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Count subarrays with equal number of occurrences of two given elements

  • Difficulty Level : Hard
  • Last Updated : 05 May, 2021

Given an array and two integers say, x and y, find the number of subarrays in which the number of occurrences of x is equal to the number of occurrences of y.

Examples: 

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Input : arr[] = {1, 2, 1},
        x = 1, y = 2 
Output : 2
The possible sub-arrays have same equal number 
of occurrences of x and y are:
1) {1, 2}, x and y have same occurrence(1).
2) {2, 1}, x and y have same occurrence(1).

Input : arr[] = {1, 2, 1},
        x = 4, y = 6
Output : 6
The possible sub-arrays have same equal number of 
occurrences of x and y are:
1) {1}, x and y have same occurrence(0).
2) {2}, x and y have same occurrence(0).
3) {1}, x and y have same occurrence(0).
1) {1, 2}, x and y have same occurrence(0).
2) {2, 1}, x and y have same occurrence(0).
3) {1, 2, 1}, x and y have same occurrence(0).

Input : arr[] = {1, 2, 1},
        x = 1, y = 1
Output : 6
The possible sub-arrays have same equal number 
of occurrences of x and y are:
1) {1}, x and y have same occurrence(1).
2) {2}, x and y have same occurrence(0).
3) {1}, x and y have same occurrence(1).
1) {1, 2}, x and y have same occurrence(1).
2) {2, 1}, x and y have same occurrence(1).
3) {1, 2, 1}, x and y have same occurrences (2).

 Brute Force Approach (Time Complexity – O(N2)):



We can simply generate all the possible sub-arrays and check for each subarray whether the number of occurrences of x is equal to that of y in that particular subarray. 

C++




/* C++ program to count number of sub-arrays in which
   number of occurrence of x is equal to that of y
    using brute force */
#include <bits/stdc++.h>
using namespace std;
 
int sameOccurrence(int arr[], int n, int x, int y)
{
    int result = 0;
 
    // Check for each subarray for the required condition
    for (int i = 0; i <= n - 1; i++) {
        int ctX = 0,  ctY = 0;
        for (int j = i; j <= n - 1; j++) {
            if (arr[j] == x)
                ctX += 1;
            else if (arr[j] == y)
                ctY += 1;
            if (ctX == ctY)
                result += 1;           
        }
    }
 
    return (result);
}
 
// Driver code
int main()
{
    int arr[] = { 1, 2, 2, 3, 4, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = 2, y = 3;
    cout << sameOccurrence(arr, n, x, y);
    return (0);
}

Java




/* Java program to count number of sub-arrays in which
number of occurrence of x is equal to that of y
    using brute force */
import java.util.*;
 
class solution
{
 
static int sameOccurrence(int arr[], int n, int x, int y)
{
    int result = 0;
 
    // Check for each subarray for the required condition
    for (int i = 0; i <= n - 1; i++) {
        int ctX = 0, ctY = 0;
        for (int j = i; j <= n - 1; j++) {
            if (arr[j] == x)
                ctX += 1;
            else if (arr[j] == y)
                ctY += 1;
            if (ctX == ctY)
                result += 1;        
        }
    }
 
    return (result);
}
 
// Driver code
public static void main(String args[])
{
    int arr[] = { 1, 2, 2, 3, 4, 1 };
    int n = arr.length;
    int x = 2, y = 3;
    System.out.println(sameOccurrence(arr, n, x, y));
 
}
}
 
// This code is contributed by
// Sahil_shelangia

Python3




# Python 3 program to count number of
# sub-arrays in which number of occurrence
# of x is equal to that of y using brute force
def sameOccurrence(arr, n, x, y):
    result = 0
 
    # Check for each subarray for
    # the required condition
    for i in range(n):
        ctX = 0
        ctY = 0
        for j in range(i, n, 1):
            if (arr[j] == x):
                ctX += 1;
            elif (arr[j] == y):
                ctY += 1
            if (ctX == ctY):
                result += 1
 
    return (result)
 
# Driver code
if __name__ == '__main__':
    arr = [1, 2, 2, 3, 4, 1]
    n = len(arr)
    x = 2
    y = 3
    print(sameOccurrence(arr, n, x, y))
 
