Count subarrays having total distinct elements same as original array

Last Updated : 09 Mar, 2023

Given an array of n integers. Count the total number of sub-arrays having total distinct elements, the same as that of the total distinct elements of the original array.

Examples:

Input  : arr[] = {2, 1, 3, 2, 3}
Output : 5
Total distinct elements in array is 3
Total sub-arrays that satisfy the condition 
are:  Subarray from index 0 to 2
      Subarray from index 0 to 3
      Subarray from index 0 to 4
      Subarray from index 1 to 3
      Subarray from index 1 to 4

Input  : arr[] = {2, 4, 5, 2, 1}
Output : 2

Input  : arr[] = {2, 4, 4, 2, 4}
Output : 9

A Naive approach is to run a loop one inside another and consider all sub-arrays and, for every sub-array, count all distinct elements by using hashing and compare them with the total distinct elements of the original array.

Initialise an unordered set unst1 to count distinct elements.
Initialise a variable totalDist for total number of distinct elements in given array.
Generate all the subarray and for every element count the distinct element in that subarray.
Check if the number of distinct elements of the current subarray is equal to totalDist then increment the count by 1.
Finally, return count.

Below is the implementation of the above approach:

C++

// C++ program Count total number of sub-arrays
// having total distinct elements same as that
// original array.
#include <bits/stdc++.h>
using namespace std;

// Function to calculate distinct sub-array
int countDistictSubarray(int arr[], int n)
{
    unordered_set<int> unst1;
    for (int i = 0; i < n; i++)
        unst1.insert(arr[i]);

    int totalDist = unst1.size();
    int count = 0;

    for (int i = 0; i < n; i++) {
        unordered_set<int> unst;
        for (int j = i; j < n; j++) {
            unst.insert(arr[j]);
            if (unst.size() == totalDist)
                count++;
        }
    }

    return count;
}

// Driver code
int main()
{
    int arr[] = { 2, 1, 3, 2, 3 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << countDistictSubarray(arr, n) << endl;
    return 0;
}

// This code is contributed by hkdass001

Java

import java.util.*;

// Function to calculate distinct sub-array
public class Gfg {
    public static int countDistictSubarray(int[] arr, int n)
    {
        Set<Integer> unst1 = new HashSet<>();
        for (int i = 0; i < n; i++)
            unst1.add(arr[i]);

        int totalDist = unst1.size();
        int count = 0;

        for (int i = 0; i < n; i++) {
            Set<Integer> unst = new HashSet<>();
            for (int j = i; j < n; j++) {
                unst.add(arr[j]);
                if (unst.size() == totalDist)
                    count++;
            }
        }

        return count;
    }

    // Driver code
    public static void main(String[] args)
    {
        int[] arr = { 2, 1, 3, 2, 3 };
        int n = arr.length;

        System.out.println(countDistictSubarray(arr, n));
    }
}

Python3

# Python3 program to count total number of sub-arrays
# having total distinct elements same as that
# original array.

# Function to calculate distinct sub-array
def countDistictSubarray(arr, n):
    unst1 = set(arr)
    totalDist = len(unst1)
    count = 0

    for i in range(n):
        unst = set()
        for j in range(i, n):
            unst.add(arr[j])
            if len(unst) == totalDist:
                count += 1

    return count

# Driver code
arr = [2, 1, 3, 2, 3]
n = len(arr)

print(countDistictSubarray(arr, n))
# This code is contributed by Prajwal Kandekar

using System;
using System.Collections.Generic;

class Gfg {
  public static int countDistictSubarray(int[] arr, int n)
  {
    HashSet<int> unst1 = new HashSet<int>();
    for (int i = 0; i < n; i++)
      unst1.Add(arr[i]);

    int totalDist = unst1.Count;
    int count = 0;

    for (int i = 0; i < n; i++) {
      HashSet<int> unst = new HashSet<int>();
      for (int j = i; j < n; j++) {
        unst.Add(arr[j]);
        if (unst.Count == totalDist)
          count++;
      }
    }

    return count;
  }

  // Driver code
  public static void Main(string[] args)
  {
    int[] arr = { 2, 1, 3, 2, 3 };
    int n = arr.Length;

    Console.WriteLine(countDistictSubarray(arr, n));
  }
}

// This code is contributed by divya_p123.

JavaScript

// Javascript program Count total number of sub-arrays
// having total distinct elements same as that
// original array.

