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There are basically two ways of traversing a binary tree
1. Depth First Traversals
2. Breadth First Traversal
Depth First Traversal
A binary tree can be traversed in three ways using the depth first approach namely
1. Inorder Traversal
template <typename T>
void BTTraveller<T>::inOrder(BSTNode<T> *node, std::deque<T> &out)
{
if(node)
{
inOrder(node->left, out);
out.push_back(node->key);
inOrder(node->right, out);
}
}
2. Preorder Traversal
template <typename T>
void BTTraveller<T>::preOrder(BSTNode<T> *node, std::deque<T> &out)
{
if(node)
{
out.push_back(node->key);
preOrder(node->left, out);
preOrder(node->right, out);
}
}
3. Postorder Traversal
template <typename T>
void BTTraveller<T>::postOrder(BSTNode<T> *node, std::deque<T> &out)
{
if(node)
{
postOrder(node->left, out);
postOrder(node->right, out);
out.push_back(node->key);
}
}
Breadth First Traversal
There is only one kind of Breadth first traversal viz. Level Order traversal. This traversal does not move along the branches of the tree but makes use of a FIFO queue. In the sample code, I have used std::deque as the helper queue for achieving the same.
template <typename T>
void BTTraveller<T>::levelOrder(BST<T> *bstree, std::deque<T> &out)
{
std::deque<BSTNode<T>*> hQ;
hQ.push_back(bstree->m_root);
levelOrder(hQ, out);
}
template <typename T>
void BTTraveller<T>::levelOrder(std::deque<BSTNode<T>*> &hQ, std::deque<T> &out)
{
while(hQ.empty() == false)
{
BSTNode<T> *current = hQ.front();
if(current != NULL)
{
hQ.pop_front();
out.push_back(current->key);
addChildren(current, hQ);
}
}
}
The BTTraveller class takes care of returning Binary Tree node elements in the order you are traversing the tree.
1 #ifndef _BTTraveller_H_
2 #define _BTTraveller_H_
3 #include "BSTNode.h"
4 #include <deque>
5
6
7 namespace algorithms
8 {
9 template <typename T>
10 class BTTraveller
11 {
12 public:
13 static void inOrder(BST<T> *bstree, std::deque<T> &elems);
14 static void preOrder(BST<T> *bstree, std::deque<T> &elems);
15 static void postOrder(BST<T> *bstree, std::deque<T> &elems);
16 static void levelOrder(BST<T> *bstree, std::deque<T> &elems);
17
18 private:
19 static void inOrder(BSTNode<T> *node, std::deque<T> &elems);
20 static void preOrder(BSTNode<T> *node, std::deque<T> &elems);
21 static void postOrder(BSTNode<T> *node, std::deque<T> &elems);
22 static void levelOrder(std::deque<BSTNode<T>*> &helperQ, std::deque<T> &elems);
23 static void addChildren(BSTNode<T> *node, std::deque<BSTNode<T>*> &helperQ);
24
25 BTTraveller();
26 BTTraveller(const BTTraveller&);
27 const BTTraveller& operator=(const BTTraveller&);
28 };
29 };
30
31 #include "BTTraveller.hpp"
32 #endif
1
2 namespace algorithms
3 {
4 template <typename T>
5 void BTTraveller<T>::inOrder(BST<T> *bstree, std::deque<T> &out)
6 {
7 inOrder(bstree->m_root, out);
8 }
9
10 template <typename T>
11 void BTTraveller<T>::preOrder(BST<T> *bstree, std::deque<T> &out)
12 {
13 preOrder(bstree->m_root, out);
14 }
15
16 template <typename T>
17 void BTTraveller<T>::postOrder(BST<T> *bstree, std::deque<T> &out)
18 {
19 postOrder(bstree->m_root, out);
20 }
21
22 template <typename T>
23 void BTTraveller<T>::levelOrder(BST<T> *bstree, std::deque<T> &out)
24 {
25 std::deque<BSTNode<T>*> hQ;
26 hQ.push_back(bstree->m_root);
27 levelOrder(hQ, out);
28 }
29
30 template <typename T>
31 void BTTraveller<T>::inOrder(BSTNode<T> *node, std::deque<T> &out)
32 {
33 if(node)
34 {
35 inOrder(node->left, out);
36 out.push_back(node->key);
37 inOrder(node->right, out);
38 }
39 }
40
41 template <typename T>
42 void BTTraveller<T>::preOrder(BSTNode<T> *node, std::deque<T> &out)
