# 目次

二分探索木とは、すべてのノードが子を最大２つまで持つような木で、かつノードの挿入・検索・削除ができるような木.

# 木の表現

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <math.h>

#define ll long long
#define Int int
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define rep(n) for(int x = 0; x < n; x++)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

struct Node {
    int key;
    Node *parent, *left, *right;
}

Node *root, *NIL;

# ノードの追加

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <math.h>

#define ll long long
#define Int int
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define rep(n) for(int x = 0; x < n; x++)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

void insert(int key) {
    Node *x = root;
    Node *y = NIL;
    Node *z = (Node *)malloc(sizeof(Node));

    z->key = key;
    z->left = NIL; z->right = NIL;

    while (x != NIL) {
        y = x;
        if (key < x->key) {
            x = x->left;
        } else {
            x = x->right;
        }
    }

    if (y == NIL) {
        root = z;
        return;
    }

    z->parent = y;
    if (key < y->key) {
        y->left =z;
    } else {
        y->right = z;
    }
}

# 走査

先行順序（自身→左→右）での走査.

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <math.h>

#define ll long long
#define Int int
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define rep(n) for(int x = 0; x < n; x++)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

void preorder(Node *node) {
    if (node == NIL) return;
    cout << " " << node->key;
    preorder(node->left);
    preorder(node->right);
}

# 検索

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <math.h>

#define ll long long
#define Int int
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define rep(n) for(int x = 0; x < n; x++)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

bool find(Node *node, int key) {
    Node* cur = node;
    while (cur != NIL && cur->key != key) {
        if (key < cur->key) {
            cur = cur->left;
        } else {
            cur = cur->right;
        }
    }

    return cur != NIL;
}

# 削除

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <math.h>

#define ll long long
#define Int int
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define rep(n) for(int x = 0; x < n; x++)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

void tDelete(Node *z) {
    Node *y, *x;
    
    if (z->left == NIL || z->right == NIL) y = z;
    else y = tSuccessor(z);
    
    if (y->left != NIL) {
        x = y->left;
    } else {
        x = y->right;
    }
    
    if (x != NIL) {
        x->parent = y->parent;
    }
    
    if (y->parent == NIL) {
        root = x;

    } else {
        if (y == y->parent->left) {
            y->parent->left = x;
        } else {
            y->parent->right = x;
        }
    }
    
    if (y != z) {
        z->key = y->key;
    }

    free(y);
}

二分探索木

# 目次

# 木の表現

# ノードの追加

# 走査

# 検索

# 削除

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