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Given a sorted array arr[] and a number x, write a function that counts the occurrences of x in arr[]. Expected time complexity is O(Logn) 

Examples: 

  Input: arr[] = {1, 1, 2, 2, 2, 2, 3,},   x = 2
Output: 4 // x (or 2) occurs 4 times in arr[]
Input: arr[] = {1, 1, 2, 2, 2, 2, 3,}, x = 3
Output: 1
Input: arr[] = {1, 1, 2, 2, 2, 2, 3,}, x = 1
Output: 2
Input: arr[] = {1, 1, 2, 2, 2, 2, 3,}, x = 4
Output: -1 // 4 doesn't occur in arr[]

Recommended Practice

Method 1 (Linear Search) 

Linearly search for x, count the occurrences of x and return the count. 

C++

#include <stdio.h>
 
// Returns number of times x occurs in arr[0..n-1]
int countOccurrences(int arr[], int n, int x)
{
    int res = 0;
    for (int i = 0; i < n; i++)
        if (x == arr[i])
            res++;
    return res;
}
 
// Driver code
int main()
{
    int arr[] = {1, 2, 2, 2, 2, 3, 4, 7, 8, 8};
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = 2;
    printf("%d", countOccurrences(arr, n, x));
    return 0;
}

                    

C

#include <stdio.h>
 
int main() {
 
    // code
    return 0;
}

                    

Java

// Java program to count occurrences
// of an element
 
class Main
{
    // Returns number of times x occurs in arr[0..n-1]
    static int countOccurrences(int arr[], int n, int x)
    {
        int res = 0;
        for (int i=0; i<n; i++)
            if (x == arr[i])
              res++;
        return res;
    }
     
    public static void main(String args[])
    {
        int arr[] = {1, 2, 2, 2, 2, 3, 4, 7 ,8 ,8 };
        int n = arr.length;
        int x = 2;
        System.out.println(countOccurrences(arr, n, x));
    }
}

                    

Python3

# Python3 program to count
# occurrences of an element
 
# Returns number of times x
# occurs in arr[0..n-1]
def countOccurrences(arr, n, x):
    res = 0
    for i in range(n):
        if x == arr[i]:
            res += 1
    return res
  
# Driver code
arr = [1, 2, 2, 2, 2, 3, 4, 7 ,8 ,8]
n = len(arr)
x = 2
print (countOccurrences(arr, n, x))

                    

C#

// C# program to count occurrences
// of an element
using System;
 
class GFG
{
    // Returns number of times x
    // occurs in arr[0..n-1]
    static int countOccurrences(int []arr,
                                int n, int x)
    {
        int res = 0;
         
        for (int i = 0; i < n; i++)
            if (x == arr[i])
            res++;
             
        return res;
    }
     
    // driver code   
    public static void Main()
    {
        int []arr = {1, 2, 2, 2, 2, 3, 4, 7 ,8 ,8 };
        int n = arr.Length;
        int x = 2;
         
        Console.Write(countOccurrences(arr, n, x));
    }
}
 
// This code is contributed by Sam007

                    

Javascript

<script>
 
// Javascript program to count occurrences
// of an element
 
 
    // Returns number of times x occurs in arr[0..n-1]
    function countOccurrences(arr,n,x)
    {
        let res = 0;
        for (let i=0; i<n; i++)
        {
            if (x == arr[i])
                res++;
        }
        return res;
    }
     
    arr=[1, 2, 2, 2, 2, 3, 4, 7 ,8 ,8]
    let  n = arr.length;
    let x = 2;
    document.write(countOccurrences(arr, n, x));
     
    // This code is contributed by avanitrachhadiya2155
     
</script>

                    

PHP

<?php
// PHP program to count occurrences
// of an element
 
// Returns number of times x
// occurs in arr[0..n-1]
function countOccurrences($arr, $n, $x)
{
    $res = 0;
    for ($i = 0; $i < $n; $i++)
        if ($x == $arr[$i])
        $res++;
    return $res;
}
 
    // Driver code
    $arr = array(1, 2, 2, 2, 2, 3, 4, 7 ,8 ,8 );
    $n = count($arr);
    $x = 2;
    echo countOccurrences($arr,$n, $x);
     
// This code is contributed by Sam007
?>

                    

Output : 

4

Time Complexity: O(n)
Space Complexity: O(1), as no extra space is used

Method 2 (Better using Binary Search) 

We first find an occurrence using binary search. Then we match toward left and right sides of the matched the found index.

C++

// C++ program to count occurrences of an element
#include <bits/stdc++.h>
using namespace std;
 
// A recursive binary search function. It returns
// location of x in given array arr[l..r] is present,
// otherwise -1
int binarySearch(int arr[], int l, int r, int x)
{
    if (r < l)
        return -1;
 
    int mid = l + (r - l) / 2;
 
    // If the element is present at the middle
    // itself
    if (arr[mid] == x)
        return mid;
 
    // If element is smaller than mid, then
    // it can only be present in left subarray
    if (arr[mid] > x)
        return binarySearch(arr, l, mid - 1, x);
 
    // Else the element can only be present
    // in right subarray
    return binarySearch(arr, mid + 1, r, x);
}
 
// Returns number of times x occurs in arr[0..n-1]
int countOccurrences(int arr[], int n, int x)
{
    int ind = binarySearch(arr, 0, n - 1, x);
 
    // If element is not present
    if (ind == -1)
        return 0;
 
    // Count elements on left side.
    int count = 1;
    int left = ind - 1;
    while (left >= 0 && arr[left] == x)
        count++, left--;
 