43 {
44 if(node)
45 {
46 out.push_back(node->key);
47 preOrder(node->left, out);
48 preOrder(node->right, out);
49 }
50 }
51
52 template <typename T>
53 void BTTraveller<T>::postOrder(BSTNode<T> *node, std::deque<T> &out)
54 {
55 if(node)
56 {
57 postOrder(node->left, out);
58 postOrder(node->right, out);
59 out.push_back(node->key);
60 }
61 }
62
63 template <typename T>
64 void BTTraveller<T>::levelOrder(std::deque<BSTNode<T>*> &hQ, std::deque<T> &out)
65 {
66 while(hQ.empty() == false)
67 {
68 BSTNode<T> *current = hQ.front();
69 if(current != NULL)
70 {
71 hQ.pop_front();
72 out.push_back(current->key);
73 addChildren(current, hQ);
74 }
75 }
76 }
77
78 template <typename T>
79 void BTTraveller<T>::addChildren(BSTNode<T> *node, std::deque<BSTNode<T>*> &hQ)
80 {
81 if(node->left != NULL)
82 {
83 hQ.push_back(node->left);
84 }
85 if(node->right != NULL)
86 {
87 hQ.push_back(node->right);
88 }
89 }
90 }
You need to include BTTraveller class as a friend class in both the BSTNode as well as BST class declarations. This ensures that the BTTraveller class has access to private data members of these two classes
The BSTNode class
1 #ifndef _BSTNode_H_
2 #define _BSTNode_H_
3 #include <iostream>
4
5
6 namespace algorithms
7 {
8 template <typename T>
9 class BST;
10
11 template <typename T>
12 class BTTraveller;
13
14 template <typename T>
15 class BSTNode
16 {
17 public:
18 BSTNode(T key);
19 ~BSTNode();
20
21 friend class BST<T>;
22 friend class BTTraveller<T>;
23
24 private:
25 BSTNode<T> *left;
26 BSTNode<T> *right;
27 T key;
28 };
29 };
30
31 #include "BSTNode.hpp"
32 #endif
The BST class
1 #ifndef _BinarySearchTree_H_
2 #define _BinarySearchTree_H_
3 #include "BSTNode.h"
4
5
6 namespace algorithms
7 {
8 template <typename T>
9 class BTTraveller;
10
11 template <typename T>
12 class BST
13 {
14 public:
15 BST();
16 ~BST();
17
18
19 void insert(T key);
20 void remove(T key);
21 void clear();
22
23
24 bool find(T key);
25 bool isEmpty() const;
26
27 friend class BTTraveller<T>;
28
29 private:
30 void remove(BSTNode<T> **node);
31 void clear(BSTNode<T> *node);
32 BSTNode<T>** find(BSTNode<T> **node, const T key);
33 BSTNode<T>** getSuccessor(BSTNode<T> **node);
34 BSTNode<T>* getNewNode(T key);
35
36
37 BSTNode<T> *m_root;
38 };
39 };
40
41 #include "BST.hpp"
42 #endif
The BSTNode.hpp and BST.hpp files remains the same as in the post
The Client Program
1 #include "BST.h"
2 #include "BTTraveller.h"
3 #define MAX 20
4 using namespace algorithms;
5
6
7
8 template <typename T>
9 void DumpDeque(std::deque<T> &q)
10 {
11 std::cout << std::endl;
12 std::deque<T>::const_iterator itr;
13 for(itr = q.cbegin(); itr != q.cend(); ++itr)
14 {
15 std::cout << *itr << " ";
16 }
17 std::cout << std::endl;
18 q.clear();
19 }
20
21 int main(int argc, char *argv[])
22 {
23 int nodes[MAX] = { 50, 40, 60, 70, 80, 20, 30, 10, 90, 15, 35, 65, 75, 5, 1, 100, 110, 130, 120, 111 };
24 BST<int> bstInt;
25 for(int i = 0; i < MAX; ++i)
26 {
27 bstInt.insert(nodes[i]);
28 }
29
30 std::deque<int> elems;
31 BTTraveller<int>::inOrder(&bstInt, elems);
32 DumpDeque(elems);
33 BTTraveller<int>::preOrder(&bstInt, elems);
34 DumpDeque(elems);
35 BTTraveller<int>::postOrder(&bstInt, elems);
36 DumpDeque(elems);
37 BTTraveller<int>::levelOrder(&bstInt, elems);
38 DumpDeque(elems);
39
40 return 0;
41 }
Output
$ ./BinarySearchTree.exe
1 5 10 15 20 30 35 40 50 60 65 70 75 80 90 100 110 111 120 130
50 40 20 10 5 1 15 30 35 60 70 65 80 75 90 100 110 130 120 111
1 5 15 10 35 30 20 40 65 75 111 120 130 110 100 90 80 70 60 50
50 40 60 20 70 10 30 65 80 5 15 35 75 90 1 100 110 130 120 111
Read more ...