# This code is contributed by
# Surendra_Gangwar

C#




/* C# program to count number of sub-arrays in which
number of occurrence of x is equal to that of y
using brute force */
using System;
 
class GFG
{
 
static int sameOccurrence(int[] arr, int n,
                            int x, int y)
{
    int result = 0;
 
    // Check for each subarray for
    // the required condition
    for (int i = 0; i <= n - 1; i++)
    {
        int ctX = 0, ctY = 0;
        for (int j = i; j <= n - 1; j++)
        {
            if (arr[j] == x)
                ctX += 1;
            else if (arr[j] == y)
                ctY += 1;
            if (ctX == ctY)
                result += 1;        
        }
    }
    return (result);
}
 
// Driver code
public static void Main()
{
    int[] arr = { 1, 2, 2, 3, 4, 1 };
    int n = arr.Length;
    int x = 2, y = 3;
    Console.Write(sameOccurrence(arr, n, x, y));
 
}
}
 
// This code is contributed by Ita_c.

PHP




<?php
// PHP program to count number of sub-arrays
// in which number of occurrence of x is equal
// to that of y using brute force
 
function sameOccurrence($arr, $n, $x, $y)
{
    $result = 0;
 
    // Check for each subarray for the
    // required condition
    for ($i = 0; $i <= $n - 1; $i++)
    {
        $ctX = 0; $ctY = 0;
        for ( $j = $i; $j <= $n - 1; $j++)
        {
            if ($arr[$j] == $x)
                $ctX += 1;
            else if ($arr[$j] == $y)
                $ctY += 1;
            if ($ctX == $ctY)
                $result += 1;    
        }
    }
 
    return ($result);
}
 
// Driver code
$arr = array( 1, 2, 2, 3, 4, 1 );
$n = count($arr);
$x = 2; $y = 3;
echo sameOccurrence($arr, $n, $x, $y);
 
// This code is contributed by 29AjayKumar
?>

Javascript




<script>
 
// Javascript program to count number
// of sub-arrays in which number of
// occurrence of x is equal to that of y
// using brute force
function sameOccurrence(arr, n, x, y)
{
    let result = 0;
     
    // Check for each subarray for the
    // required condition
    for(let i = 0; i <= n - 1; i++)
    {
        let ctX = 0, ctY = 0;
        for(let j = i; j <= n - 1; j++)
        {
            if (arr[j] == x)
                ctX += 1;
            else if (arr[j] == y)
                ctY += 1;
            if (ctX == ctY)
                result += 1;        
        }
    }
    return(result);
}
 
// Driver code
let arr = [ 1, 2, 2, 3, 4, 1 ];
let n = arr.length;
let x = 2, y = 3;
 
document.write(sameOccurrence(arr, n, x, y));
 
// This code is contributed by avanitrachhadiya2155
 
</script>

Output: 

7

Time Complexity – O(N^2) 
Auxiliary Space – O(1)
 

Efficient Approach (O(N) Time Complexity) :

In this solution, auxiliary space is O(N) and the time complexity is also O(N). We create two arrays say, countX[] and countY[], which denotes the number of occurrences of x and y, respectively, till that point in the array. Then, we evaluate another array, say diff which stores (countX[i]-countY[i]), i be the index of the array. Now, store the count of each element of array diff in a map, say m. Initialize result as m[0] since the occurrence of 0 in diff array gives us subarray count where the required condition is followed. Now, iterate through the map and using handshake formula, update the result, since two same values in diff array indicate that the subarray contains the same number of occurrences of x and y.

Explanation:
arr[] = {1, 2, 2, 3, 4, 1};
x = 2, y = 3;

Two arrays countX[] and countY[] are be evaluated as-
countX[] = {0, 1, 2, 2, 2, 2};
countY[] = {0, 0, 0, 1, 1, 1};

Hence, diff[] = {0, 1, 2, 1, 1, 1}; 
(diff[i] = countX[i]-countY[i], i be the index of array)

Now, create a map and store the count of each element of diff in it,
so, finally, we get-
m[0] = 1, m[1] = 4, m[2] = 1;

Initialize result as m[0]
i.e result = m[0] = 1

Further, using handshake formula, updating the 
result as follows-
result  = result + (1*(1-1))/2 = 1 + 0 = 1
result  = result + (4*(4-1))/2 = 1 + 6 = 7
result  = result + (1*(1-1))/2 = 7 + 0 = 7

so, the final result will be 7, required subarrays having 
same number of occurrences of x and y.

