Data Structures 12 - Binary Tree Construction and Traversal

Code

#include <stdio.h>
#include <malloc.h>
#include <stdbool.h>

#define QUEUE_SIZE 5 // Define queue size

typedef struct BTNode{
    char element; // Element stored in the node
    struct BTNode* left; // Left child pointer
    struct BTNode* right; // Right child pointer
} BTNode, *BTNodePtr;

typedef struct BTNodePtrQueue{
    BTNodePtr* nodePtrs; // Array storing node pointers
    int front; // Queue front index
    int rear; // Queue rear index
} BTNodePtrQueue, *QueuePtr;

// Initialize the queue
QueuePtr initQueue(){
    QueuePtr resultQueuePtr = (QueuePtr)malloc(sizeof(struct BTNodePtrQueue));
    resultQueuePtr->nodePtrs = (BTNodePtr*)malloc(QUEUE_SIZE * sizeof(BTNodePtr));
    resultQueuePtr->front = 0;
    resultQueuePtr->rear = 1;
    return resultQueuePtr;
}

// Check if the queue is empty
bool isQueueEmpty(QueuePtr paraQueuePtr){
    if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
        return true;
    }
    return false;
}

// Enqueue operation
void enqueue(QueuePtr paraQueuePtr, BTNodePtr paraBTNodePtr){
    printf("front = %d, rear = %d.\r\n", paraQueuePtr->front, paraQueuePtr->rear);
    if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
        printf("Error, trying to enqueue %c. queue full.\r\n", paraBTNodePtr->element);
        return;
    }
    paraQueuePtr->nodePtrs[paraQueuePtr->rear] = paraBTNodePtr;
    paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
    printf("enqueue %c ends.\r\n", paraBTNodePtr->element);
}

// Dequeue operation
BTNodePtr dequeue(QueuePtr paraQueuePtr){
    if (isQueueEmpty(paraQueuePtr)) {
        printf("Error, empty queue\r\n");
        return NULL;
    }
    paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
    printf("dequeue %c ends.\r\n", paraQueuePtr->nodePtrs[paraQueuePtr->front]->element);
    return paraQueuePtr->nodePtrs[paraQueuePtr->front];
}

// Construct a new node
BTNodePtr constructBTNode(char paraChar){
    BTNodePtr resultPtr = (BTNodePtr)malloc(sizeof(BTNode));
    resultPtr->element = paraChar;
    resultPtr->left = NULL;
    resultPtr->right = NULL;
    return resultPtr;
}

// Convert a string to a binary tree
BTNodePtr stringToBTree(char* paraString){
    int i;
    char ch;
    QueuePtr tempQueuePtr = initQueue();
    BTNodePtr resultHeader;
    BTNodePtr tempParent, tempLeftChild, tempRightChild;
    i = 0;
    ch = paraString[i];
    resultHeader = constructBTNode(ch);
    enqueue(tempQueuePtr, resultHeader);

    while(!isQueueEmpty(tempQueuePtr)) {
        tempParent = dequeue(tempQueuePtr);
        i++;
        ch = paraString[i];
        if (ch == '#') {
            tempParent->left = NULL;
        } else {
            tempLeftChild = constructBTNode(ch);
            enqueue(tempQueuePtr, tempLeftChild);
            tempParent->left = tempLeftChild;
        }
        i++;
        ch = paraString[i];
        if (ch == '#') {
            tempParent->right = NULL;
        } else {
            tempRightChild = constructBTNode(ch);
            enqueue(tempQueuePtr, tempRightChild);
            tempParent->right = tempRightChild;
        }
    }
    return resultHeader;
}

// Level-order traversal of the binary tree
void levelwise(BTNodePtr paraTreePtr){
    char tempString[100];
    int i = 0;
    QueuePtr tempQueuePtr = initQueue();
    BTNodePtr tempNodePtr;
    enqueue(tempQueuePtr, paraTreePtr);
    while(!isQueueEmpty(tempQueuePtr)) {
        tempNodePtr = dequeue(tempQueuePtr);
        tempString[i] = tempNodePtr->element;
        i++;
        if (tempNodePtr->left != NULL){
            enqueue(tempQueuePtr, tempNodePtr->left);
        }
        if (tempNodePtr->right != NULL){
            enqueue(tempQueuePtr, tempNodePtr->right);
        }
    }
    tempString[i] = '\0';
    printf("Levelwise: %s\r\n", tempString);
}