A Binary Tree is a tree where each node may have 0, 1 or 2 children and a Binary Search Tree is a binary tree with a special property that the value of node under discussion is less than all the nodes in its right subtree and greater than all the nodes in its left subtree.
The programs below describes the three basic operations in a binary search tree viz. search, insert and remove
1. Searching a node
template <typename T>
BSTNode<T>** BST<T>::find(BSTNode<T> **node, const T key)
{
if(*node == NULL || (*node)->key == key)
{
return node;
}
else if((*node)->key > key)
{
return find(&(*node)->left, key);
}
else
{
return find(&(*node)->right, key);
}
}
2. Inserting a node
template <typename T>
void BST<T>::insert(T key)
{
BSTNode<T> **node = find(&m_root, key);
if(*node == NULL)
{
*node = getNewNode(key);
}
}
3. Removing a node
Removing a node from binary search tree is the trickiest of all the operations. There are three cases to be considered when removing a node from a binary search tree:
Case 1. If both left and right child are null, the node can simply be deleted.
Case 2. If only one of the right child or left child is null, the address of the node is set to point to the left child or the right child which ever is not null and the current node is deleted.
Case 3. The complex of the three cases, if both left and right child are present. This requires finding the successor of the current node which is to be removed.
template <typename T>
void BST<T>::remove(BSTNode<T> **node)
{
BSTNode<T> *old = *node;
if((*node)->left == NULL)
{
*node = (*node)->right;
delete old;
}
else if((*node)->right == NULL)
{
*node = (*node)->left;
delete old;
}
else
{
BSTNode<T> **successor = getSuccessor(node);
(*node)->key = (*successor)->key;
remove(successor);
}
}
Following is the complete example showing the implementation details of the search, find and remove operations in a binary search tree.
The BST Node Class
1 #ifndef _BSTNode_H_
2 #define _BSTNode_H_
3 #include <iostream>
4
5
6 namespace algorithms
7 {
8 template <typename T>
9 class BST;
10
11 template <typename T>
12 class BSTNode
13 {
14 public:
15 BSTNode(T key);
16 ~BSTNode();
17
18 friend class BST<T>;
19
20 private:
21 BSTNode<T> *left;
22 BSTNode<T> *right;
23 T key;
24 };
25 };
26
27 #include "BSTNode.hpp"
28 #endif
1
2 namespace algorithms
3 {
4 template <typename T>
5 BSTNode<T>::BSTNode(T key) : left(0), right(0)
6 {
7 this->key = key;
8 }
9
10 template <typename T>
11 BSTNode<T>::~BSTNode()
12 {
13 }
14 }
15
The Binary Search Tree Class
1 #ifndef _BinarySearchTree_H_
2 #define _BinarySearchTree_H_
3 #include "BSTNode.h"
4
5
6 namespace algorithms
7 {
8 template <typename T>
9 class BST
10 {
11 public:
12 BST();
13 ~BST();
14
15
16 void insert(T key);
17 void remove(T key);
18 void clear();
19
20
21 bool find(T key);
22 bool isEmpty() const;
23
24 private:
25 void remove(BSTNode<T> **node);
26 void clear(BSTNode<T> *node);
27 BSTNode<T>** find(BSTNode<T> **node, const T key);
28 BSTNode<T>** getSuccessor(BSTNode<T> **node);
29 BSTNode<T>* getNewNode(T key);
30
31
32 BSTNode<T> *m_root;
33 };
34 };
35
36 #include "BST.hpp"
37 #endif
1
2 namespace algorithms
3 {
4 template <typename T>
5 BST<T>::BST()
6 {
7 m_root = 0;
8 }
9
10 template <typename T>
