Minimum common element in subarrays of all possible lengths

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Given an array arr[] consisting of N integers from the range [1, N]( repetition allowed ), the task is to find the minimum common element for each possible subarray length. If no such element exists for any particular length of the subarray, then print -1.

Examples:

Input: arr[] = {1, 3, 4, 5, 6, 7}
Output: -1 -1 -1 4 3 1
Explanation:
K = 1: No common element exists. Therefore, print -1.
K = 2: No common element exists. Therefore, print -1.
K = 3: No common element exists. Therefore, print -1.
K = 4: Since 4 is common in all subarrays of size 4, print 4.
K = 5: Since 3 and 4 is common in all subarrays of size 5, print 3 as it is the minimum.
K = 6: Print 1 as it is the minimum element in the array.

Input: arr[]: {1, 2, 2, 2, 1}
Output: -1 2 2 1 1

Approach: Follow the steps below to solve the problem:

Traverse the array and store the last occurrence of every element in a Map.
Initialize an array temp[] and store in it for each value, the maximum distance between any pair of consecutive repetitions of it in the array.
Once the above step is completed, update temp[] by comparing temp[i] with the distance of the last occurrence of i from the end of the array.
Now, store the minimum comment element for all subarrays of length 1 to N one by one and print them.

Below is the implementation of the above approach:

C++

// C++ Program to implement the
// above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find maximum distance
// between every two element
void max_distance(int a[], int temp[], int n)
{
    // Stores index of last occurrence
    // of each array element
    map<int, int> mp;
 
    // Initialize temp[] with -1
    for (int i = 1; i <= n; i++) {
        temp[i] = -1;
    }
 
    // Traverse the array
    for (int i = 0; i < n; i++) {
 
        // If array element has
        // not occurred previously
        if (mp.find(a[i]) == mp.end())
 
            // Update index in temp
            temp[a[i]] = i + 1;
 
        // Otherwise
        else
 
            // Compare temp[a[i]] with distance
            // from its previous occurrence and
            // store the maximum
            temp[a[i]] = max(temp[a[i]],
                             i - mp[a[i]]);
 
        mp[a[i]] = i;
    }
 
    for (int i = 1; i <= n; i++) {
 
        // Compare temp[i] with distance
        // of its last occurrence from the end
        // of the array and store the maximum
        if (temp[i] != -1)
            temp[i] = max(temp[i], n - mp[i]);
    }
}
 
// Function to find the minimum common
// element in subarrays of all possible lengths
void min_comm_ele(int a[], int ans[],
                  int temp[], int n)
{
    // Function call to find the maximum
    // distance between every pair of repetition
    max_distance(a, temp, n);
 
    // Initialize ans[] to -1
    for (int i = 1; i <= n; i++) {
        ans[i] = -1;
    }
 
    for (int i = 1; i <= n; i++) {
 
        // Check if subarray of length
        // temp[i] contains i as one
        // of the common elements
        if (ans[temp[i]] == -1)
            ans[temp[i]] = i;
    }
 
    for (int i = 1; i <= n; i++) {
 
        // Find the minimum of all
        // common elements
        if (i > 1 && ans[i - 1] != -1) {
 
            if (ans[i] == -1)
                ans[i] = ans[i - 1];
            else
                ans[i] = min(ans[i],
                             ans[i - 1]);
        }
 
        cout << ans[i] << " ";
    }
}
 
// Driver Code
int main()
{
    int N = 6;
    int a[] = { 1, 3, 4, 5, 6, 7 };
    int temp[100], ans[100];
    min_comm_ele(a, ans, temp, N);
 
    return 0;
}

Java

// Java program to implement the
// above approach
import java.util.*;
 
class GFG{
    
// Function to find maximum distance
// between every two element
static void max_distance(int a[], int temp[], int n)
{
     
    // Stores index of last occurrence
    // of each array element
    Map<Integer,
        Integer> mp = new HashMap<Integer,
                                  Integer>(); 
 
    // Initialize temp[] with -1
    for(int i = 1; i <= n; i++) 
    {
        temp[i] = -1;
    }
 
    // Traverse the array
    for(int i = 0; i < n; i++) 
    {
         
        // If array element has
        // not occurred previously
        if (mp.get(a[i]) == null)
         
            // Update index in temp
            temp[a[i]] = i + 1;
 