    // Count elements on right side.
    int right = ind + 1;
    while (right < n && arr[right] == x)
        count++, right++;
 
    return count;
}
 
// Driver code
int main()
{
    int arr[] = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = 2;
    cout << countOccurrences(arr, n, x);
    return 0;
}

                    

C

#include <stdio.h>
 
// A recursive binary search function. It returns
// location of x in given array arr[l..r] if present,
// otherwise -1
int binarySearch(int arr[], int l, int r, int x)
{
    if (r < l)
        return -1;
 
    int mid = l + (r - l) / 2;
 
    // If the element is present at the middle
    // itself
    if (arr[mid] == x)
        return mid;
 
    // If element is smaller than mid, then
    // it can only be present in the left subarray
    if (arr[mid] > x)
        return binarySearch(arr, l, mid - 1, x);
 
    // Else the element can only be present
    // in the right subarray
    return binarySearch(arr, mid + 1, r, x);
}
 
// Returns number of times x occurs in arr[0..n-1]
int countOccurrences(int arr[], int n, int x)
{
    int ind = binarySearch(arr, 0, n - 1, x);
 
    // If the element is not present
    if (ind == -1)
        return 0;
 
    // Count elements on the left side
    int count = 1;
    int left = ind - 1;
    while (left >= 0 && arr[left] == x)
    {
        count++;
        left--;
    }
 
    // Count elements on the right side
    int right = ind + 1;
    while (right < n && arr[right] == x)
    {
        count++;
        right++;
    }
 
    return count;
}
 
// Driver code
int main()
{
    int arr[] = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = 2;
    printf("%d", countOccurrences(arr, n, x));
    return 0;
}

                    

Java

// Java program to count
// occurrences of an element
class GFG
{
 
    // A recursive binary search
    // function. It returns location
    // of x in given array arr[l..r]
    // is present, otherwise -1
    static int binarySearch(int arr[], int l,
                            int r, int x)
    {
        if (r < l)
            return -1;
 
        int mid = l + (r - l) / 2;
 
        // If the element is present
        // at the middle itself
        if (arr[mid] == x)
            return mid;
 
        // If element is smaller than
        // mid, then it can only be
        // present in left subarray
        if (arr[mid] > x)
            return binarySearch(arr, l,
                                mid - 1, x);
 
        // Else the element can
        // only be present in
        // right subarray
        return binarySearch(arr, mid + 1, r, x);
    }
 
    // Returns number of times x
    // occurs in arr[0..n-1]
    static int countOccurrences(int arr[],
                                int n, int x)
    {
        int ind = binarySearch(arr, 0,
                               n - 1, x);
 
        // If element is not present
        if (ind == -1)
            return 0;
 
        // Count elements on left side.
        int count = 1;
        int left = ind - 1;
        while (left >= 0 &&
               arr[left] == x)
        {
            count++;
            left--;
        }
 
        // Count elements
        // on right side.
        int right = ind + 1;
        while (right < n &&
               arr[right] == x)
        {
            count++;
            right++;
        }
 
        return count;
    }
 
 
    // Driver code
    public static void main(String[] args)
    {
        int arr[] = {1, 2, 2, 2, 2,
                     3, 4, 7, 8, 8};
        int n = arr.length;
        int x = 2;
        System.out.print(countOccurrences(arr, n, x));
    }
}
 
// This code is contributed
// by ChitraNayal

                    

Python 3

# Python 3 program to count
# occurrences of an element
 
# A recursive binary search
# function. It returns location
# of x in given array arr[l..r]
# is present, otherwise -1
def binarySearch(arr, l, r, x):
    if (r < l):
        return -1
 
    mid = int( l + (r - l) / 2)
 
    # If the element is present
    # at the middle itself
    if arr[mid] == x:
        return mid
 
    # If element is smaller than
    # mid, then it can only be
    # present in left subarray
    if arr[mid] > x:
        return binarySearch(arr, l,
                            mid - 1, x)
 
    # Else the element
    # can only be present
    # in right subarray
    return binarySearch(arr, mid + 1,
                                r, x)
 
# Returns number of times
# x occurs in arr[0..n-1]
def countOccurrences(arr, n, x):
    ind = binarySearch(arr, 0, n - 1, x)
 
    # If element is not present
    if ind == -1:
        return 0
 
    # Count elements
    # on left side.
    count = 1
    left = ind - 1
    while (left >= 0 and
           arr[left] == x):
        count += 1
        left -= 1
 
    # Count elements on
    # right side.
    right = ind + 1;
    while (right < n and
           arr[right] == x):
        count += 1
        right += 1
 
    return count
 
# Driver code
arr = [ 1, 2, 2, 2, 2,
        3, 4, 7, 8, 8 ]
n = len(arr)
x = 2
print(countOccurrences(arr, n, x))
 
# This code is contributed
# by ChitraNayal

                    

C#

// C# program to count
// occurrences of an element
using System;
 
class GFG
{
 
    // A recursive binary search
    // function. It returns location
    // of x in given array arr[l..r]
    // is present, otherwise -1
    static int binarySearch(int[] arr, int l,
                            int r, int x)
    {
        if (r < l)
            return -1;
 
        int mid = l + (r - l) / 2;
 
        // If the element is present
        // at the middle itself
        if (arr[mid] == x)
            return mid;
 
        // If element is smaller than
        // mid, then it can only be
        // present in left subarray
        if (arr[mid] > x)
            return binarySearch(arr, l,
                                mid - 1, x);
 
