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>

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

void pre(struct Node *T, int h) {
    if (h == -1) return;
    printf(" %d", T[h].key);
    pre(T, T[h].left);
    pre(T, T[h].right);
}
void in(struct Node *T, int h) {
    if (h == -1) return;
    in(T, T[h].left);
    printf(" %d", T[h].key);
    in(T, T[h].right);
}


int find(struct Node *T, int k, int h) {
    int x = h;
    while (x != -1) {
        if (k == T[x].key) break;
        else if (k < T[x].key) x = T[x].left;
        else x = T[x].right;
    }
    return x;
}

int main(void) {
    int m, n, i, h = -1;
    char command[10];
    scanf("%d", &m);
    struct Node *T = malloc(sizeof(struct Node) * m);
    for (i = 0; i < m; i++) {
        T[i].parent = -1;
        T[i].left = T[i].right = -1;
    }
    for (i = 0; i < m; i++) {
        scanf("%s", command);
        if (command[0] == 'i') {
            int x = h, y = -1, z;
            scanf("%d", &z);
            T[i].key = z;
            while (x != -1) {
                y = x;
                if (z < T[x].key) x = T[x].left;
                else x = T[x].right;
            }
            T[i].parent = y;
            if (y == -1) h = i;
            else if (z < T[y].key) T[y].left = i;
            else T[y].right = i;
        }
        else if (command[0] == 'f') {
            int x, k;
            scanf("%d", &k);
            x = find(T, k, h);
            if (x != -1) printf("yes\n");
            else printf("no\n");
        }
        else if (command[0] == 'd') {
            int x, k;
            scanf("%d", &k);
            x = find(T, k, h);
            if (x == h) {
                if (T[x].left == -1 && T[x].right == -1) {
                    h = -1;
                    T[x].parent = T[x].left = T[x].right = -1;
                }
                else if (T[x].left == -1 && T[x].right != -1) {
                    h = T[x].right;
                    T[h].parent = -1;
                    T[x].parent = T[x].left = T[x].right = -1;
                }
                else if (T[x].right == -1 && T[x].left != -1) {
                    h = T[x].left;
                    T[h].parent = -1;
                    T[x].parent = T[x].left = T[x].right = -1;
                }
                else {
                    int l = T[x].right;
                    while (T[l].left != -1) l = T[l].left;
                    T[x].key = T[l].key;

                    if (T[l].right == -1) {
                        int p = T[l].parent;
                        if (T[p].left == l) T[p].left = -1;
                        else T[p].right = -1;
                        T[l].parent = T[l].left = T[l].right = -1;
                    }
                    else {
                        int p = T[l].parent;
                        if (T[p].left == l) T[p].left = T[l].right;
                        else T[p].right = T[l].right;
                        T[T[l].right].parent = p;
                        T[l].parent = T[l].left = T[l].right = -1;
                    }
                }
            }
            else if (x != -1) {
                if (T[x].left == -1 && T[x].right == -1) {
                    int p = T[x].parent;
                    if (T[p].left == x) T[p].left = -1;
                    else T[p].right = -1;
                    T[x].parent = T[x].left = T[x].right = -1;
                }
                else if (T[x].left == -1 && T[x].right != -1) {
                    int p = T[x].parent;
                    if (T[p].left == x) T[p].left = T[x].right;
                    else T[p].right = T[x].right;
                    T[T[x].right].parent = p;
                    T[x].parent = T[x].left = T[x].right = -1;
                }
                else if (T[x].right == -1 && T[x].left != -1) {
                    int p = T[x].parent;
                    if (T[p].left == x) T[p].left = T[x].left;
                    else T[p].right = T[x].left;
                    T[T[x].left].parent = p;
                    T[x].parent = T[x].left = T[x].right = -1;
                }
                else {
                    int l = T[x].right;
                    while (T[l].left != -1) l = T[l].left;
                    T[x].key = T[l].key;

                    if (T[l].right == -1) {
                        int p = T[l].parent;
                        if (T[p].left == l) T[p].left = -1;
                        else T[p].right = -1;
                        T[l].parent = T[l].left = T[l].right = -1;
                    }
                    else {
                        int p = T[l].parent;
                        if (T[p].left == l) T[p].left = T[l].right;
                        else T[p].right = T[l].right;
                        T[T[l].right].parent = p;
                        T[l].parent = T[l].left = T[l].right = -1;
                    }
                }
            }

        }
        else if (command[0] == 'p') {
            in(T, h);
            printf("\n");
            pre(T, h);
            printf("\n");
        }
    }

    return 0;
}