C++




/* C++ program to count number of sub-arrays in which
  number of occurrence of x is equal to that of y using
  efficient approach in terms of time */
#include <bits/stdc++.h>
using namespace std;
 
int sameOccurrence(int arr[], int n, int x, int y)
{
    int countX[n], countY[n];
 
    map<int, int> m; // To store counts of same diffs
 
    // Count occurrences of x and y
    for (int i = 0; i < n; i++) {
        if (arr[i] == x) {
            if (i != 0)
                countX[i] = countX[i - 1] + 1;
            else
                countX[i] = 1;
        } else {
            if (i != 0)
                countX[i] = countX[i - 1];
            else
                countX[i] = 0;
        }
        if (arr[i] == y) {
            if (i != 0)
                countY[i] = countY[i - 1] + 1;
            else
                countY[i] = 1;
        } else {
            if (i != 0)
                countY[i] = countY[i - 1];
            else
                countY[i] = 0;
        }
   
         // Increment count of current
         m[countX[i] - countY[i]]++;
    }
 
    // Traverse map and commute result.
    int result = m[0];
    for (auto it = m.begin(); it != m.end(); it++)
        result = result + ((it->second) * ((it->second) - 1)) / 2;
     
    return (result);
}
 
// Driver code
int main()
{
    int arr[] = { 1, 2, 2, 3, 4, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = 2, y = 3;
    cout << sameOccurrence(arr, n, x, y);
    return (0);
}

Java




/* Java program to count number of sub-arrays in which
number of occurrence of x is equal to that of y using
efficient approach in terms of time */
import java.util.*;
 
class GFG
{
 
static int sameOccurrence(int arr[], int n, int x, int y)
{
    int []countX = new int[n];
    int []countY = new int[n];
 
    Map<Integer,Integer> m = new HashMap<>();
     
    // To store counts of same diff
    // Count occurrences of x and y
    for (int i = 0; i < n; i++)
    {
        if (arr[i] == x)
        {
            if (i != 0)
                countX[i] = countX[i - 1] + 1;
            else
                countX[i] = 1;
        }
        else
        {
            if (i != 0)
                countX[i] = countX[i - 1];
            else
                countX[i] = 0;
        }
        if (arr[i] == y)
        {
            if (i != 0)
                countY[i] = countY[i - 1] + 1;
            else
                countY[i] = 1;
        }
        else
        {
            if (i != 0)
                countY[i] = countY[i - 1];
            else
                countY[i] = 0;
        }
     
        // Increment count of current
        if(m.containsKey(countX[i] - countY[i]))
        {
            m.put(countX[i] - countY[i], m.get(countX[i] - countY[i])+1);
        }
        else
        {
            m.put(countX[i] - countY[i], 1);
        }
    }
 
    // Traverse map and commute result.
    int result = m.get(0);
    for (Map.Entry<Integer,Integer> it : m.entrySet())
        result = result + ((it.getValue()) * ((it.getValue()) - 1)) / 2;
     
    return (result);
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = { 1, 2, 2, 3, 4, 1 };
    int n = arr.length;
    int x = 2, y = 3;
    System.out.println(sameOccurrence(arr, n, x, y));
}
}
 
// This code is contributed by Rajput-Ji

Python3




# Python3 program to count number of
# sub-arrays in which number of occurrence
# of x is equal to that of y using efficient
# approach in terms of time */
def sameOccurrence( arr, n, x, y):
 
    countX = [0 for i in range(n)]
    countY = [0 for i in range(n)]
 
    # To store counts of same diffs
    m = dict()
 
    # Count occurrences of x and y
    for i in range(n):
        if (arr[i] == x):
            if (i != 0):
                countX[i] = countX[i - 1] + 1
            else:
                countX[i] = 1
        else:
            if (i != 0):
                countX[i] = countX[i - 1]
            else:
                countX[i] = 0
 
        if (arr[i] == y):
            if (i != 0):
                countY[i] = countY[i - 1] + 1
            else:
                countY[i] = 1
        else:
            if (i != 0):
                countY[i] = countY[i - 1]
            else:
                countY[i] = 0
         