11 BST<T>::~BST()
12 {
13 clear();
14 }
15
16 template <typename T>
17 void BST<T>::clear()
18 {
19 clear(m_root);
20 }
21
22 template <typename T>
23 void BST<T>::clear(BSTNode<T> *node)
24 {
25 if(node != NULL)
26 {
27 clear(node->left);
28 clear(node->right);
29 delete node;
30 }
31 }
32
33 template <typename T>
34 void BST<T>::insert(T key)
35 {
36 BSTNode<T> **node = find(&m_root, key);
37 if(*node == NULL)
38 {
39 *node = getNewNode(key);
40 }
41 }
42
43 template <typename T>
44 void BST<T>::remove(T key)
45 {
46 BSTNode<T> **node = find(&m_root, key);
47 remove(node);
48 }
49
50 template <typename T>
51 void BST<T>::remove(BSTNode<T> **node)
52 {
53 BSTNode<T> *old = *node;
54 if((*node)->left == NULL)
55 {
56 *node = (*node)->right;
57 delete old;
58 }
59 else if((*node)->right == NULL)
60 {
61 *node = (*node)->left;
62 delete old;
63 }
64 else
65 {
66 BSTNode<T> **successor = getSuccessor(node);
67 (*node)->key = (*successor)->key;
68 remove(successor);
69 }
70 }
71
72 template <typename T>
73 BSTNode<T>** BST<T>::getSuccessor(BSTNode<T> **node)
74 {
75 BSTNode<T> **tmp = &(*node)->left;
76 while((*tmp)->right != NULL)
77 {
78 tmp = &(*tmp)->right;
79 }
80 return tmp;
81 }
82
83 template <typename T>
84 bool BST<T>::find(const T key)
85 {
86 BSTNode<T> **pos = find(&m_root, key);
87 return *pos != NULL;
88 }
89
90 template <typename T>
91 bool BST<T>::isEmpty() const
92 {
93 return m_root == 0;
94 }
95
96 template <typename T>
97 BSTNode<T>** BST<T>::find(BSTNode<T> **node, const T key)
98 {
99 if(*node == NULL || (*node)->key == key)
100 {
101 return node;
102 }
103 else if((*node)->key > key)
104 {
105 return find(&(*node)->left, key);
106 }
107 else
108 {
109 return find(&(*node)->right, key);
110 }
111 }
112
113 template <typename T>
114 BSTNode<T>* BST<T>::getNewNode(T key)
115 {
116 BSTNode<T> *node = new BSTNode<T>(key);
117 if(node == NULL)
118 {
119 std::cerr << "ERROR: Insufficient Memory";
120 std::cerr << std::endl;
121 }
122 return node;
123 }
124 }
The Client Program for testing the BST code above
1 #include "BST.h"
2 #define MAX 20
3 using namespace algorithms;
4
5
6 int main(int argc, char *argv[])
7 {
8 int nodes[MAX] = { 50, 40, 60, 70, 80, 20, 30, 10, 90, 15, 35, 65, 75, 5, 1, 100, 110, 130, 120 };
9 BST<int> bstInt;
10 for(int i = 0; i < MAX; ++i)
11 {
12 bstInt.insert(nodes[i]);
13 }
14
15 std::cout << (bstInt.find(130) ? "true" : "false");
16 bstInt.remove(50);
17 std::cout << (bstInt.find(50) ? "true" : "false");
18
19 return 0;
20 }
Output of the run
$ ./BinarySearchTree.exe
truefalse
Read more ...
Static library is a group of object files bundled together in an archive by the archiver program. The static libraries have a .a extension.
Advantages
1. The executable is not dependent on any library as the library code is included in the binary
2. In some cases performance improvement Command for creating a static library
ar rcs -o libmylibrary.a file1.o file2.o file3.o
Steps for generating the static library libemployee.a for the Employee Program written in the previous post
1. Compiling source files to object files
g++ -Wall -c -fPIC -O -I. -o Employee.o Employee.cpp 2. Command for building the archive file libemployee.a
ar -rcs -o libemployee.a Employee.o
Read more ...
