二叉搜索樹詳解（c++）

|| 二叉搜索樹（Binary Search Tree）主要用於搜索和動態排序

|| 二叉搜索樹的基本原理 :

• 左子節點小於自身。
• 右子節點大於自身。
• 所有子節點均遵從第一條規則。

---

C++ code(class):

聲明：

class BTree {
private:
	bool Empty;
	int val;
	BTree* Right;
	BTree* Left;
public:
	BTree() { Empty = true; }
	BTree(BTree& t);
	void Print();
	//void Add(int val_new);  //少用void，好程序用bool 
	bool Add(int val_new);

};

插入：

bool BTree::Add(int val_new) {
	if (Empty == true) {
		Empty = false;
		val = val_new;
		Left = new BTree();
		Right = new BTree();
		return true;
	}
	return (val_new == val) ? false : (val_new < val) ? Left->Add(val_new) : Right->Add(val_new); 

}

查找：

BTree BTree::Search(int num) {
	BTree t;
	if (val == num) { t = BTree(*this); return t; }
	if (Empty == true) { t = BTree(*this); return t; }

	if (val > num) Left-> Search(num);
	if (val < num) Right -> Search(num);

}

刪除

遍歷

void BTree::Print() {
	if (Empty) return;

	cout << val << " ";
	Right->Print();
	Left->Print();

}

---

C++ code(struct):

#include "StdAfx.h"

struct Node {
    int key;
    int value;
    // Node* parent;
    Node* left;
    Node* right;
};

Node* NewNode(int key, int value) {
    Node* p = (Node*)malloc(sizeof(Node));   // 刪除節點時要注意放掉內存
    p->key = key;
    p->value = value;
    // p->parent = parent;
    p->left = NULL;
    p->right = NULL;
    return p;
}

Node** nSearch(Node** n, int key) {
    if (*n == NULL) {
        return n;
    }
    else if (key == (*n)->key) {
        return n;
    }
    else if (key < (*n)->key) {
        return nSearch(&(*n)->left, key);
    }
    else {
        return nSearch(&(*n)->right, key);
    }
}

void nAdd(Node** r, int key, int value) {
    Node** n = nSearch(r, key);
    if (*n == NULL) {
        *n = NewNode(key, value);
    }
    else {
        (*n)->value = value;
    }
}

int nGet(Node** n, int key) {
    Node** result = nSearch(n, key);
    if ((*result) == NULL) {
        return NULL;
    }
    else {
        return (*result)->value;
    }
}

void nWalk(Node* n) {
    if (n == NULL) {
        return;
    }
    if (n->left != NULL) {
        nWalk(n->left);
    }
    printf("%d\n", n->key);
    if (n->right != NULL) {
        nWalk(n->right);
    }
}

Node** nMin(Node** n) {
    if ((*n)->left == NULL) {
        return n;
    }
    else {
        return nMin(&(*n)->left);
    }
}

Node** nSuccessor(Node** n) {
    if ((*n)->right == NULL) {
        return NULL;
    }
    else {
        return nMin(&(*n)->right);
    }
}

int nRemove(Node** n, int key) {
    Node** d = nSearch(n, key);
    if ((*d) == NULL) {
        return -1; // 要刪除的幾點不存在
    }


    if ((*d)->left != NULL && (*d)->right != NULL) {
        Node** suc = nSuccessor(d);
        (*d)->key = (*suc)->key;
        (*d)->value = (*suc)->value;
        return nRemove(suc, (*suc)->key);
    }
    else {
        // 因爲使用二級指針，不在需要判斷要刪除的節點本身是處在左邊還是右邊，因爲指針中已經指向了原始我們要修改的位置。
        Node* d_child;
        if ((*d)->left != NULL) {
            d_child = (*d)->left;
            // d_child->parent = (*d)->parent;
        }
        else if ((*d)->right != NULL) {
            d_child = (*d)->right;
            // d_child->parent = (*d)->parent;
        }
        else {
            d_child = NULL;
        }

        free(*d); 
        // 同樣的，這裏也不再需要判斷是不是根節點
        *d = d_child;
        return 0;
    }
}

int main() {
    int testData[20][2] = {
        {61, 6161},
        {30, 3030},
        {98, 9898},
        {3, 33},
        {36, 3636},
        {30, 3030},
        {6, 66},
        {54, 5454},
        {63, 6363},
        {93, 9393},
        {93, 9393},
        {76, 7676},
        {84, 8484},
        {16, 1616},
        {13, 1313},
        {76, 7676},
        {78, 7878},
        {29, 2929},
        {9, 99},
        {76, 7676}
    };