        // Else the element
        // can only be present
        // in right subarray
        return binarySearch(arr, mid + 1,
                                   r, x);
    }
 
    // Returns number of times x
    // occurs in arr[0..n-1]
    static int countOccurrences(int[] arr,
                                int n, int x)
    {
        int ind = binarySearch(arr, 0,
                               n - 1, x);
 
        // If element is not present
        if (ind == -1)
            return 0;
 
        // Count elements on left side.
        int count = 1;
        int left = ind - 1;
        while (left >= 0 &&
               arr[left] == x)
        {
            count++;
            left--;
        }
 
        // Count elements on right side.
        int right = ind + 1;
        while (right < n &&
               arr[right] == x)
        {
            count++;
            right++;
        }
 
        return count;
    }
 
 
    // Driver code
    public static void Main()
    {
        int[] arr = {1, 2, 2, 2, 2,
                     3, 4, 7, 8, 8};
        int n = arr.Length;
        int x = 2;
        Console.Write(countOccurrences(arr, n, x));
    }
}
 
// This code is contributed
// by ChitraNayal

                    

Javascript

<script>
 
// Javascript program to count occurrences of an element
 
// A recursive binary search function. It returns
// location of x in given array arr[l..r] is present,
// otherwise -1
function binarySearch(arr, l, r, x)
{
    if (r < l)
        return -1;
 
    var mid = l + parseInt((r - l) / 2);
 
    // If the element is present at the middle
    // itself
    if (arr[mid] == x)
        return mid;
 
    // If element is smaller than mid, then
    // it can only be present in left subarray
    if (arr[mid] > x)
        return binarySearch(arr, l, mid - 1, x);
 
    // Else the element can only be present
    // in right subarray
    return binarySearch(arr, mid + 1, r, x);
}
 
// Returns number of times x occurs in arr[0..n-1]
function countOccurrences(arr, n, x)
{
    var ind = binarySearch(arr, 0, n - 1, x);
 
    // If element is not present
    if (ind == -1)
        return 0;
 
    // Count elements on left side.
    var count = 1;
    var left = ind - 1;
    while (left >= 0 && arr[left] == x)
        count++, left--;
 
    // Count elements on right side.
    var right = ind + 1;
    while (right < n && arr[right] == x)
        count++, right++;
 
    return count;
}
 
// Driver code
var arr = [ 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 ];
var n = arr.length;
var x = 2;
document.write(countOccurrences(arr, n, x));
 
// This code is contributed by noob2000.
</script>

                    

PHP

<?php
// PHP program to count
// occurrences of an element
 
// A recursive binary search
// function. It returns location
// of x in given array arr[l..r]
// is present, otherwise -1
function binarySearch(&$arr, $l,
                         $r, $x)
{
    if ($r < $l)
        return -1;
 
    $mid = $l + ($r - $l) / 2;
 
    // If the element is present
    // at the middle itself
    if ($arr[$mid] == $x)
        return $mid;
 
    // If element is smaller than
    // mid, then it can only be
    // present in left subarray
    if ($arr[$mid] > $x)
        return binarySearch($arr, $l,  
                            $mid - 1, $x);
 
    // Else the element
    // can only be present
    // in right subarray
    return binarySearch($arr, $mid + 1,
                                $r, $x);
}
 
// Returns number of times
// x occurs in arr[0..n-1]
function countOccurrences($arr, $n, $x)
{
    $ind = binarySearch($arr, 0,
                        $n - 1, $x);
 
    // If element is not present
    if ($ind == -1)
        return 0;
 
    // Count elements
    // on left side.
    $count = 1;
    $left = $ind - 1;
    while ($left >= 0 &&
           $arr[$left] == $x)
    {
        $count++;
        $left--;
    }
     
    // Count elements on right side.
    $right = $ind + 1;
    while ($right < $n &&
           $arr[$right] == $x)
    {
        $count++;
        $right++;
    }
    return $count;
}
 
// Driver code
$arr = array( 1, 2, 2, 2, 2,
              3, 4, 7, 8, 8 );
$n = sizeof($arr);
$x = 2;
echo countOccurrences($arr, $n, $x);
 
// This code is contributed
// by ChitraNayal
?>

                    

Output : 

4

Time Complexity : O(Log n + count) where count is number of occurrences.
Space Complexity: O(logn), due to recursive stack space

 

Method 3 (Best using Improved Binary Search) 

1) Use Binary search to get index of the first occurrence of x in arr[]. Let the index of the first occurrence be i. 
2) Use Binary search to get index of the last occurrence of x in arr[]. Let the index of the last occurrence be j. 
3) Return (j – i + 1);

C++

// C++ program to count occurrences of an element
// in a sorted array.
# include <bits/stdc++.h>
using namespace std;
 
/* if x is present in arr[] then returns the count
    of occurrences of x, otherwise returns 0. */
int count(int arr[], int x, int n)
{   
  /* get the index of first occurrence of x */
  int *low = lower_bound(arr, arr+n, x);
 
  // If element is not present, return 0
  if (low == (arr + n) || *low != x)
     return 0;
    
  /* Else get the index of last occurrence of x.
     Note that we  are only looking in the
     subarray after first occurrence */  
  int *high = upper_bound(low, arr+n, x);    
    
  /* return count */
  return high - low;
}
 
/* driver program to test above functions */
int main()
{
  int arr[] = {1, 2, 2, 3, 3, 3, 3};
  int x =  3;  // Element to be counted in arr[]
  int n = sizeof(arr)/sizeof(arr[0]);
  int c = count(arr, x, n);
  printf(" %d occurs %d times ", x, c);
  return 0;
}