// Function to calculate distinct sub-array
function countDistinctSubarray(arr, n) {
  const unst1 = new Set(arr);
  const totalDist = unst1.size;
  let count = 0;

  for (let i = 0; i < n; i++) {
    const unst = new Set();
    for (let j = i; j < n; j++) {
      unst.add(arr[j]);
      if (unst.size === totalDist) {
        count += 1;
      }
    }
  }

  return count;
}

// Driver code
const arr = [2, 1, 3, 2, 3];
const n = arr.length;

console.log(countDistinctSubarray(arr, n));

Output

Time Complexity: O(n*n)
Auxiliary Space: O(n)

An efficient approach is to use a sliding window to count all distinct elements in one iteration.

Find the number of distinct elements in the entire array. Let this number be k <= N. Initialize Left = 0, Right = 0 and window = 0.
Increment right until the number of distinct elements in the range [Left=0, Right] is equal to k(or window size would not equal to k), let this right be R₁. Now, since the sub-array [Left = 0, R₁] has k distinct elements, so all the sub-arrays starting at Left = 0 and ending after R₁ will also have k distinct elements. Thus, add N-R₁+1 to the answer because [Left.. R₁], [Left.. R₁+1], [Left.. R₁+2] ... [Left.. N-1] contains all the distinct numbers.
Now keeping R₁ same, increment left. Decrease the frequency of the previous element i.e., arr[0], and if its frequency becomes 0, decrease the window size. Now, the sub-array is [Left = 1, Right = R₁].
Repeat the same process from step 2 for other values of Left and Right till Left < N.

Implementation:

C++

// C++ program Count total number of sub-arrays
// having total distinct elements same as that
// original array.
#include<bits/stdc++.h>
using namespace std;

// Function to calculate distinct sub-array
int countDistictSubarray(int arr[], int n)
{
    // Count distinct elements in whole array
    unordered_map<int, int>  vis;
    for (int i = 0; i < n; ++i)
        vis[arr[i]] = 1;
    int k = vis.size();

    // Reset the container by removing all elements
    vis.clear();

    // Use sliding window concept to find
    // count of subarrays having k distinct
    // elements.
    int ans = 0, right = 0, window = 0;
    for (int left = 0; left < n; ++left)
    {
        while (right < n && window < k)
        {
            ++vis[ arr[right] ];

            if (vis[ arr[right] ] == 1)
                ++window;

            ++right;
        }

        // If window size equals to array distinct 
        // element size, then update answer
        if (window == k)
            ans += (n - right + 1);

        // Decrease the frequency of previous element
        // for next sliding window
        --vis[ arr[left] ];

        // If frequency is zero then decrease the
        // window size
        if (vis[ arr[left] ] == 0)
                --window;
    }
    return ans;
}

// Driver code
int main()
{
    int arr[] = {2, 1, 3, 2, 3};
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << countDistictSubarray(arr, n) <<"n";
    return 0;
}

Java

// Java program Count total number of sub-arrays
// having total distinct elements same as that
// original array.

import java.util.HashMap;

class Test
{
    // Method to calculate distinct sub-array
    static int countDistictSubarray(int arr[], int n)
    {
        // Count distinct elements in whole array
        HashMap<Integer, Integer>  vis = new HashMap<Integer,Integer>(){
            @Override
            public Integer get(Object key) {
                if(!containsKey(key))
                    return 0;
                return super.get(key);
            }
        };
        
        for (int i = 0; i < n; ++i)
            vis.put(arr[i], 1);
        int k = vis.size();
     
        // Reset the container by removing all elements
        vis.clear();
     
        // Use sliding window concept to find
        // count of subarrays having k distinct
        // elements.
        int ans = 0, right = 0, window = 0;
        for (int left = 0; left < n; ++left)
        {
            while (right < n && window < k)
            {
                vis.put(arr[right], vis.get(arr[right]) + 1);
     
                if (vis.get(arr[right])== 1)
                    ++window;
     
                ++right;
            }
     
            // If window size equals to array distinct 
            // element size, then update answer
            if (window == k)
                ans += (n - right + 1);
     
            // Decrease the frequency of previous element
            // for next sliding window
            vis.put(arr[left], vis.get(arr[left]) - 1);
     
            // If frequency is zero then decrease the
            // window size
            if (vis.get(arr[left]) == 0)
                    --window;
        }
        return ans;
    }

    // Driver method
    public static void main(String args[])
    {
        int arr[] = {2, 1, 3, 2, 3};

        System.out.println(countDistictSubarray(arr, arr.length));
    }
}

Python3

# Python3 program Count total number of 
# sub-arrays having total distinct elements 
# same as that original array.

# Function to calculate distinct sub-array
def countDistictSubarray(arr, n):

    # Count distinct elements in whole array
    vis = dict()
    for i in range(n):
        vis[arr[i]] = 1
    k = len(vis)