        // Otherwise
        else
 
            // Compare temp[a[i]] with distance
            // from its previous occurrence and
            // store the maximum
            temp[a[i]] = Math.max(temp[a[i]], 
                   i - mp.getOrDefault(a[i], 0));
 
        mp.put(a[i], i);
    }
 
    for(int i = 1; i <= n; i++) 
    {
         
        // Compare temp[i] with distance
        // of its last occurrence from the end
        // of the array and store the maximum
        if (temp[i] != -1)
            temp[i] = Math.max(temp[i],
                               n - mp.getOrDefault(i, 0));
    }
}
 
// Function to find the minimum common
// element in subarrays of all possible lengths
static void min_comm_ele(int a[], int ans[],
                         int temp[], int n)
{
     
    // Function call to find the maximum
    // distance between every pair of repetition
    max_distance(a, temp, n);
 
    // Initialize ans[] to -1
    for(int i = 1; i <= n; i++) 
    {
        ans[i] = -1;
    }
 
    for(int i = 1; i <= n; i++) 
    {
         
        // Check if subarray of length
        // temp[i] contains i as one
        // of the common elements
        if (temp[i] >= 0 && ans[temp[i]] == -1)
            ans[temp[i]] = i;
    }
 
    for(int i = 1; i <= n; i++)
    {
         
        // Find the minimum of all
        // common elements
        if (i > 1 && ans[i - 1] != -1)
        {
            if (ans[i] == -1)
                ans[i] = ans[i - 1];
            else
                ans[i] = Math.min(ans[i],
                                  ans[i - 1]);
        }
        System.out.print(ans[i] + " ");
    }
}
 
// Driver Code
public static void main(String args[])
{
    int N = 6;
    int a[] = { 1, 3, 4, 5, 6, 7 };
     
    int []temp = new int[100];
    Arrays.fill(temp, 0);
     
    int []ans = new int[100];
    Arrays.fill(ans, 0);
     
    min_comm_ele(a, ans, temp, N);
}
}
 
// This code is contributed by SURENDRA_GANGWAR

Python3

# Python3 Program to implement 
# the above approach
 
def min_comm_ele(a):
 
    n = len(a)
    seen = {}
 
    ans = [-1]*(n+1)
    temp = {}
 
    for i in range(n):
 
        # If array element has
        # not occurred previously
        if (a[i] not in seen):
 
            # Update index in temp
            temp[a[i]] = i + 1
 
        # Otherwise
        else:
 
            # Compare temp[a[i]] with 
            # distance from its previous 
            # occurrence and store the maximum
            temp[a[i]] = max(temp[a[i]], i - seen[a[i]])
         
        # Update the latest seen
        seen[a[i]] = i
 
    for i in range(n):
 
        # Compare temp[a[i]] with
        # distance from last occurrence
        # to the end of the array
        # and store the maximum
        if (temp[a[i]] != -1):
            temp[a[i]] = max(temp[a[i]], n - seen[a[i]])
 
    # We now have a hashmap 'temp'
    # which contains for all values in A
    # the smallest size of subarray
    # for which they will always be visible
 
    # ans[i] is the smallest value
    # visible with subarray size i
    # We can extract this value
    # by iterating through temp:
 
    for i in temp:
        if ans[temp[i]] == -1:
            ans[temp[i]] = i
        else:
            ans[temp[i]] = min(ans[temp[i]], i)
 
    # If no specific value had 
    # size i as the minimum,
    # we use the previous subarray's
    # value (if it exists) for i
    # If a value is visible in all
    # subarrays of size n, it must
    # be visible in subarrays of
    # size n+1
 
    for i in range(1,n+1):
        if ans[i] == -1 and ans[i-1] != -1:
            ans[i] = ans[i-1]
 
    # Return the results for 1 to n
    return ans[1:n+1]
 
# Driver Code
if __name__ == "__main__":
    a = [1,3,4,5,6,7]
    res = min_comm_ele(a)
    for m in res:
        print(m, end=" ")
 
# This code is contributed by jmcpeak

C#

// C# program to implement the
// above approach
using System;
using System.Collections.Generic;
class GFG {
     
    // Function to find maximum distance
    // between every two element
    static void max_distance(int[] a, int[] temp, int n)
    {
          
        // Stores index of last occurrence
        // of each array element
        Dictionary<int, int> mp = new Dictionary<int, int>();  
      
        // Initialize temp[] with -1
        for(int i = 1; i <= n; i++) 
        {
            temp[i] = -1;
        }
      
        // Traverse the array
        for(int i = 0; i < n; i++) 
        {
              
            // If array element has
            // not occurred previously
            if (!mp.ContainsKey(a[i]))
              
                // Update index in temp
                temp[a[i]] = i + 1;
      