                    

C

# include <stdio.h>
 
/* if x is present in arr[] then returns
   the index of FIRST occurrence
   of x in arr[0..n-1], otherwise returns -1 */
int first(int arr[], int low, int high, int x, int n)
{
  if(high >= low)
  {
    int mid = (low + high)/2;  /*low + (high - low)/2;*/
    if( ( mid == 0 || x > arr[mid-1]) && arr[mid] == x)
      return mid;
    else if(x > arr[mid])
      return first(arr, (mid + 1), high, x, n);
    else
      return first(arr, low, (mid -1), x, n);
  }
  return -1;
}
 
/* if x is present in arr[] then returns the
   index of LAST occurrence of x in arr[0..n-1],
   otherwise returns -1 */
int last(int arr[], int low, int high, int x, int n)
{
  if (high >= low)
  {
    int mid = (low + high)/2;  /*low + (high - low)/2;*/
    if( ( mid == n-1 || x < arr[mid+1]) && arr[mid] == x )
      return mid;
    else if(x < arr[mid])
      return last(arr, low, (mid -1), x, n);
    else
      return last(arr, (mid + 1), high, x, n);     
  }
  return -1;
}
 
/* if x is present in arr[] then returns the count
   of occurrences of x, otherwise returns -1. */
int count(int arr[], int x, int n)
{
  int i; // index of first occurrence of x in arr[0..n-1]
  int j; // index of last occurrence of x in arr[0..n-1]
     
  /* get the index of first occurrence of x */
  i = first(arr, 0, n-1, x, n);
 
  /* If x doesn't exist in arr[] then return -1 */
  if(i == -1)
    return i;
    
  /* Else get the index of last occurrence of x.
     Note that we are only looking in the subarray
     after first occurrence */  
  j = last(arr, i, n-1, x, n);    
    
  /* return count */
  return j-i+1;
}
 
/* driver program to test above functions */
int main()
{
  int arr[] = {1, 2, 2, 3, 3, 3, 3};
  int x =  3;  // Element to be counted in arr[]
  int n = sizeof(arr)/sizeof(arr[0]);
  int c = count(arr, x, n);
  printf(" %d occurs %d times ", x, c);
  getchar();
  return 0;
}

                    

Java

// Java program to count occurrences
// of an element
 
class Main
{
    /* if x is present in arr[] then returns
       the count of occurrences of x,
       otherwise returns -1. */
    static int count(int arr[], int x, int n)
    {
      // index of first occurrence of x in arr[0..n-1]   
      int i;
       
      // index of last occurrence of x in arr[0..n-1]
      int j;
          
      /* get the index of first occurrence of x */
      i = first(arr, 0, n-1, x, n);
      
      /* If x doesn't exist in arr[] then return -1 */
      if(i == -1)
        return i;
         
      /* Else get the index of last occurrence of x.
         Note that we are only looking in the
         subarray after first occurrence */ 
      j = last(arr, i, n-1, x, n);    
         
      /* return count */
      return j-i+1;
    }
      
    /* if x is present in arr[] then returns the
       index of FIRST occurrence of x in arr[0..n-1],
       otherwise returns -1 */
    static int first(int arr[], int low, int high, int x, int n)
    {
      if(high >= low)
      {
        /*low + (high - low)/2;*/ 
        int mid = (low + high)/2
        if( ( mid == 0 || x > arr[mid-1]) && arr[mid] == x)
          return mid;
        else if(x > arr[mid])
          return first(arr, (mid + 1), high, x, n);
        else
          return first(arr, low, (mid -1), x, n);
      }
      return -1;
    }
      
    /* if x is present in arr[] then returns the
       index of LAST occurrence of x in arr[0..n-1],
       otherwise returns -1 */
    static int last(int arr[], int low, int high, int x, int n)
    {
      if(high >= low)
      {
        /*low + (high - low)/2;*/     
        int mid = (low + high)/2;
        if( ( mid == n-1 || x < arr[mid+1]) && arr[mid] == x )
          return mid;
        else if(x < arr[mid])
          return last(arr, low, (mid -1), x, n);
        else
          return last(arr, (mid + 1), high, x, n);     
      }
      return -1;
    }
      
    public static void main(String args[])
    {
        int arr[] = {1, 2, 2, 3, 3, 3, 3};
         
        // Element to be counted in arr[]
        int x =  3;
        int n = arr.length;
        int c = count(arr, x, n);
        System.out.println(x+" occurs "+c+" times");
    }
}

                    

Python3

# Python3 program to count
# occurrences of an element
 
# if x is present in arr[] then
# returns the count of occurrences
# of x, otherwise returns -1.
def count(arr, x, n):
 
    # get the index of first
    # occurrence of x
    i = first(arr, 0, n-1, x, n)
  
    # If x doesn't exist in
    # arr[] then return -1
    if i == -1:
        return i
     
    # Else get the index of last occurrence
    # of x. Note that we are only looking
    # in the subarray after first occurrence  
    j = last(arr, i, n-1, x, n);    
     
    # return count
    return j-i+1;
 
# if x is present in arr[] then return
# the index of FIRST occurrence of x in
# arr[0..n-1], otherwise returns -1
def first(arr, low, high, x, n):
    if high >= low:
 
        # low + (high - low)/2
        mid = (low + high)//2     
         
        if (mid == 0 or x > arr[mid-1]) and arr[mid] == x:
            return mid
        elif x > arr[mid]:
            return first(arr, (mid + 1), high, x, n)
        else:
            return first(arr, low, (mid -1), x, n)
    return -1;
  
