Check if all subarrays contains at least one unique element

Given an array arr[] consisting of N integers, the task is to check if all subarrays of the array have at least one unique element in it or not. If found to be true, then print “Yes”. Otherwise, print “No”.

Examples:

Input: arr[] = {1, 2, 1}
Output: Yes
Explanation:
For Subarrays of size 1: {1}, {2}, {1}, the condition will always be true.
For Subarrays of size 2: {1, 2}, {2, 1}, each subarray has at least one unique element.
For Subarrays of size 3 = {1, 2, 1}, in this subarray we have 2 as the only unique element.
Since each subarray has at least one unique element, print “Yes”.

Input: arr[] = {1, 2, 3, 1, 2, 3}
Output: No
Explanation:
Subarrays of size 6: {1, 2, 3, 1, 2, 3} contains no unique element. Therefore, print “No”.

Naive Approach: The simplest approach is to generate all subarrays and use HashMap for each subarray to store the frequency of each element of that subarray. If any subarray does not have at least one unique element, then print “No”. Otherwise, print “Yes”.



Below is the implementation of the above approach:

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// C++ program for above approach
#include<bits/stdc++.h>
using namespace std;
 
// Function to check if all subarrays
// of array have at least one unique element
string check(int arr[], int n)
{
     
    // Stores frequency of subarray
    // elements
    map<int, int> hm;
     
    // Generate all subarrays
    for(int i = 0; i < n; i++)
    {
         
        // Insert first element in map
        hm[arr[i]] = 1;
         
        for(int j = i + 1; j < n; j++)
        {
             
            // Update frequency of current
            // subarray in the HashMap
            hm[arr[j]]++;
 
            bool flag = false;
 
            // Check if at least one element
            // occurs once in current subarray
            for(auto x : hm)
            {
                if (x.second == 1)
                {
                    flag = true;
                    break;
                }
            }
 
            // If any subarray doesn't
            // have unique element
            if (!flag)
                return "No";
        }
 
        // Clear map for next subarray
        hm.clear();
    }
 
    // Return Yes if all subarray
    // having at least 1 unique element
    return "Yes";
}
 
// Driver Code
int main()
{
     
    // Given array arr[]
    int arr[] = { 1, 2, 1 };
 
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    cout << check(arr, N);
}
 
// This code is contributed by bgangwar59
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// Java program for above approach
 
import java.util.*;
import java.lang.*;
 
class GFG {
 
    // Function to check if all subarrays
    // of array have at least one unique element
    static String check(int arr[], int n)
    {
        // Stores frequency of subarray
        // elements
        Map<Integer, Integer> hm
            = new HashMap<>();
 
        // Generate all subarrays
        for (int i = 0; i < n; i++) {
 
            // Insert first element in map
            hm.put(arr[i], 1);
 
            for (int j = i + 1; j < n; j++) {
 
                // Update frequency of current
                // subarray in the HashMap
                hm.put(
                    arr[j],
                    hm.getOrDefault(arr[j], 0) + 1);
 
                boolean flag = false;
 
                // Check if at least one element
                // occurs once in current subarray
                for (Integer k : hm.values()) {
                    if (k == 1) {
                        flag = true;
                        break;
                    }
                }
 
                // If any subarray doesn't
                // have unique element
                if (!flag)
                    return "No";
            }
 
            // Clear map for next subarray
            hm.clear();
        }
 
        // Return Yes if all subarray
        // having at least 1 unique element
        return "Yes";
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        // Given array arr[]
        int[] arr = { 1, 2, 1 };
 
        int N = arr.length;
 
        // Function Call
        System.out.println(check(arr, N));
    }
}
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# Python3 program for
# the above approach
from collections import defaultdict
 
# Function to check if
# all subarrays of array
# have at least one unique
# element
def check(arr, n):
 
    # Stores frequency of
    # subarray elements
    hm = defaultdict (int)
 
    # Generate all subarrays
    for i in range(n):
 
        # Insert first element
        # in map
        hm[arr[i]] += 1
 
        for j in range(i + 1, n):
             
            # Update frequency of
            # current subarray in
            # the HashMap
            hm[arr[j]] += 1
 
            flag = False
 
            # Check if at least one
            # element occurs once in
            # current subarray
            for k in hm.values():
                if (k == 1):
                    flag = True
                    break
                
            # If any subarray doesn't
            # have unique element
            if (not flag):
               return "No"
 
        # Clear map for next
        # subarray
        hm.clear()
 
    # Return Yes if all
    # subarray having at
    # least 1 unique element
    return "Yes"
 
# Driver Code
if __name__ == "__main__":
   
    # Given array arr[]
    arr = [1, 2, 1]
 
    N = len(arr)
 
    # Function Call
    print(check(arr, N))
 
# This code is contributed by Chitranayal
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// C# program for the
// above approach
using System;
using System.Collections.Generic;
class GFG{
 
// Function to check if all
// subarrays of array have at
// least one unique element
static String check(int []arr,
                    int n)
{
  // Stores frequency of
  // subarray elements
  Dictionary<int,
             int> hm =
             new Dictionary<int,
                            int>();
 
  // Generate all subarrays
  for (int i = 0; i < n; i++)
  {
    // Insert first element
    // in map
    hm.Add(arr[i], 1);
 
    for (int j = i + 1; j < n; j++)
    {
      // Update frequency of current
      // subarray in the Dictionary
      if(hm.ContainsKey(arr[j]))
        hm[arr[j]]++;
      else
        hm.Add(arr[j], 1);
 
      bool flag = false;
 
