Make sum of all subarrays of length K equal by only inserting elements

Given an array arr[] of length N such that (1 <= arr[i] <= N), the task is to modify the array, by only inserting elements within the range [1, N], such that the sum of all subarrays of length K become equal. Print the modified array, if possible. Else print “Not possible”.
Examples:

Input: arr[] = {1, 2, 2, 1}, K = 2 
Output: 1 2 1 2 1 
Explanation:
Insert 1 between second and third element. 
Now all subarray of length K has an equal sum of 3.
Input: arr[] = {1, 2, 3, 4}, K = 3 
Output: Not possible

Approach:

• Since the removal of elements is not allowed, therefore the only case when such a modified array can be achieved, is when there are at most K distinct elements in the array.
• Therefore, Firstly check if there are more than K distinct elements in the given array. If yes, then print “Not possible”.
• Else, store all the distinct elements of the given array in a vector.
• If the number of distinct elements is less than K, then add/repeat some elements in the vector and make the size of the vector equal to K.
• The vector has now K elements. Now repeat the elements of the vector in the same order to show the modified array. This repetition is done to show all the subarrays of length K have the same sum.

Below is the implementation of the above approach

C++

// C++ implementation of above approach

#include <bits/stdc++.h>
using namespace std;

// Function that prints another array
// whose all subarray of length k
// have an equal sum
void MakeArray(int a[], int n, int k)
{
    unordered_map<int, int> mp;

    // Store all distinct elements in
    // the unordered map
    for (int i = 0; i < n; i++) {
        if (mp.find(a[i]) == mp.end())
            mp[a[i]] = 1;
    }

    // Condition if the number of
    // distinct elements is greater
    // than k
    if (mp.size() > k) {
        cout << "Not possible\n";
        return;
    }

    vector<int> ans;

    // Push all distinct elements
    // in a vector
    for (auto i : mp) {
        ans.push_back(i.first);
    }

    // Push 1 while the size of
    // vector not equal to k
    while (ans.size() < k) {
        ans.push_back(1);
    }

    // Print the vector 2 times
    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < k; j++)
            cout << ans[j] << " ";
    }
}

// Driver Code
int main()
{
    int arr[] = { 1, 2, 2, 1 };
    int K = 2;
    int size = sizeof(arr) / sizeof(arr[0]);

    MakeArray(arr, size, K);

    return 0;
}

Java

// Java implementation of above approach
import java.util.*;
class GFG{

// Function that prints another array
// whose all subarray of length k
// have an equal sum
static void MakeArray(int a[], int n, int k)
{
    HashMap<Integer,
              Integer> mp = new HashMap<Integer,
                                        Integer>();

    // Store all distinct elements in
    // the unordered map
    for (int i = 0; i < n; i++)
    {
        if (!mp.containsKey(a[i]))
            mp.put(a[i], 1);
    }

    // Condition if the number of
    // distinct elements is greater
    // than k
    if (mp.size() > k)
    {
        System.out.print("Not possible\n");
        return;
    }

    Vector<Integer> ans = new Vector<Integer>();

    // Push all distinct elements
    // in a vector
    for (Map.Entry<Integer,Integer> i : mp.entrySet())
    {
        ans.add(i.getKey());
    }

    // Push 1 while the size of
    // vector not equal to k
    while (ans.size() < k)
    {
        ans.add(1);
    }

    // Print the vector 2 times
    for (int i = 0; i < 2; i++)
    {
        for (int j = 0; j < k; j++)
            System.out.print(ans.get(j) + " ");
    }
}

// Driver Code
public static void main(String[] args)
{
    int arr[] = { 1, 2, 2, 1 };
    int K = 2;
    int size = arr.length;

    MakeArray(arr, size, K);
}
}

// This code is contributed by Rohit_ranjan

Python3

# Python3 implementation of above approach

# Function that prints another array
# whose all subarray of length k
# have an equal sum
def MakeArray(a, n, k):
    mp = dict()

    # Store all distinct elements in
    # the unordered map
    for i in a:
        if i not in mp:
            mp[a[i]] = 1

    # Condition if the number of
    # distinct elements is greater
    # than k
    if(len(mp) > k):
       print("Not possible")
       return

    ans = []

    # Push all distinct elements
    # in a vector
    for i in mp:
        ans.append(i)

    # Push 1 while the size of
    # vector not equal to k
    while(len(ans) < k):
          ans.append(1)

    # Print the vector 2 times
    for i in range(2):
        for j in range(k):
            print(ans[j], end = " ")

# Driver Code
if __name__ == '__main__':

    arr = [ 1, 2, 2, 1 ]
    K = 2
    size = len(arr)

    MakeArray(arr, size, K)

# This code is contributed by mohit kumar 29

C#

// C# implementation of above approach
using System;
using System.Collections.Generic;

class GFG{

// Function that prints another array
// whose all subarray of length k
// have an equal sum
static void MakeArray(int []a, int n, int k)
{
    Dictionary<int,
               int> mp = new Dictionary<int,
                                        int>();

    // Store all distinct elements in
    // the unordered map
    for(int i = 0; i < n; i++)
    {
        if (!mp.ContainsKey(a[i]))
             mp.Add(a[i], 1);
    }

    // Condition if the number of
    // distinct elements is greater
    // than k
    if (mp.Count > k)
    {
        Console.Write("Not possible\n");
        return;
    }

    List<int> ans = new List<int>();

    // Push all distinct elements
    // in a vector
    foreach(KeyValuePair<int, int> i in mp)
    {
        ans.Add(i.Key);
    }

    // Push 1 while the size of
    // vector not equal to k
    while (ans.Count < k)
    {
        ans.Add(1);
    }

    // Print the vector 2 times
    for(int i = 0; i < 2; i++)
    {
        for(int j = 0; j < k; j++)
            Console.Write(ans[j] + " ");
    }
}

// Driver Code
public static void Main(String[] args)
{
    int []arr = { 1, 2, 2, 1 };
    int K = 2;
    int size = arr.Length;

    MakeArray(arr, size, K);
}
}

// This code is contributed by amal kumar choubey

Javascript

<script>

// Javascript implementation of above approach

// Function that prints another array
// whose all subarray of length k
// have an equal sum
function MakeArray(a, n, k)
{
    var mp = new Map();

    // Store all distinct elements in
    // the unordered map
    for (var i = 0; i < n; i++) {
        if (!mp.has(a[i]))
            mp.set(a[i], 1);
    }

    // Condition if the number of
    // distinct elements is greater
    // than k
    if (mp.count > k) {
        document.write( "Not possible<br>");
        return;
    }

    var ans = [];

    // Push all distinct elements
    // in a vector
    mp.forEach((value, key) => {
        ans.push(key);
    });


    // Push 1 while the size of
    // vector not equal to k
    while (ans.length < k) {
        ans.push(1);
    }

    // Print the vector 2 times
    for (var i = 0; i < 2; i++) {
        for (var j = 0; j < k; j++)
            document.write( ans[j] + " ");
    }
}

// Driver Code
var arr = [1, 2, 2, 1];
var K = 2;
var size = arr.length;
MakeArray(arr, size, K);

// This code is contributed by rutvik_56.
</script>

Output:

2 1 2 1

Time Complexity: O(N), where N is the size of the given array.
Auxiliary Space: O(N), in order to store elements in HashMap.