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>

#define UND_NODE -1
#define UND_HEIGHT -1
#define MAX_CMD_LENGTH 10

typedef struct {
//    int id;
    int right;
    int left;
    int parent;
    int height;
} BinaryNode;



int nodeDepthFromId(BinaryNode nodes[], int length, int id) {
    int i = 0;
    while (nodes[id].parent != UND_NODE) {
        i++;
        id = nodes[id].parent;
    }
    return i;
}

int nodeSiblingFromId(BinaryNode nodes[], int length, int id) {
    if (nodes[id].parent == UND_NODE)
        return UND_NODE;
    
    BinaryNode parentNode = nodes[nodes[id].parent];
    
    if (parentNode.left == id && parentNode.right != UND_NODE)
        return parentNode.right;
    
    if (parentNode.right == id && parentNode.left != UND_NODE)
        return parentNode.left;
    
    // no sibling
    return UND_NODE;
}

int constructHeights(BinaryNode nodes[], int length) {
    int i, parentId, heightCount;
    int rootId = 0; // assuming only single root
    
    for (i = 0; i < length; i++) {
        if (nodes[i].left == UND_NODE && nodes[i].right == UND_NODE) {
            nodes[i].height = 0;

            parentId = nodes[i].parent;
            heightCount = 1;
            while (1) {
                if (parentId == UND_NODE) {
                    rootId = parentId;
                    break;
                }
                if (nodes[parentId].height < heightCount)
                    nodes[parentId].height = heightCount;
                

                heightCount++;
                parentId = nodes[parentId].parent;
            }
        }
    }
    
    return rootId;
}

void printArray(int array[], int length) {
    for (int i = 0; i < length; i++) {
        if (i) printf(", ");
        printf("%d", array[i]);
    }
}






struct BSTnode {
    int key;
    struct BSTnode * right;
    struct BSTnode * left;
    struct BSTnode * parent;
    int height;
};

typedef struct BSTnode * Node; // pointer

typedef struct {
    Node root;
} Tree;

Node nodeCreate(int key) {
    Node node = (Node)malloc(sizeof(struct BSTnode));
    node->key = key;
    node->height = UND_HEIGHT;
    node->right = node->left = node->parent = NULL;
    return node;
}

int destory(Node node) {
    int key = node->key;
    free(node);
    return key;
}

int nodeDepth(Node node) {
    int i = 0;
    while (node->parent != NULL) {
        i++;
        node = node->parent;
    }
    return i;
}

Node nodeSibling(Node node) {
    if (node->parent == NULL)	
        return NULL; // NULL POINTER
    
    Node parentNode = node->parent;
    
    if (parentNode->left == node && parentNode->right != NULL)
        return parentNode->right;
    
    if (parentNode->right == node && parentNode->left != NULL)
        return parentNode->left;
    
    // no sibling
    return NULL; // NULL POINTER
}

void treeInsert(Node *p_root, Node newNode) {
    Node nodeParent = NULL;
    Node nodeX = *p_root;

    // find its place
    //- it should be a leaf
    while (nodeX != NULL) {
        nodeParent = nodeX;
        
        if (newNode->key < nodeX->key)
            nodeX = nodeX->left;  // <
        else
            nodeX = nodeX->right; // >=
    }
    newNode->parent = nodeParent;
    

    // put it in as a leaf
    if (nodeParent == NULL)// tree is empty
        *p_root = newNode;
    else if (newNode->key < nodeParent->key) 
        nodeParent->left = newNode;
    else
        nodeParent->right = newNode;
}
Node treeSearch(Node root, int key) {
    if (root == NULL || key == root->key)
        return root;
    
    if (key < root->key)
        return treeSearch(root->left, key);
    else
        return treeSearch(root->right, key);
}

// max and min are HIGHLY DEPENDENT on how we INSERT nodes
Node treeMinimum(Node root) {
    while (root->left != NULL)
        root = root->left;
    return root;
}
Node treeMaxiumum(Node root) {
    while (root->right != NULL)
        root = root->right;
    return root;
}
Node successor(Node node) {
    if (node->right != NULL)
        return treeMinimum(node->right); // case 1
    
    Node parentNode = node->parent;
    while (parentNode != NULL && node == parentNode->right) {
        node = parentNode;
        parentNode = node->parent;
    }
    return parentNode; // case 2
}
void treeDelete(Node root, Node removingNode) {
    Node nodeX, nodeY;
    
    // 
    if (removingNode->left == NULL || removingNode->right == NULL)
        // case no child: delete directly
        nodeY = removingNode;
    else
        // case has child: move up only child or replace with successor
        nodeY = successor(removingNode);
    
    // nodeX be nodeY's child of non-NULL
    if (nodeY->left != NULL)
        nodeX = nodeY->left;
    else
        nodeX = nodeY->right;
    // if nodeX is NULL, this is from case no child
    
    //
    if (nodeX != NULL)
        nodeX->parent = nodeY->parent;
    
    //
    if (nodeY->parent == NULL)
        root = nodeX;
    else if (nodeY == nodeY->parent->left)
        nodeY->parent->left = nodeX;
    else
        nodeY->parent->right = nodeX;
    
    if (nodeY != removingNode) 
        removingNode->key = nodeY->key;
    
//    // destroy malloc after removing from tree
//    free(removingNode);
}

void preParse(Node node) {
    if (node == NULL)
        return;
    
    printf(" %d", node->key);
    preParse(node->left);
    preParse(node->right);
}

void inParse(Node node) {
    if (node == NULL)
        return;
    
    inParse(node->left);
    printf(" %d", node->key);
    inParse(node->right);
}

void postParse(Node node) {
    if (node == NULL)
        return;
    
    postParse(node->left);
    postParse(node->right);
    printf(" %d", node->key);
}






int main(int argc, char** argv) {
    int nCommands;
    scanf("%d", &nCommands);
    
    char command[MAX_CMD_LENGTH];
    
    Node root;
    Node node;
    int i, j, nodeKey;
    
    root = NULL;
    
    for (i = 0; i < nCommands; i++) {
        scanf("%s", command);
        
        if (strcmp(command, "insert") == 0) {
            scanf("%d", &(nodeKey));
            node = nodeCreate(nodeKey);
            treeInsert(&root, node);
        }
        else if (strcmp(command, "find") == 0) {
            scanf("%d", &(nodeKey));
            node = treeSearch(root, nodeKey);
            if (node != NULL)
                printf("yes\n");
            else
                printf("no\n");
        }
        else if (strcmp(command, "delete") == 0) {
            scanf("%d", &(nodeKey));
            node = treeSearch(root, nodeKey);
            treeDelete(root, node);
        }
        else if (strcmp(command, "print") == 0) {
            inParse(root);
            printf("\n");
            preParse(root);
            printf("\n");
        }
    }
    
//    // for height
//    rootId = constructHeights(nodes, nNodes);
    
    

    return (EXIT_SUCCESS);
}