      // Check if at least one 
      // element occurs once
      // in current subarray
      foreach (int k in hm.Values)
      {
        if (k == 1)
        {
          flag = true;
          break;
        }
      }
 
      // If any subarray doesn't
      // have unique element
      if (!flag)
        return "No";
    }
 
    // Clear map for next
    // subarray
    hm.Clear();
  }
 
  // Return Yes if all subarray
  // having at least 1 unique
  // element
  return "Yes";
}
 
// Driver Code
public static void Main(String[] args)
{
  // Given array []arr
  int[] arr = {1, 2, 1};
 
  int N = arr.Length;
 
  // Function Call
  Console.WriteLine(check(arr, N));
}
}
 
// This code is contributed by Rajput-Ji
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Output
Yes



Time Complexity: O(N3)
Auxiliary Space: O(N)

Efficient Approach: Follow the steps below to optimize the above approach:

Below is the implementation of the above approach:

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// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;
 
// Function to check if all subarrays
// have at least one unique element
string check(int arr[], int n)
{
     
    // Generate all subarray
    for(int i = 0; i < n; i++)
    {
         
        // Store frequency of
        // subarray's elements
        map<int, int> hm;
         
        int count = 0;
 
        // Traverse the array over
        // the range [i, N]
        for(int j = i; j < n; j++)
        {
             
            // Update frequency of
            // current subarray in map
            hm[arr[j]]++;
 
            // Increment count
            if (hm[arr[j]] == 1)
                count++;
 
            // Decrement count
            if (hm[arr[j]] == 2)
                count--;
 
            if (count == 0)
                return "No";
        }
    }
 
    // If all subarrays have at
    // least 1 unique element
    return "Yes";
}
 
// Driver Code
int main()
{
     
    // Given array arr[]
    int arr[] = { 1, 2, 1 };
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    cout << check(arr, N);
}
 
// This code is contributed by SURENDRA_GANGWAR
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// Java program for the above approach
 
import java.util.*;
import java.lang.*;
 
class GFG {
 
    // Function to check if all subarrays
    // have at least one unique element
    static String check(int arr[], int n)
    {
        // Generate all subarray
        for (int i = 0; i < n; i++) {
 
            // Store frequency of
            // subarray's elements
            Map<Integer, Integer> hm
                = new HashMap<>();
 
            int count = 0;
 
            // Traverse the array over
            // the range [i, N]
            for (int j = i; j < n; j++) {
 
                // Update frequency of
                // current subarray in map
                hm.put(arr[j],
                       hm.getOrDefault(arr[j], 0) + 1);
 
                // Increment count
                if (hm.get(arr[j]) == 1)
                    count++;
 
                // Decrement count
                if (hm.get(arr[j]) == 2)
                    count--;
 
                if (count == 0)
                    return "No";
            }
        }
 
        // If all subarrays have at
        // least 1 unique element
        return "Yes";
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        // Given array arr[]
        int[] arr = { 1, 2, 1 };
        int N = arr.length;
 
        // Function Call
        System.out.println(check(arr, N));
    }
}
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# Python3 program for the above approach
 
# Function to check if all subarrays
# have at least one unique element
def check(arr, n):
     
    # Generate all subarray
    for i in range(n):
         
        # Store frequency of
        # subarray's elements
        hm = {}
 
        count = 0
 
        # Traverse the array over
        # the range [i, N]
        for j in range(i, n):
             
            # Update frequency of
            # current subarray in map
            hm[arr[j]] = hm.get(arr[j], 0) + 1
 
            # Increment count
            if (hm[arr[j]] == 1):
                count += 1
 
            # Decrement count
            if (hm[arr[j]] == 2):
                count -= 1
 
            if (count == 0):
                return "No"
 
    # If all subarrays have at
    # least 1 unique element
    return "Yes"
 
# Driver Code
if __name__ == '__main__':
     
    # Given array arr[]
    arr = [ 1, 2, 1 ]
    N = len(arr)
 
    # Function Call
    print(check(arr, N))
 
# This code is contributed by mohit kumar 29
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// C# program for the
// above approach
using System;
using System.Collections.Generic;
class GFG {
 
// Function to check if all
// subarrays have at least
// one unique element
static String check(int []arr,
                    int n)
{
  // Generate all subarray
  for (int i = 0; i < n; i++)
  {
    // Store frequency of
    // subarray's elements
    Dictionary<int,
               int> hm =
               new Dictionary<int,
                              int>();
    int count = 0;
 
    // Traverse the array over
    // the range [i, N]
    for (int j = i; j < n; j++)
    {
      // Update frequency of
      // current subarray in map
      if(hm.ContainsKey((arr[j])))
        hm[arr[j]]++;
      else
        hm.Add(arr[j], 1);
 
      // Increment count
      if (hm[arr[j]] == 1)
        count++;
 
      // Decrement count
      if (hm[arr[j]] == 2)
        count--;
 
      if (count == 0)
        return "No";
    }
  }
 
  // If all subarrays have at
  // least 1 unique element
  return "Yes";
}
 
// Driver Code
public static void Main(String[] args)
{
  // Given array []arr
  int[] arr = {1, 2, 1};
  int N = arr.Length;
 
  // Function Call
  Console.WriteLine(check(arr, N));
}
}
 
// This code is contributed by gauravrajput1
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Output
Yes



Time Complexity: O(N2)
Auxiliary Space: O(N) 

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