# C++ Program to Count Number of Occurrences of a Given Number using Binary Search

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C++ Program to find the number of occurrences of a given number using binary search approach.

Problem Description

1. Implement binary search tree to find the number of occurrences of a given number.
2. The worst case time complexity of Binary search is O(n) but for the average case, it is O(log(n)).

Problem Solution

1. Construct binary search tree for the given unsorted data array and maintain an additional count variable.
2. If any element is repeated then increase the count of that node.
3. Proceed with the search by comparing an element to the data of the node and print the count of that particular data element.
4. Exit.

Program/Source Code

C++ program to count the number of occurrences of a given number using binary search approach.
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

```#include<iostream>

using namespace std;

// A structure representing a node of a tree.
struct node
{
int data;
int count;
node *left;
node *right;
};

// A function creating a new node of the tree and assigning the data.
node* CreateNode(int data)
{
node *newnode = new node;
newnode->data = data;
newnode->count = 1;
newnode->left = NULL;
newnode->right = NULL;

return newnode;
}

// A function creating binary search tree.
node* InsertIntoTree(node* root, int data)
{
// Create node using data from argument list.
node *temp = CreateNode(data);
node *t = new node;
t = root;

// If root is null, assign it to the node created.
if(root == NULL)
root = temp;
else
{
// Find the position for the new node to be inserted.
while(t != NULL)
{
// If the new data is already there then just increase the counter.
if(t->data == data)
{
t->count++;
break;
}
else if(t->data < data )
{
if(t->right == NULL)
{
// If current node is NULL then insert the node.
t->right = temp;
break;
}
// Shift pointer to the left.
t = t->right;
}
else if(t->data > data)
{
if(t->left == NULL)
{
// If current node is NULL then insert the node.
t->left = temp;
break;
}
// Shift pointer to the left.
t = t->left;
}
}
}
return root;
}

// A function to search item in a BST.
void Search(node *root, int data)
{
node *temp = new node;
temp = root;
// Run the loop until temp points to a NULL pointer or data element is found.
while(temp != NULL)
{
if(temp->data == data)
{
cout<<"\nData item "<<data<<" is present "<<temp->count<<" number of times.";
return;
}
// Shift pointer to left child.
else if(temp->data > data)
temp = temp->left;
// Shift pointer to right child.
else
temp = temp->right;
}

return;
}

int main()
{
char ch;
int n, i, a = {89, 53, 95, 1, 9, 67, 72, 66, 75, 89, 72, 89, 89, 53, 77, 18, 24, 35, 90, 38, 41, 49, 81, 27, 97};
node *root = new node;
root = NULL;

// Construct the BST.
for(i = 0; i < 25; i++)
root = InsertIntoTree(root, a[i]);

up:
cout<<"\nEnter the Element to be searched: ";
cin>>n;

Search(root, n);

// Ask user to enter choice for further searching.
cout<<"\n\n\tDo you want to search more...enter choice(y/n)?";
cin>>ch;
if(ch == 'y' || ch == 'Y')
goto up;

return 0;
}```
Program Explanation

1. Construct binary search tree for the given unsorted data array by inserting data into tree one by one, using InsertIntoTree().
2. In the node structure, maintain an additional count variable for each node.
3. Inside InsertIntoTree(), compare the data with data part of the node.
4. If this node is null, then insert the new node.
5. If data = temp->data, increase the count of that particular node.
6. If data < temp->data, move the temp pointer to the left child.
7. If data > temp->data, move the temp pointer to the right child.
8. Take the input of data to be searched in the BST.
9. Starting from the root node, compare the data with data part of the node.
10. If data < temp->data, move the temp pointer to the left child.
11. If data > temp->data, move the temp pointer to the right child.
12. If data = temp->data, print the item found and it’s count and then, return to main.
14. Ask user if he wants to search more, if yes, repeat from 10.
15. Exit.

Runtime Test Cases
```Case 1:
Enter the Element to be searched: 89

Data item 89 is present 4 number of times.

Do you want to search more...enter choice(y/n)?y

Enter the Element to be searched: 27

Data item 27 is present 1 number of times.

Do you want to search more...enter choice(y/n)?y

Enter the Element to be searched: 72

Data item 72 is present 2 number of times.

Do you want to search more...enter choice(y/n)?y

Enter the Element to be searched: 28

Do you want to search more...enter choice(y/n)?n```

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