    Node* root = NULL;
    Node** rootP = &root;

    int i;
    for (i = 0; i < 20; i++) {
        nAdd(rootP, testData[i][0], testData[i][1]);
    }
    nWalk(root);

    for (i = 0; i < 20; i++) {
        nRemove(rootP, testData[i][0]);
    }
    printf("\n\n");
    nWalk(root);

    return 0;
}

---

Python code:

class Node(object):
    def __init__(self, key, data, parent=None):
        self.key = key
        self.data = data
        self.parent = parent
        self.left = None
        self.right = None

    def add_child(self, key, data):
        if key == self.key:
            self.data = data
            return
        elif key < self.key:
            if self.left is None:
                self.left = Node(key, data, self)
            else:
                self.left.add_child(key, data)
        else:
            if self.right is None:
                self.right = Node(key, data, self)
            else:
                self.right.add_child(key, data)

    def get(self, key):
        if key == self.key:
            return self
        elif key < self.key:
            if self.left is None:
                return None
            else:
                return self.left.get(key)
        else:
            if self.right is None:
                return None
            else:
                return self.right.get(key)

    def get_data(self, key):
        r = self.get(key)
        if r is None:
            return None
        else:
            return r.data

    def in_order_walk(self):
        if self.left is not None:
            self.left.in_order_walk()
        print(self.key)
        if self.right is not None:
            self.right.in_order_walk()

    def get_max(self):
        if self.right is None:
            return self
        else:
            return self.right.get_max()

    def get_min(self):
        if self.left is None:
            return self
        else:
            return self.left.get_min()

    def predecessor(self):
        if self.left is not None:
            return self.left.get_max()
        else:
            return None

    def successor(self):
        if self.right is not None:
            return self.right.get_min()
        else:
            return None

    def remove(self, key):
        d = self.get(key)

        if not d.left and not d.right:
            if d.parent is None:
                # self = None
                return
            elif d.parent.left == d:
                d.parent.left = None
            else:
                d.parent.right = None
        elif bool(d.left) is not bool(d.right):
            if d.left:
                if d.parent.left == d:
                    d.parent.left = d.left
                    d.left.parent = d.parent
                else:
                    d.parent.right = d.left
                    d.left.parent = d.parent
            else:
                if d.parent.right == d:
                    d.parent.right = d.right
                    d.right.parent = d.parent
                else:
                    d.parent.left = d.right
                    d.right.parent = d.parent
        else:
            successor = d.successor()
            d.key = successor.key
            d.data = successor.data
            successor.remove(successor.key)


class Tree(object):
    def __init__(self, root):
        self.root = root

    def remove(self, key):
        d = self.root.get(key)
        if d.left and d.right:
            successor = d.successor()
            d.key = successor.key
            d.data = successor.data
            d = successor
        else:
            pass

        if d.left:
            d_child = d.left
            d_child.parent = d.parent
        elif d.right:
            d_child = d.right
            d_child.parent = d.parent
        else:
            d_child = None

        if d.parent:
            if d.parent.left == d:
                d.parent.left = d_child
            else:
                d.parent.right = d_child
        else:
            self.root = None

    def in_order_walk(self):
        if self.root:
            self.root.in_order_walk()
        else:
            print(None)

    def __getattr__(self, item):
        return getattr(self.root, item)

def main():
    data_list = [
        [20, 2222],
        [30, 3333],
        [40, 4444],
        [50, 5555],
        [60, 6666],
        [70, 7777],
        [80, 8888],
        [90, 9999],
    ]
    middle = data_list[5]
    tree = Tree(Node(middle[0], middle[1]))
    for i in data_list:
        tree.root.add_child(i[0], i[1])
    tree.add_child(1, 111)
    tree.remove(70)
    tree.in_order_walk()


if __name__ == '__main__':
    main()

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參考：https://www.jianshu.com/p/6e05da24905b