Problem:
Binary Search Tree III

Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

delete $k$: Delete a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:

If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).

If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.

If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ or print are given.

Output

For each find $k$ operation, print "yes" if $T$ has a node containing $k$, "no" if not.

In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key

Constraints

The number of operations $\leq 500,000$

The number of print operations $\leq 10$.

$-2,000,000,000 \leq key \leq 2,000,000,000$

The height of the binary tree does not exceed 100 if you employ the above pseudo code.

The keys in the binary search tree are all different.

Sample Input 1

18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print

Sample Output 1

yes
yes
yes
no
no
no
yes
yes
1 2 3 7 8 22
8 2 1 3 7 22
1 2 8 22
8 2 1 22

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in C (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef struct node {
    int value;
    struct node* parent;
    struct node* left;
    struct node* right;
} Node;

typedef Node* NodePointer;

NodePointer serialize(int val) {
    NodePointer newNode = malloc(sizeof(Node));
    newNode->value = val;
    newNode->parent = NULL;
    newNode->left = NULL;
    newNode->right = NULL;
    return newNode;
}

NodePointer insert(NodePointer node, int val) {
    NodePointer currentNode = node;
    int flag = 0;
    int dir = 0;
    while(!flag) {
        if (currentNode->value > val) {
            if (currentNode->left == NULL) flag = 1;
            else currentNode = currentNode->left;
            dir = 0;
        } else if (currentNode->value < val) {
            if (currentNode->right == NULL) flag = 1;
            else currentNode = currentNode->right;
            dir = 1;
        } else {
            return node;
        }
    }

    if (dir) {
        currentNode->right = serialize(val);
        currentNode->right->parent = currentNode;
    } else {
        currentNode->left = serialize(val);
        currentNode->left->parent = currentNode;
    }

    return node;
}

int search(NodePointer node, int val) {
    NodePointer currentNode = node;
    while(currentNode != NULL) {
        if (currentNode->value == val) {
            return 1;
        } else if (currentNode->value > val) {
            currentNode = currentNode->left;
        } else {
            currentNode = currentNode->right;
        }
    }

    return 0;
}

NodePointer min(NodePointer node) {
    NodePointer currentNode = node;
    int flag = 0;
    while (!flag) {
        if (currentNode->left == NULL) flag = 1;
        else currentNode = currentNode->left;
    }

    return currentNode;
}

NodePointer delete(NodePointer node, int val) {
    NodePointer currentNode = node;
    while(currentNode->value != val) {
        if (currentNode->value > val) {
            if (currentNode->left == NULL) return node;
            currentNode = currentNode->left;
        } if (currentNode->value < val) {
            if (currentNode->right == NULL) return node;
            currentNode = currentNode->right;
        }
    }

    // ノードに子がいない
    if (currentNode->right == NULL && currentNode->left == NULL) {
        if (currentNode->parent->left == currentNode) currentNode->parent->left = NULL;
        else currentNode->parent->right = NULL;
    // ノードの左にだけ子がいる
    } else if (currentNode->right == NULL) {
        if (currentNode->parent->left == currentNode) {
            currentNode->parent->left = currentNode->left;
            currentNode->left->parent = currentNode->parent;
        } else {
            currentNode->parent->right = currentNode->left;
            currentNode->left->parent = currentNode->parent;
        }
    // ノードの右にだけ子がいる
    } else if (currentNode->left == NULL) {
        if (currentNode->parent->left == currentNode) {
            currentNode->parent->left = currentNode->right;
            currentNode->right->parent = currentNode->parent;
        } else {
            currentNode->parent->right = currentNode->right;
            currentNode->right->parent = currentNode->parent;
        } 
    // どちらにも子がいる
    } else {
        NodePointer minPtr = min(currentNode->right);
        if (minPtr->parent->left == minPtr) minPtr->parent->left = NULL;
        else minPtr->parent->right = NULL;
        if (currentNode->parent->left == currentNode) {
            currentNode->parent->left = minPtr;
            minPtr->parent = currentNode->parent;
        } else {
            currentNode->parent->right = minPtr;
            minPtr->parent = currentNode->parent;
        }
        minPtr->left = currentNode->left;
        minPtr->right = currentNode->right;
    }
    free(currentNode); 

    return node;
}

void inorderPrint(NodePointer node) {
    if (node == NULL) return;
    inorderPrint(node->left);
    printf(" %d", node->value);
    inorderPrint(node->right);
}

void preorderPrint(NodePointer node) {
    if (node == NULL) return;
    printf(" %d", node->value);
    preorderPrint(node->left);
    preorderPrint(node->right);
}

void nodePrint(NodePointer node) {
    inorderPrint(node);
    printf("\n");
    preorderPrint(node);
    printf("\n");
}

int main() {
    NodePointer node = NULL;
    int n, m;
    char cmd[16];
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
        scanf("%s", cmd);
        if (!strcmp(cmd, "insert")) {
            scanf("%d", &m);
            if (node == NULL) node = serialize(m);
            else insert(node, m);
        } else if (!strcmp(cmd, "print")) {
            nodePrint(node);
        } else if (!strcmp(cmd, "find")) {
            scanf("%d", &m);
            if (search(node, m)) {
                printf("yes\n");
            } else {
                printf("no\n");
            }
        } else if (!strcmp(cmd, "delete")) {
            scanf("%d", &m);
            delete(node, m);
        }
    }
    return 0;
}