# if x is present in arr[] then return
# the index of LAST occurrence of x
# in arr[0..n-1], otherwise returns -1
def last(arr, low, high, x, n):
    if high >= low:
 
        # low + (high - low)/2
        mid = (low + high)//2;
  
        if(mid == n-1 or x < arr[mid+1]) and arr[mid] == x :
            return mid
        elif x < arr[mid]:
            return last(arr, low, (mid -1), x, n)
        else:
            return last(arr, (mid + 1), high, x, n)    
    return -1
 
# driver program to test above functions
arr = [1, 2, 2, 3, 3, 3, 3]
x = 3  # Element to be counted in arr[]
n = len(arr)
c = count(arr, x, n)
print ("%d occurs %d times "%(x, c))

                    

C#

// C# program to count occurrences
// of an element
using System;
 
class GFG
{
     
    /* if x is present in arr[] then returns
    the count of occurrences of x,
    otherwise returns -1. */
    static int count(int []arr, int x, int n)
    {
    // index of first occurrence of x in arr[0..n-1]
    int i;
         
    // index of last occurrence of x in arr[0..n-1]
    int j;
         
    /* get the index of first occurrence of x */
    i = first(arr, 0, n-1, x, n);
     
    /* If x doesn't exist in arr[] then return -1 */
    if(i == -1)
        return i;
         
    /* Else get the index of last occurrence of x.
        Note that we are only looking in the
        subarray after first occurrence */
    j = last(arr, i, n-1, x, n);    
         
    /* return count */
    return j-i+1;
    }
     
    /* if x is present in arr[] then returns the
    index of FIRST occurrence of x in arr[0..n-1],
    otherwise returns -1 */
    static int first(int []arr, int low, int high,
                                     int x, int n)
    {
    if(high >= low)
    {
        /*low + (high - low)/2;*/
        int mid = (low + high)/2;
        if( ( mid == 0 || x > arr[mid-1])
                            && arr[mid] == x)
        return mid;
        else if(x > arr[mid])
        return first(arr, (mid + 1), high, x, n);
        else
        return first(arr, low, (mid -1), x, n);
    }
    return -1;
    }
     
    /* if x is present in arr[] then returns the
    index of LAST occurrence of x in arr[0..n-1],
    otherwise returns -1 */
    static int last(int []arr, int low,
                        int high, int x, int n)
    {
    if(high >= low)
    {
        /*low + (high - low)/2;*/   
        int mid = (low + high)/2;
        if( ( mid == n-1 || x < arr[mid+1])
                            && arr[mid] == x )
        return mid;
        else if(x < arr[mid])
        return last(arr, low, (mid -1), x, n);
        else
        return last(arr, (mid + 1), high, x, n);    
    }
    return -1;
    }
     
    public static void Main()
    {
        int []arr = {1, 2, 2, 3, 3, 3, 3};
         
        // Element to be counted in arr[]
        int x = 3;
        int n = arr.Length;
        int c = count(arr, x, n);
         
        Console.Write(x + " occurs " + c + " times");
    }
}
// This code is contributed by Sam007

                    

Javascript

<script>
 
// Javascript program to count occurrences
// of an element
 
/* if x is present in arr[] then returns
the count of occurrences of x,
otherwise returns -1. */
function count(arr, x, n)
{
     
    // Index of first occurrence of x in arr[0..n-1]   
    let i;
     
    // Index of last occurrence of x in arr[0..n-1]
    let j;
     
    // Get the index of first occurrence of x
    i = first(arr, 0, n - 1, x, n);
     
    // If x doesn't exist in arr[] then return -1
    if (i == -1)
        return i;
     
    // Else get the index of last occurrence of x.
    // Note that we are only looking in the
    // subarray after first occurrence
    j = last(arr, i, n - 1, x, n);    
     
    // return count
    return j - i + 1;
}
     
// if x is present in arr[] then returns the
// index of FIRST occurrence of x in arr[0..n-1],
// otherwise returns -1
function first(arr, low, high, x, n)
{
    if (high >= low)
    {
         
        // low + (high - low)/2;
        let mid = (low + high) / 2; 
         
        if ((mid == 0 || x > arr[mid - 1]) &&
        arr[mid] == x)
            return mid;
        else if (x > arr[mid])
            return first(arr, (mid + 1), high, x, n);
        else
            return first(arr, low, (mid - 1), x, n);
    }
    return -1;
}
 
// If x is present in arr[] then returns the
// index of LAST occurrence of x in arr[0..n-1],
// otherwise returns -1
function last(arr, low, high, x, n)
{
    if (high >= low)
    {
        /*low + (high - low)/2;*/     
        let mid = Math.floor((low + high) / 2);
        if ((mid == n - 1 || x < arr[mid + 1]) &&
        arr[mid] == x)
            return mid;
        else if (x < arr[mid])
            return last(arr, low, (mid - 1), x, n);
        else
            return last(arr, (mid + 1), high, x, n);     
    }
    return -1;
}
 
// Driver code
let arr = [ 1, 2, 2, 3, 3, 3, 3 ];
 
// Element to be counted in arr[]
let x =  3;
let n = arr.length;
let c = count(arr, x, n);
 
document.write(x + " occurs " + c + " times");
 
// This code is contributed by target_2
 
</script>

                    

Output:  

3 occurs 4 times

Time Complexity: O(Logn) 

Auxiliary Space: O(1), as no extra space is used
Programming Paradigm: Divide & Conquer

Method 4 (Using Collections.frequency() method of java)

C++

// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to count occurrences
int countOccurrences(int arr[],
                        int x, int N)
{
    int count = 0;
    for (int i=0; i < N; i++)
        if (arr[i] == x)
            count++;
    return count;
}
 
// Driver Code
int main()
{
    int arr[] = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
    int x = 2;
    int N = sizeof(arr) / sizeof(arr[0]);
  
    // displaying the frequency of x in ArrayList
    cout <<x << " occurs "
                    << countOccurrences(arr, x, N)
                           << " times";
                            
    return 0;
}
 
// This code is contributed by code_hunt.