// Preorder traversal of the binary tree
void preorder(BTNodePtr tempPtr){
    if (tempPtr == NULL){
        return;
    }
    printf("%c", tempPtr->element);
    preorder(tempPtr->left);
    preorder(tempPtr->right);
}

// Inorder traversal of the binary tree
void inorder(BTNodePtr tempPtr){
    if (tempPtr == NULL) {
        return;
    }
    inorder(tempPtr->left);
    printf("%c", tempPtr->element);
    inorder(tempPtr->right);
}

// Postorder traversal of the binary tree
void postorder(BTNodePtr tempPtr){
    if (tempPtr == NULL) {
        return;
    }
    postorder(tempPtr->left);
    postorder(tempPtr->right);
    printf("%c", tempPtr->element);
}

int main(){
    BTNodePtr tempHeader;
    tempHeader = constructBTNode('c');
    printf("There is only one node. Preorder visit: ");
    preorder(tempHeader);
    printf("\r\n");

    char* tempString = "acde#bf######";

    tempHeader = stringToBTree(tempString);
    printf("Preorder: ");
    preorder(tempHeader);
    printf("\r\n");
    printf("Inorder: ");
    inorder(tempHeader);
    printf("\r\n");
    printf("Postorder: ");
    postorder(tempHeader);
    printf("\r\n");
    printf("Levelwise: ");
    levelwise(tempHeader);
    printf("\r\n");

    return 1;
}

Code Summary

This code implements a simple binary tree and its traversal operations, mainly including the following features:

1. Binary tree node and queue definitions:

   • The BTNode structure defines a binary tree node, where each node contains a character element and left/right child pointers.
   • The BTNodePtrQueue structure defines a queue for storing binary tree node pointers, to implement level-order traversal.

2. Queue operations:

   • The initQueue function initializes a new queue.
   • The isQueueEmpty function checks if the queue is empty.
   • The enqueue function enqueues a binary tree node pointer.
   • The dequeue function dequeues a binary tree node pointer.

3. Binary tree node construction and string-to-binary-tree conversion:

   • The constructBTNode function creates a new binary tree node.
   • The stringToBTree function converts a string to a binary tree. Each character in the string represents a node, and # represents an empty node.

4. Binary tree traversal:

   • The levelwise function implements level-order traversal of the binary tree, using a queue to track nodes at the current level and output them level by level.
   • The preorder function implements preorder traversal.
   • The inorder function implements inorder traversal.
   • The postorder function implements postorder traversal.

5. Main function:

   • In the main function, a single-node tree is created first and its preorder traversal result is output.
   • Then the string "acde#bf######" is converted to a binary tree, and the preorder, inorder, postorder, and level-order traversal results are output.

Running Result

There is only one node. Preorder visit: c
front = 0, rear = 1.
enqueue a ends.
dequeue a ends.
front = 1, rear = 2.
enqueue c ends.
front = 1, rear = 3.
enqueue d ends.
dequeue c ends.
front = 2, rear = 4.
enqueue e ends.
dequeue d ends.
front = 3, rear = 0.
enqueue b ends.
front = 3, rear = 1.
enqueue f ends.
dequeue e ends.
dequeue b ends.
dequeue f ends.
Preorder: acedbf
Inorder: ecabdf
Postorder: ecbfda
Levelwise: front = 0, rear = 1.
enqueue a ends.
dequeue a ends.
front = 1, rear = 2.
enqueue c ends.
front = 1, rear = 3.
enqueue d ends.
dequeue c ends.
front = 2, rear = 4.
enqueue e ends.
dequeue d ends.
front = 3, rear = 0.
enqueue b ends.
front = 3, rear = 1.
enqueue f ends.
dequeue e ends.
dequeue b ends.
dequeue f ends.
Levelwise: acdebf
 
 
 
...Program finished with exit code 1
Press ENTER to exit console.