    # Reset the container by removing
    # all elements
    vid = dict()

    # Use sliding window concept to find
    # count of subarrays having k distinct
    # elements.
    ans = 0
    right = 0
    window = 0
    for left in range(n):
    
        while (right < n and window < k):

            if arr[right] in vid.keys():
                vid[ arr[right] ] += 1
            else:
                vid[ arr[right] ] = 1

            if (vid[ arr[right] ] == 1):
                window += 1

            right += 1
        
        # If window size equals to array distinct 
        # element size, then update answer
        if (window == k):
            ans += (n - right + 1)

        # Decrease the frequency of previous 
        # element for next sliding window
        vid[ arr[left] ] -= 1

        # If frequency is zero then decrease 
        # the window size
        if (vid[ arr[left] ] == 0):
            window -= 1
    
    return ans

# Driver code
arr = [2, 1, 3, 2, 3]
n = len(arr)

print(countDistictSubarray(arr, n))

# This code is contributed by
# mohit kumar 29

// C# program Count total number of sub-arrays
// having total distinct elements same as that
// original array.
using System;
using System.Collections.Generic;

class Test
{
    // Method to calculate distinct sub-array
    static int countDistictSubarray(int []arr, int n)
    {
        // Count distinct elements in whole array
        Dictionary<int, int> vis = new Dictionary<int,int>();

        for (int i = 0; i < n; ++i)
            if(!vis.ContainsKey(arr[i]))
                vis.Add(arr[i], 1);
        int k = vis.Count;
    
        // Reset the container by removing all elements
        vis.Clear();
    
        // Use sliding window concept to find
        // count of subarrays having k distinct
        // elements.
        int ans = 0, right = 0, window = 0;
        for (int left = 0; left < n; ++left)
        {
            while (right < n && window < k)
            {
                if(vis.ContainsKey(arr[right]))
                    vis[arr[right]] = vis[arr[right]] + 1;
                else
                    vis.Add(arr[right], 1);
    
                if (vis[arr[right]] == 1)
                    ++window;
    
                ++right;
            }
    
            // If window size equals to array distinct 
            // element size, then update answer
            if (window == k)
                ans += (n - right + 1);
    
            // Decrease the frequency of previous element
            // for next sliding window
            if(vis.ContainsKey(arr[left]))
                    vis[arr[left]] = vis[arr[left]] - 1;

    
            // If frequency is zero then decrease the
            // window size
            if (vis[arr[left]] == 0)
                    --window;
        }
        return ans;
    }

    // Driver method
    public static void Main(String []args)
    {
        int []arr = {2, 1, 3, 2, 3};

        Console.WriteLine(countDistictSubarray(arr, arr.Length));
    }
}

// This code is contributed by PrinciRaj1992

JavaScript

<script>
// Javascript program Count total number of sub-arrays
// having total distinct elements same as that
// original array.
    
    // Method to calculate distinct sub-array
    function countDistictSubarray(arr,n)
    {
        // Count distinct elements in whole array
        let  vis = new Map();
          
        for (let i = 0; i < n; ++i)
            vis.set(arr[i], 1);
        let k = vis.size;
       
        // Reset the container by removing all elements
        let vid=new Map();
       
        // Use sliding window concept to find
        // count of subarrays having k distinct
        // elements.
        let ans = 0, right = 0, window = 0;
        for (let left = 0; left < n; left++)
        {
            while (right < n && window < k)
            {
                if(vid.has(arr[right]))
                    vid.set(arr[right], vid.get(arr[right]) + 1);
                else
                    vid.set(arr[right], 1);
       
                if (vid.get(arr[right])== 1)
                    window++;
       
                right++;
            }
               
            // If window size equals to array distinct 
            // element size, then update answer
            if (window == k)
                ans += (n - right + 1);
       
            // Decrease the frequency of previous element
            // for next sliding window
            if(vid.has(arr[left]))
                vid.set(arr[left], vid.get(arr[left])- 1);
       
            // If frequency is zero then decrease the
            // window size
            if (vid.get(arr[left]) == 0)
                    --window;
        }
        
        return ans;
        
    }
    
    // Driver method
    let arr=[2, 1, 3, 2, 3];
    document.write(countDistictSubarray(arr, arr.length));
    

// This code is contributed by patel2127
</script>

Output

5n

Time complexity: O(n)
Auxiliary space: O(n)

Maximum array from two given arrays keeping order same

Shubham Bansal

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Count subarrays having total distinct elements same as original array

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