                    

Java

/*package whatever //do not write package name here */
import java.util.ArrayList;
import java.util.Collections;
 
public class GFG {
   
    // Function to count occurrences
    static int countOccurrences(ArrayList<Integer> clist,
                                int x)
    {
        // returning the frequency of
        // element x in the ArrayList
        // using Collections.frequency() method
        return Collections.frequency(clist, x);
    }
 
    // Driver Code
    public static void main(String args[])
    {
        int arr[] = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
        int x = 2;
        ArrayList<Integer> clist = new ArrayList<>();
 
        // adding elements of array to
        // ArrayList
        for (int i : arr)
            clist.add(i);
 
        // displaying the frequency of x in ArrayList
        System.out.println(x + " occurs "
                           + countOccurrences(clist, x)
                           + " times");
    }
}

                    

Python3

# Python code to implement the approach
 
# Function to count occurrences
def countOccurrences(arr, x) :
 
    count = 0
    n = len(arr)
    for i in range(n) :
        if (arr[i] == x):
            count += 1
             
    return count
    
# Driver Code
if __name__ == "__main__":
         
    arr = [ 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 ]
    x = 2
   
    # displaying the frequency of x in ArrayList
    print(x , "occurs"
                        , countOccurrences(arr, x)
                        , "times")
     
    # This code is contributed by sanjoy_62.

                    

C#

// C# program for the above approach
using System;
 
public class GFG
{
 
    // Function to count occurrences
    static int countOccurrences(int[] arr,
                                int x)
    {
        int count = 0;
        int n = arr.Length;
        for (int i=0; i < n; i++)
        if (arr[i] == x)
            count++;
        return count;
    }   
   
    // Driver Code
    public static void Main (string[] args)
    {
        int[] arr = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
        int x = 2;
  
        // displaying the frequency of x in ArrayList
        Console.WriteLine(x + " occurs "
                           + countOccurrences(arr, x)
                           + " times");
  
    }
}
 
// This code is contributed by avijitmondal1998.

                    

Javascript

<script>
 
// javascript program for above approach
 
    // Function to count occurrences
    function countOccurrences(arr, x)
    {
        let count = 0;
        let n = arr.length;
        for (let i=0; i < n; i++)
        if (arr[i] == x)
            count++;
        return count;
    }   
   
// Driver Code
    let arr = [ 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 ];
    let x = 2;
  
    // displaying the frequency of x in ArrayList
    document.write(x + " occurs "
                     + countOccurrences(arr, x)
                        + " times");
 
// This code is contributed by splevel62.
</script>

                    

Output:

2 occurs 4 times

Time Complexity: O(n)
Auxiliary Space: O(1), as no extra space is used

Method 5: Using Hashing

We can also use hashing method to count occurrences (or frequency) of a specific element in a sorted array.

Steps:

We use following steps to find occurrence-

  1. First we create an unsorted_map to store elements with their frequency.
  2. Now we iterate through the array and store its elements inside the map.
  3. Then by using map.find() function, we can easily find the occurrences (or frequency) of any element.

Below is the implementation:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to count occurrences
int countOccurrences(int arr[], int x, int N)
{
    unordered_map<int, int> mp;
    for (int i = 0; i < N; i++) {
        mp[arr[i]]++;
    }
    if (mp.find(x) == mp.end())
        return 0;
    auto it = mp.find(x);
    return it->second;
}
 
// Driver Code
int main()
{
    int arr[] = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
    int x = 2;
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // displaying the frequency of x in Array
    cout << x << " occurs " << countOccurrences(arr, x, N)
         << " times";
    return 0;
}
 
// This code is contributed by Susobhan Akhuli

                    

Java

// Java program for the above approach
import java.util.HashMap;
import java.util.Map;
 
public class Main
{
 
  // Function to count occurrences
  static int countOccurrences(int[] arr, int x, int N)
  {
    Map<Integer, Integer> mp
      = new HashMap<Integer, Integer>();
    for (int i = 0; i < N; i++) {
      mp.put(arr[i], mp.getOrDefault(arr[i], 0) + 1);
    }
    if (!mp.containsKey(x))
      return 0;
    return mp.get(x);
  }
 
  // Driver Code
  public static void main(String[] args)
  {
    int[] arr = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
    int x = 2;
    int N = arr.length;
 
    // displaying the frequency of x in Array
    System.out.println(x + " occurs "
                       + countOccurrences(arr, x, N)
                       + " times");
  }
}
 
// This code is contributed by Susobhan Akhuli

                    

Python3

# Python program for the above approach
 
# Function to count occurrences
def countOccurrences(arr, x, N):
    mp = {}
    for i in range(N):
        if arr[i] in mp:
            mp[arr[i]] += 1
        else:
            mp[arr[i]] = 1
 
    if x not in mp:
        return 0
 
    return mp[x]
 