A shared library is a library required by an executable to run properly. Such executables are called incomplete executables as they call routines present in the shared library code. The executables generated from the shared library are smaller in size than the ones generated from a static library
When an executable built with shared library is run, the dynamic loader identifies the list of dependent libraries to be loaded and searches for them in the standard default locations and the locations pointed to by the environment variable LD_LIBRARY_PATH (Linux), SHLIB_PATH (HP-UX), LIBPATH (AIX)
Shown below is the Employee class which we will use to generate the shared library libemployee.so
1 #ifndef _Employee_H_
2 #define _Employee_H_
3
4
5
6 #include <iostream>
7
8 class Employee
9 {
10 public:
11 Employee();
12 Employee(const std::string name, int age);
13 virtual ~Employee();
14
15
16 void setName(const std::string name);
17 void setAge(int age);
18
19
20 const char* getName() const;
21 int getAge() const;
22
23 private:
24 std::string m_name;
25 int m_age;
26 };
27
28 #endif
1 #include "Employee.h"
2
3
4 Employee::Employee()
5 {
6 }
7
8 Employee::Employee(const std::string name, int age)
9 {
10 m_name = name;
11 m_age = age;
12 }
13
14 Employee::~Employee()
15 {
16 }
17
18 void Employee::setName(const std::string name)
19 {
20 m_name = name;
21 }
22
23 void Employee::setAge(int age)
24 {
25 m_age = age;
26 }
27
28 const char* Employee::getName() const
29 {
30 return m_name.c_str();
31 }
32
33 int Employee::getAge() const
34 {
35 return m_age;
36 }
Compiling the Employee source files to object files g++ -Wall -c -fPIC -O -I. -o Employee.o Employee.cpp
Linking the object files to generate the shared library libemployee.so gcc -o libemployee.so Employee.o -shared -fPIC -Wl,-rpath,. -L. -lstdc++
Read more ...
In our earlier post, we have written multithreaded program using win32 apis. This post deals with writing the multithreaded programs using POSIX thread apis. The important POSIX thread apis are namely pthread_create, pthread_exit and pthread_join
Create a thread int pthread_create
(
pthread_t *thread,
const pthread_attr_t *attr,
void *( *start_routine)(void *),
void *arg
);
Terminate a thread
void pthread_exit (void *retval);
Wait on a thread
int pthread_join (pthread_t thread, void **status);
The Complete Example
#include <pthread.h>
#include <iostream>
//File: SimpleThreadExample.cpp
#define MAX_THREADS 3
using namespace std;
void* func(void *args)
{
int tp = *(int *)args * 10;
while(tp--)
{
cout << *(int *) args;
fflush(stdout);
sleep(1);
}
cout << endl;
pthread_exit((void *)10);
return (void *)10;
}
int main(void)
{
pthread_t tid[MAX_THREADS] = {0};
int param[MAX_THREADS] = { 1, 2, 3 };
int rc;
for(int i = 0; i < MAX_THREADS; ++i)
{
rc = pthread_create(&tid[i], NULL, func, ¶m[i]);
if(0 != rc)
{
cout << "ERROR: Thread Creation failed" << endl;
}
cout << "Thread[" << tid[i] << "] Created" << endl;
}
void *status[3];
for(int i = 0; i < MAX_THREADS; ++i)
{
rc = pthread_join(tid[i], &status[i]);
}
for(int i = 0; i < MAX_THREADS; ++i)
{
cout << "Thread[" << tid[i] << "] returned with exit code=" << (long) status[i] << endl;
}
cout << "Main thread terminating" << endl;
return 0;
}
The makefile for the project
#-----------------------------------------------------------------------
# A simple thread example
#-----------------------------------------------------------------------
PROJECT := SimpleThreadExample
SRCEXT := .h .cpp
OBJEXT := .o
EXEEXT := .exe
#compilers
CC := gcc
CXX := g++
#flags
CFLAGS := -o
CXXFLAGS := -o
LDFLAGS := -lpthread -o
#disable implicit suffix rules
.SUFFIXES:
.SUFFIXES: $(SRCEXT) $(OBJEXT) $(EXEEXT)
SRC := \
SimpleThreadExample.cpp
OBJ := \
$(SRC:.cpp=.o)
EXE := \
$(PROJECT)$(EXEEXT)
#define dummy targets
.PHONY: all clean compile link
all : compile link
clean :
@echo
@echo "Cleaning Temporary Files..."
$(RM) $(OBJ) $(EXE)
compile : $(OBJ)
link : $(EXE)
$(OBJ) :
@echo
@echo "Compiling Source Files..."
$(CXX) $(CXXFLAGS) $(OBJ) $(SRC)
$(EXE) :
@echo
@echo "Linking..."
$(LD) $(OBJ) $(LDFLAGS) $(EXE)
run :
@echo
@$(EXE)
Building the project. (The output is from Cygwin Environment. You may need to modify the makefile to compile it on a linux environment)
$ gmake clean all
Cleaning Temporary Files...
rm -f SimpleThreadExample.o SimpleThreadExample.exe
Compiling Source Files...
g++ -o SimpleThreadExample.o SimpleThreadExample.cpp
Linking...
ld SimpleThreadExample.o -lpthread -o SimpleThreadExample.exe
Output:
Read more ...
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