        # Increment count of current
        m[countX[i] - countY[i]] = m.get(countX[i] -
                                         countY[i], 0) + 1
     
    # Traverse map and commute result.
    result = m[0]
    for j in m:
        result += (m[j] * (m[j] - 1)) // 2
     
    return result
 
# Driver code
arr = [1, 2, 2, 3, 4, 1]
n = len(arr)
x, y = 2, 3
print(sameOccurrence(arr, n, x, y))
  
# This code is contributed
# by mohit kumar

C#




/* C# program to count number of sub-arrays in which
number of occurrence of x is equal to that of y using
efficient approach in terms of time */
using System;
using System.Collections.Generic;
 
class GFG
{
 
static int sameOccurrence(int []arr, int n, int x, int y)
{
    int []countX = new int[n];
    int []countY = new int[n];
 
    Dictionary<int,int> m = new Dictionary<int,int>();
     
    // To store counts of same diff
    // Count occurrences of x and y
    for (int i = 0; i < n; i++)
    {
        if (arr[i] == x)
        {
            if (i != 0)
                countX[i] = countX[i - 1] + 1;
            else
                countX[i] = 1;
        }
        else
        {
            if (i != 0)
                countX[i] = countX[i - 1];
            else
                countX[i] = 0;
        }
        if (arr[i] == y)
        {
            if (i != 0)
                countY[i] = countY[i - 1] + 1;
            else
                countY[i] = 1;
        }
        else
        {
            if (i != 0)
                countY[i] = countY[i - 1];
            else
                countY[i] = 0;
        }
     
        // Increment count of current
        if(m.ContainsKey(countX[i] - countY[i]))
        {
            var v = m[countX[i] - countY[i]]+1;
            m.Remove(countX[i] - countY[i]);
            m.Add(countX[i] - countY[i], v);
        }
        else
        {
            m.Add(countX[i] - countY[i], 1);
        }
    }
 
    // Traverse map and commute result.
    int result = m[0];
    foreach(KeyValuePair<int, int> it in m)
        result = result + ((it.Value) * ((it.Value) - 1)) / 2;
     
    return (result);
}
 
// Driver code
public static void Main(String[] args)
{
    int []arr = { 1, 2, 2, 3, 4, 1 };
    int n = arr.Length;
    int x = 2, y = 3;
    Console.WriteLine(sameOccurrence(arr, n, x, y));
}
}
 
// This code is contributed by Princi Singh

Javascript




<script>
 
/* Javascript program to count number of sub-arrays in which
number of occurrence of x is equal to that of y using
efficient approach in terms of time */
     
    function sameOccurrence(arr,n,x,y)
    {
        let countX = new Array(n);
        let countY = new Array(n);
         
        let m = new Map();
         
        // To store counts of same diff
    // Count occurrences of x and y
    for (let i = 0; i < n; i++)
    {
        if (arr[i] == x)
        {
            if (i != 0)
                countX[i] = countX[i - 1] + 1;
            else
                countX[i] = 1;
        }
        else
        {
            if (i != 0)
                countX[i] = countX[i - 1];
            else
                countX[i] = 0;
        }
        if (arr[i] == y)
        {
            if (i != 0)
                countY[i] = countY[i - 1] + 1;
            else
                countY[i] = 1;
        }
        else
        {
            if (i != 0)
                countY[i] = countY[i - 1];
            else
                countY[i] = 0;
        }
      
        // Increment count of current
        if(m.has(countX[i] - countY[i]))
        {
            m.set(countX[i] - countY[i], m.get(countX[i] - countY[i])+1);
        }
        else
        {
            m.set(countX[i] - countY[i], 1);
        }
    }
  
    // Traverse map and commute result.
    let result = m.get(0);
    for (let [key, value] of m.entries())
        result = result + (value) * ((value) - 1) / 2;
      
    return (result);
    }
     
    // Driver code
    let arr=[1, 2, 2, 3, 4, 1];
    let n = arr.length;
    let x = 2, y = 3;
    document.write(sameOccurrence(arr, n, x, y));
     
     
    // This code is contributed by rag2127
</script>

Output: 

7

Time Complexity – O(N) 
Auxiliary Space – O(N)

This article is contributed by Divyanshu_Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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