# Driver Code
arr = [1, 2, 2, 2, 2, 3, 4, 7, 8, 8]
x = 2
N = len(arr)
 
# displaying the frequency of x in Array
print(x, "occurs", countOccurrences(arr, x, N), "times")
 
# This code is contributed by Susobhan Akhuli

                    

C#

using System;
using System.Collections.Generic;
 
class Program {
    // Function to count occurrences
    static int CountOccurrences(int[] arr, int x)
    {
        Dictionary<int, int> frequencyMap
            = new Dictionary<int, int>();
 
        // Count occurrences and store in the dictionary
        foreach(int num in arr)
        {
            if (frequencyMap.ContainsKey(num))
                frequencyMap[num]++;
            else
                frequencyMap[num] = 1;
        }
 
        // Check if x exists in the dictionary, return its
        // frequency, or 0 if not found
        int frequency;
        if (frequencyMap.TryGetValue(x, out frequency))
            return frequency;
        else
            return 0;
    }
 
    // Driver Code
    static void Main()
    {
        int[] arr = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
        int x = 2;
 
        // Display the frequency of x in the array
        Console.WriteLine(x + " occurs "
                          + CountOccurrences(arr, x)
                          + " times");
    }
}

                    

Javascript

// JavaScript program for the above approach
 
// Function to count occurrences
function countOccurrences(arr, x, N)
{
      let mp = new Map();
      for (let i = 0; i < N; i++) {
           mp.set(arr[i], (mp.get(arr[i]) || 0) + 1);
       }
      if (!mp.has(x))
           return 0;
      return mp.get(x);
}
 
// Driver Code
let arr = [1, 2, 2, 2, 2, 3, 4, 7, 8, 8];
let x = 2;
let N = arr.length;
 
// displaying the frequency of x in Array
console.log(x + " occurs " + countOccurrences(arr, x,N) + " times");

                    

Output
2 occurs 4 times







Time Complexity: O(N), where N is the number of elements in the array.
Auxiliary Space: O(K), where K is the number of unique elements in the array.

Another Approach:

  • For the first occurrence, we will first find the index of the number and then search again in the left subarray as long as we are finding the number.
  • For the last occurrence, we will first find the index of the number and then search again in the right subarray as long as we are finding the number

Follow the steps mentioned below to implement the idea:

  • Create a function search(int[] nums, int target, boolean findStartIndex) to find the index value of target.
  • And for first occurrence set firstIndex = search(arr, target, true) and last occurrence set lastIndex = search(arr, target, false) and these function do following things:

                ? Set ans = -1 , start = 0 , end = arr.length – 1 .

                ? Iterate a loop while start <= end , such as:

                            ? Set mid = start + (end – start) / 2 .

                            ? Check if target < arr[mid] ,then set end = mid – 1.

                            ?  Else check if target > arr[mid], then set start = mid + 1.

                            ? Otherwise , set ans = mid and check further such as

                                       ? If findStartIndex == true , then set end = mid – 1 .

                                       ? Else set start = mid + 1.

              ? Check if (firstIndex != -1 && lastIndex != -1 ) is true then return firstIndex- lastIndex +1 as the occurrences of x ,otherwise return 0.

Below is the implementation of the above approach:

C++

#include <iostream>
#include <vector>
using namespace std;
 
int search(vector<int>& nums, int target, bool findStartIndex)
{
    int answer = -1;
    int start = 0;
    int end = nums.size() - 1;
    while (start <= end) {
        int mid = start + (end - start) / 2;
        if (target < nums[mid]) {
            end = mid - 1;
        }
        else if (target > nums[mid]) {
            start = mid + 1;
        }
        else {
            answer = mid;
            if (findStartIndex) {
                end = mid - 1;
            }
            else {
                start = mid + 1;
            }
        }
    }
    return answer;
}
 
int countOccurrences(vector<int>& nums, int x)
{
    int firstIndex = search(nums, x, true);
    int lastIndex = search(nums, x, false);
    if (firstIndex != -1 && lastIndex != -1)
        return lastIndex - firstIndex + 1;
    else
        return 0;
}
 
int main()
{
    vector<int> arr{ 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
    int x = 2;
    int c = countOccurrences(arr, x);
    cout << x << " occurs " << c << " times" << endl;
    return 0;
}

                    

C

#include <stdio.h>
 
// Returns the index of the first occurrence
// or last occurrence of target in nums[]
int search(int nums[], int target, int findStartIndex, int length)
{
    int answer = -1;
    int start = 0;
    int end = length - 1;
    while (start <= end) {
        int mid = start + (end - start) / 2;
        if (target < nums[mid]) {
            end = mid - 1;
        }
        else if (target > nums[mid]) {
            start = mid + 1;
        }
        else {
            answer = mid;
            if (findStartIndex) {
                end = mid - 1;
            }
            else {
                start = mid + 1;
            }
        }
    }
    return answer;
}
 
// Returns the count of occurrences of x in arr[]
int countOccurrences(int arr[], int length, int x)
{
    int firstIndex = search(arr, x, 1, length);
    int lastIndex = search(arr, x, 0, length);
    if (firstIndex != -1 && lastIndex != -1)
        return lastIndex - firstIndex + 1;
    else
        return 0;
}
 
// Driver code
int main()
{
    int arr[] = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = 2;
    int c = countOccurrences(arr, n, x);
    printf("%d occurs %d times\n", x, c);
    return 0;
}

                    

