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Number of sub-arrays that have at least one duplicate

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  • Difficulty Level : Medium
  • Last Updated : 09 Sep, 2022
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Given an array arr of n elements, the task is to find the number of the sub-arrays of the given array that contain at least one duplicate element.

Examples: 

Input: arr[] = {1, 2, 3} 
Output:
There is no sub-array with duplicate elements.

Input: arr[] = {4, 3, 4, 3} 
Output:
Possible sub-arrays are {4, 3, 4}, {4, 3, 4, 3} and {3, 4, 3} 

Approach: 

  • First, find the total number of sub-arrays that can be formed from the array and denote this by total then total = (n*(n+1))/2.
  • Now find the sub-arrays that have all the elements distinct (can be found out using window sliding technique) and denote this by unique.
  • Finally, the number of sub-arrays that have at least one element duplicate are (total – unique)

Below is the implementation of the above approach:

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
#define ll long long int
using namespace std;
 
// Function to return the count of the
// sub-arrays that have at least one duplicate
ll count(ll arr[], ll n)
{
    ll unique = 0;
 
    // two pointers
    ll i = -1, j = 0;
 
    // to store frequencies of the numbers
    unordered_map<ll, ll> freq;
    for (j = 0; j < n; j++) {
        freq[arr[j]]++;
 
        // number is not distinct
        if (freq[arr[j]] >= 2) {
            i++;
            while (arr[i] != arr[j]) {
                freq[arr[i]]--;
                i++;
            }
            freq[arr[i]]--;
            unique = unique + (j - i);
        }
        else
            unique = unique + (j - i);
    }
 
    ll total = n * (n + 1) / 2;
 
    return total - unique;
}
 
// Driver code
int main()
{
    ll arr[] = { 4, 3, 4, 3 };
    ll n = sizeof(arr) / sizeof(arr[0]);
    cout << count(arr, n) << endl;
    return 0;
}

Java




// Java implementation of the approach
import java.util.*;
 
class GFG
{
 
// Function to return the count of the
// sub-arrays that have at least one duplicate
static Integer count(Integer arr[], Integer n)
{
    Integer unique = 0;
 
    // two pointers
    Integer i = -1, j = 0;
 
    // to store frequencies of the numbers
    Map<Integer, Integer> freq = new HashMap<>();
    for (j = 0; j < n; j++)
    {
        if(freq.containsKey(arr[j]))
        {
            freq.put(arr[j], freq.get(arr[j]) + 1);
        }
        else
        {
            freq.put(arr[j], 1);
        }
 
        // number is not distinct
        if (freq.get(arr[j]) >= 2)
        {
            i++;
            while (arr[i] != arr[j])
            {
                freq.put(arr[i], freq.get(arr[i]) - 1);
                i++;
            }
            freq.put(arr[i], freq.get(arr[i]) - 1);
            unique = unique + (j - i);
        }
        else
            unique = unique + (j - i);
    }
 
    Integer total = n * (n + 1) / 2;
 
    return total - unique;
}
 
// Driver code
public static void main(String[] args)
{
    Integer arr[] = { 4, 3, 4, 3 };
    Integer n = arr.length;
    System.out.println(count(arr, n));
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python3 implementation of the approach
from collections import defaultdict
 
# Function to return the count of the
# sub-arrays that have at least one duplicate
def count(arr, n):
 
    unique = 0
 
    # two pointers
    i, j = -1, 0
 
    # to store frequencies of the numbers
    freq = defaultdict(lambda:0)
    for j in range(0, n):
        freq[arr[j]] += 1
 
        # number is not distinct
        if freq[arr[j]] >= 2:
            i += 1
             
            while arr[i] != arr[j]:
                freq[arr[i]] -= 1
                i += 1
             
            freq[arr[i]] -= 1
            unique = unique + (j - i)
         
        else:
            unique = unique + (j - i)
     
    total = (n * (n + 1)) // 2
 
    return total - unique
 
# Driver Code
if __name__ == "__main__":
 
    arr = [4, 3, 4, 3]
    n = len(arr)
    print(count(arr, n))
 
# This code is contributed
# by Rituraj Jain

C#




// C# implementation of the approach
using System;
using System.Collections.Generic;            
 
class GFG
{
 
// Function to return the count of the
// sub-arrays that have at least one duplicate
static int count(int []arr, int n)
{
    int unique = 0;
 
    // two pointers
    int i = -1, j = 0;
 
    // to store frequencies of the numbers
    Dictionary<int,
               int> freq = new Dictionary<int,
                                          int>();
    for (j = 0; j < n; j++)
    {
        if(freq.ContainsKey(arr[j]))
        {
            freq[arr[j]] = freq[arr[j]] + 1;
        }
        else
        {
            freq.Add(arr[j], 1);
        }
 
        // number is not distinct
        if (freq[arr[j]] >= 2)
        {
            i++;
            while (arr[i] != arr[j])
            {
                freq[arr[i]] = freq[arr[i]] - 1;
                i++;
            }
            freq[arr[i]] = freq[arr[i]] - 1;
            unique = unique + (j - i);
        }
        else
            unique = unique + (j - i);
    }
 
    int total = n * (n + 1) / 2;
 
    return total - unique;
}
 
// Driver code
public static void Main(String[] args)
{
    int []arr = { 4, 3, 4, 3 };
    int n = arr.Length;
    Console.WriteLine(count(arr, n));
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
// Javascript implementation of the approach
 
// Function to return the count of the
// sub-arrays that have at least one duplicate
function count(arr, n)
{
    let unique = 0;
 
    // two pointers
    let i = -1, j = 0;
 
    // to store frequencies of the numbers
    let freq = new Map();
    for (j = 0; j < n; j++) {
        if(freq.has(arr[j])){
            freq.set(arr[j], freq.get(arr[j]) + 1)
        }else{
            freq.set(arr[j], 1)
        }
 
        // number is not distinct
        if (freq.get(arr[j]) >= 2) {
            i++;
            while (arr[i] != arr[j]) {
                freq.set(arr[i], freq.get(arr[i]) - 1)
                i++;
            }
            freq.set(arr[i], freq.get(arr[i]) - 1)
            unique = unique + (j - i);
        }
        else
            unique = unique + (j - i);
    }
 
    let total =  n *(n + 1) / 2;
 
    return total - unique;
}
 
// Driver code
    let arr = [ 4, 3, 4, 3 ];
    let n = arr.length;
    document.write(count(arr, n) + "<br>");
 
// This code is contributed by _saurabh_jaiswal
</script>

Output

3

Complexity Analysis:

  • Time Complexity: O(N)
  • Auxiliary Space: O(N)

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