            // Otherwise
            else
      
                // Compare temp[a[i]] with distance
                // from its previous occurrence and
                // store the maximum
                temp[a[i]] = Math.Max(temp[a[i]], i - mp[a[i]]);
             
            if(mp.ContainsKey(a[i]))
            {
                mp[a[i]] = i;
            }
            else{
                mp.Add(a[i], i);
            }
        }
      
        for(int i = 1; i <= n; i++) 
        {
              
            // Compare temp[i] with distance
            // of its last occurrence from the end
            // of the array and store the maximum
            if (temp[i] != -1)
            {
                if(mp.ContainsKey(i))
                {
                    temp[i] = Math.Max(temp[i], n - mp[i]);
                }
                else{
                    temp[i] = Math.Max(temp[i], n);
                }
            }
        }
    }
      
    // Function to find the minimum common
    // element in subarrays of all possible lengths
    static void min_comm_ele(int[] a, int[] ans,
                             int[] temp, int n)
    {
          
        // Function call to find the maximum
        // distance between every pair of repetition
        max_distance(a, temp, n);
      
        // Initialize ans[] to -1
        for(int i = 1; i <= n; i++) 
        {
            ans[i] = -1;
        }
      
        for(int i = 1; i <= n; i++) 
        {
              
            // Check if subarray of length
            // temp[i] contains i as one
            // of the common elements
            if (temp[i] >= 0 && ans[temp[i]] == -1)
                ans[temp[i]] = i;
        }
      
        for(int i = 1; i <= n; i++)
        {
              
            // Find the minimum of all
            // common elements
            if (i > 1 && ans[i - 1] != -1)
            {
                if (ans[i] == -1)
                    ans[i] = ans[i - 1];
                else
                    ans[i] = Math.Min(ans[i],
                                      ans[i - 1]);
            }
            Console.Write(ans[i] + " ");
        }
    }
 
  // Driver code
  static void Main() 
  {
       
        int N = 6;
        int[] a = { 1, 3, 4, 5, 6, 7 };
          
        int[] temp = new int[100];
        Array.Fill(temp, 0);
          
        int[] ans = new int[100];
        Array.Fill(ans, 0);
          
        min_comm_ele(a, ans, temp, N);
  }
}
 
// This code is contributed by divyeshrabadiya07

Javascript

<script>
  
// JavaScript Program to implement the
// above approach
 
// Function to find maximum distance
// between every two element
function max_distance(a, temp, n)
{
    // Stores index of last occurrence
    // of each array element
    var mp = new Map();
 
    // Initialize temp[] with -1
    for (var i = 1; i <= n; i++) {
        temp[i] = -1;
    }
 
    // Traverse the array
    for (var i = 0; i < n; i++) {
 
        // If array element has
        // not occurred previously
        if (!mp.has(a[i]))
 
            // Update index in temp
            temp[a[i]] = i + 1;
 
        // Otherwise
        else
 
            // Compare temp[a[i]] with distance
            // from its previous occurrence and
            // store the maximum
            temp[a[i]] = Math.max(temp[a[i]],
                             i - mp[a[i]]);
 
        mp.set(a[i], i);
    }
 
    for (var i = 1; i <= n; i++) {
 
        // Compare temp[i] with distance
        // of its last occurrence from the end
        // of the array and store the maximum
        if (temp[i] != -1)
            temp[i] = Math.max(temp[i], n - mp.get(i));
    }
}
 
// Function to find the minimum common
// element in subarrays of all possible lengths
function min_comm_ele(a, ans, temp, n)
{
    // Function call to find the maximum
    // distance between every pair of repetition
    max_distance(a, temp, n);
 
    // Initialize ans[] to -1
    for (var i = 1; i <= n; i++) {
        ans[i] = -1;
    }
 
    for (var i = 1; i <= n; i++) {
 
        // Check if subarray of length
        // temp[i] contains i as one
        // of the common elements
        if (ans[temp[i]] == -1)
            ans[temp[i]] = i;
    }
 
    for (var i = 1; i <= n; i++) {
 
        // Find the minimum of all
        // common elements
        if (i > 1 && ans[i - 1] != -1) {
 
            if (ans[i] == -1)
                ans[i] = ans[i - 1];
            else
                ans[i] = Math.min(ans[i],
                             ans[i - 1]);
        }
 
        document.write( ans[i] + " ");
    }
}
 
// Driver Code
var N = 6;
var a = [1, 3, 4, 5, 6, 7];
var temp =  new Array(100), ans = Array(100);
min_comm_ele(a, ans, temp, N);
 
 
</script>

Output

-1 -1 -1 4 3 1

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

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