Java

// Java program to count occurrences
// of an element
import java.util.*;
class GFG {
    /* if x is present in arr[] then returns
       the count of occurrences of x,
       otherwise returns -1. */
    static int count(int arr[], int x)
    {
        int firstIndex = search(arr, x, true);
        int lastIndex = search(arr, x, false);
        if (firstIndex != -1 && lastIndex != -1)
            return lastIndex - firstIndex + 1;
        else
            return 0;
    }
 
    // if target is present in arr[] then
    // returns the index of FIRST
    // occurrence and last occurrence of target in
    // arr[0..n-1], otherwise returns -1
    static int search(int[] nums, int target,
                      boolean findStartIndex)
    {
        int ans = -1;
        int start = 0;
        int end = nums.length - 1;
        while (start <= end) {
            // find the middle element
            // int mid = (start + end) / 2;
            //  might be possible that (start + end)
            //  exceeds the range of int in  java
            int mid = start + (end - start) / 2;
 
            if (target < nums[mid]) {
                end = mid - 1;
            }
            else if (target > nums[mid]) {
                start = mid + 1;
            }
            else {
                // potential ans found
                ans = mid;
                if (findStartIndex) {
                    end = mid - 1;
                }
                else {
                    start = mid + 1;
                }
            }
        }
 
        return ans;
    }
 
    // Driver program
    public static void main(String[] args)
    {
        int arr[] = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
        int n = arr.length;
        int x = 2;
        int c = count(arr, x);
        System.out.println(x + " occurs " + c + " times");
    }
}

                    

Python3

def count(nums, target):
    # Find the first and last occurrences of the target
    first_index = search(nums, target, True)
    last_index = search(nums, target, False)
 
    # If both first and last occurrences are found, calculate the count
    if first_index != -1 and last_index != -1:
        return last_index - first_index + 1
    else:
        return 0
 
 
def search(nums, target, find_start_index):
    # Initialize the answer to -1
    ans = -1
    start = 0
    end = len(nums) - 1
 
    # Perform binary search
    while start <= end:
        mid = start + (end - start) // 2
 
        if target < nums[mid]:
            # If the target is smaller, search in the left half
            end = mid - 1
        elif target > nums[mid]:
            # If the target is larger, search in the right half
            start = mid + 1
        else:
            # If the target is found, update the potential answer
            ans = mid
            if find_start_index:
                # Adjust the search range for the first occurrence
                end = mid - 1
            else:
                # Adjust the search range for the last occurrence
                start = mid + 1
 
    return ans
 
 
# Driver program
arr = [1, 2, 2, 2, 2, 3, 4, 7, 8, 8]
n = len(arr)
x = 2
c = count(arr, x)
print(f"{x} occurs {c} times")

                    

C#

// C# program for the above approach
using System;
 
public class GFG {
    /* if x is present in arr[] then returns
    the count of occurrences of x,
    otherwise returns 0. */
    static int Count(int[] arr, int x)
    {
        int firstIndex = Search(arr, x, true);
        int lastIndex = Search(arr, x, false);
        if (firstIndex != -1 && lastIndex != -1)
            return lastIndex - firstIndex + 1;
        else
            return 0;
    }
 
    // if target is present in arr[] then
    // returns the index of FIRST
    // occurrence and last occurrence of target in
    // arr[0..n-1], otherwise returns -1
    static int Search(int[] nums, int target,
                      bool findStartIndex)
    {
        int ans = -1;
        int start = 0;
        int end = nums.Length - 1;
        while (start <= end) {
            // find the middle element
            // int mid = (start + end) / 2;
            // might be possible that (start + end)
            // exceeds the range of int in C#
            int mid = start + (end - start) / 2;
 
            if (target < nums[mid]) {
                end = mid - 1;
            }
            else if (target > nums[mid]) {
                start = mid + 1;
            }
            else {
                // potential ans found
                ans = mid;
                if (findStartIndex) {
                    end = mid - 1;
                }
                else {
                    start = mid + 1;
                }
            }
        }
 
        return ans;
    }
 
    // Driver program
    public static void Main()
    {
        int[] arr = { 1, 2, 2, 2, 2, 3, 4, 7, 8, 8 };
        int n = arr.Length;
        int x = 2;
        int c = Count(arr, x);
        Console.WriteLine(x + " occurs " + c + " times");
    }
}
 
// This code is contributed by Susobhan Akhuli

                    

Javascript

// JavaScript program to count occurrences
// of an element
 
// Function to count occurrences of x in arr
function count(arr, x) {
    const firstIndex = search(arr, x, true);
    const lastIndex = search(arr, x, false);
    if (firstIndex !== -1 && lastIndex !== -1)
        return lastIndex - firstIndex + 1;
    else
        return 0;
}
 
// Function to search for the index of the target
function search(nums, target, findStartIndex) {
    let ans = -1;
    let start = 0;
    let end = nums.length - 1;
    while (start <= end) {
        let mid = start + Math.floor((end - start) / 2);
 
        if (target < nums[mid]) {
            end = mid - 1;
        }
        else if (target > nums[mid]) {
            start = mid + 1;
        }
        else {
            ans = mid;
            if (findStartIndex) {
                end = mid - 1;
            }
            else {
                start = mid + 1;
            }
        }
    }
 
    return ans;
}
 
// Driver program
const arr = [1, 2, 2, 2, 2, 3, 4, 7, 8, 8];
const x = 2;
const c = count(arr, x);
console.log(x + " occurs " + c + " times");
 
// This code is contributed by Susobhan Akhuli

                    

Output
2 occurs 4 times








Time Complexity: O(log n)
Auxiliary Space: O(1) 

Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem. 



Last Updated : 20 Dec, 2023
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