recur" << endl;
    in_order_recur(T);
    cout << endl;
    cout << "in_order_iter" << endl;
    in_order_iter(T);
    cout << endl << endl;

    cout << "post_order_recur" << endl;
    post_order_recur(T);
    cout << endl;
    cout << "post_order_iter" << endl;
    post_order_iter(T);
    cout << endl << endl;

    cout << "level_order" << endl;
    level_order(T);
    cout << endl << endl;
    cout << "level_order_line" << endl;
    level_order_line(T);
    cout << endl << endl;

    cout << "level_order_s" << endl;
    level_order_s(T);
    cout << endl << endl;

    cout << "height_recur" << endl;
    cout << height_recur(T) << endl;
    cout << "height_iter" << endl;
    cout << height_iter(T);
    cout << endl << endl;

    cout << "width" << endl;
    cout << width(T);
    cout << endl << endl;

    // if (true == is_balanced1(T)) {
    if (true == is_balanced2(T)) {
        cout << "is balanced" << endl << endl;
    } else {
        cout << "is not balanced" << endl << endl;
    }

    if (true == is_equal(T, T)) {
        cout << "is equal" << endl << endl;
    } else {
        cout << "is not equal" << endl << endl;
    }

    /*
    Node *T1 = mirror(T);
    // if (true == is_symmetrical(T)) {
    if (true == is_symmetrical(T, T1)) {
        cout << "is symmetrical" << endl << endl;
    } else {
        cout << "is not symmetrical" << endl << endl;
    }
    */

    Node *T2 = T->lchild;
    if (true == has_subtree(T, T2)) {
        cout << "1 has 2" << endl << endl;
    } else {
        cout << "1 has no 2" << endl << endl;
    }

    if (true == is_perfect_tree(T)) {
        cout << "is pefect tree" << endl << endl;
    } else {
        cout << "is not perfect tree" << endl << endl;
    }

    if (true == is_complete_tree(T)) {
        cout << "is complete tree" << endl << endl;
    } else {
        cout << "is not complete tree" << endl << endl;
    }

    Node *post = build_tree(0, 8, 0, 8);
    post_order_iter(post);
    cout << endl << endl;

    int B[] = {2, 1, 4, 6, 5, 7, 9, 8, 3};
    if (true == verify_sequence_of_BST(B, 9)) {
        cout << "is valid BST sequence" << endl << endl;
    } else {
        cout << "is not valid BST sequence" << endl << endl;
    }

    cout << "find path in a tree with confirmed sum" << endl;
    find_path(T, 27);
    cout << endl;

    /*
    cout << "convert a tree into a link list" << endl;
    Node *convert_ret = convert(T);
    while (convert_ret != NULL) {
        cout << convert_ret->value << ' ';
        convert_ret = convert_ret->rchild;
    }
    cout << endl << endl;
    */

    cout << "2th node's value" << endl;
    Node *kth_ret = kth_node(T, 2);
    cout << kth_ret->value << endl << endl;

    cout << "max distance" << endl;
    RESULT max_ret = get_max_distance(T);
    cout << max_ret.max_distance << endl << endl;

    cout << "common parent of node1 and node2" << endl;
    Node *node1 = T->lchild, *node2 = T->rchild;
    cout << "node1: " << node1->value << ", node2: " << node2->value << endl;
    Node *common_ret = common_parent1(T, node1, node2);
    // Node *common_ret = common_parent2(T, node1, node2);
    cout << common_ret->value << endl << endl;

    cout << "find a path to leaf_node" << endl;
    Node *leaf = T->lchild->rchild;
    vector<Node *> path;
    if (true == find_leaf_node(T, leaf, path)) {
        cout << "path is" << endl;
        for (int i = 0; i < path.size(); ++i) {
            cout << path[i]->value << ' ';
        }
        cout << endl << endl;
    } else {
        cout << "no path" << endl << endl;
    }

    /*
    flatten(T);
    pre_order_recur(T);
    cout << endl;
    in_order_recur(T);
    cout << endl << endl;
    */

    if (true == is_valid_BST(T)) {
        cout << "is valid bst" << endl << endl;
    } else {
        cout << "is not valid bst" << endl << endl;
    }

    return 0;
}