Remove elements to make array sorted

Given an array of integers, the task is to remove elements from the array to make the array sorted. That is, remove the elements which do not follow an increasing order.

Examples:  

Input: arr[] = {1, 2, 4, 3, 5, 7, 8, 6, 9, 10} 
Output: 1 2 4 5 7 8 9 10

Input: arr[] = {10, 12, 9, 5, 2, 13, 14} 
Output: 10 12 13 14  

Approach: Traverse the given array and for every element which is greater than or equal to the previously taken element, add this element to another array else skip to the next element. In the end, the newly created array will be sorted according to Stalin sort. 

1. For each element check if the element is greater than the previous element or not. 
   
   • If yes then check for the next element.
   • Else remove that element.
2. After all the elements have been traversed, we will get a sorted array.

Algorithm:

Step 1: Initialize an empty array brr[] of size n and a variable i to 1 to keep track of the index of the sorted array.
Step 2: Set the first element of brr[] to the first element of arr[].
Step 3: Loop through the array arr from index 1 to n-1.
            a. If the current element at index i is greater than or equal to the last element of the sorted array brr[i-1],then insert the element at index i                      to the sorted array brr at index i and increment l by 1.
Step 4: Print the sorted array brr from index 0 to i-1.

Below is the implementation of the above approach:  

// C++ implementation of the approach

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

// Function to sort the array
// by removing misplaced elements
void removeElements(int arr[], int n)
{

    // brr[] is used to store
    // the sorted array elements
    int brr[n], l = 1;

    brr[0] = arr[0];
    for (int i = 1; i < n; i++) {
        if (brr[l - 1] <= arr[i]) {
            brr[l] = arr[i];
            l++;
        }
    }

    // Print the sorted array
    for (int i = 0; i < l; i++)
        cout << brr[i] << " ";
}

// Driver code
int main()
{
    int arr[] = { 10, 12, 9, 10, 2, 13, 14 };
    int n = sizeof(arr) / sizeof(arr[0]);
    removeElements(arr, n);

    return 0;
}

// Java implementation of the approach

class GFG
{
    
// Function to sort the array
// by removing misplaced elements
static void removeElements(int []arr, int n)
{

    // brr[] is used to store
    // the sorted array elements
    int []brr = new int[n];
    int l = 1;

    brr[0] = arr[0];
    for (int i = 1; i < n; i++)
    {
        if (brr[l - 1] <= arr[i]) 
        {
            brr[l] = arr[i];
            l++;
        }
    }

    // Print the sorted array
    for (int i = 0; i < l; i++)
        System.out.print(brr[i] + " ");
}

// Driver code
static public void main (String[] args)
{
    int []arr = { 10, 12, 9, 10, 2, 13, 14 };
    int n = arr.length;
    removeElements(arr, n);
}
}

// This code is contributed by Code_Mech.

# Python3 implementation of the approach 

# Function to sort the array 
# by removing misplaced elements 
def removeElements(arr,  n) : 

    # brr[] is used to store 
    # the sorted array elements 
    brr = [0]*n; l = 1; 

    brr[0] = arr[0]; 
    for i in range(1,n) :
        if (brr[l - 1] <= arr[i]) :
            brr[l] = arr[i]; 
            l += 1; 

    # Print the sorted array 
    for i in range(l) :
        print(brr[i],end=" "); 


# Driver code 
if __name__ == "__main__" : 

    arr = [ 10, 12, 9, 10, 2, 13, 14 ]; 
    n = len(arr); 
    removeElements(arr, n); 

    # This code is contributed by AnkitRai01

// C# implementation of the approach
using System;

class GFG
{
    
// Function to sort the array
// by removing misplaced elements
static void removeElements(int []arr, int n)
{

    // brr[] is used to store
    // the sorted array elements
    int []brr = new int[n];
    int l = 1;

    brr[0] = arr[0];
    for (int i = 1; i < n; i++)
    {
        if (brr[l - 1] <= arr[i]) 
        {
            brr[l] = arr[i];
            l++;
        }
    }

    // Print the sorted array
    for (int i = 0; i < l; i++)
        Console.Write(brr[i] + " ");
}

// Driver code
static public void Main ()
{
    int []arr = { 10, 12, 9, 10, 2, 13, 14 };
    int n = arr.Length;
    removeElements(arr, n);
}
}

// This code is contributed by jit_t

<script>
    // Javascript implementation of the approach
    
    // Function to sort the array
    // by removing misplaced elements
    function removeElements(arr, n)
    {

        // brr[] is used to store
        // the sorted array elements
        let brr = new Array(n);
        brr.fill(0);
        let l = 1;

        brr[0] = arr[0];
        for (let i = 1; i < n; i++)
        {
            if (brr[l - 1] <= arr[i]) 
            {
                brr[l] = arr[i];
                l++;
            }
        }

        // Print the sorted array
        for (let i = 0; i < l; i++)
            document.write(brr[i] + " ");
    }
    
    let arr = [ 10, 12, 9, 10, 2, 13, 14 ];
    let n = arr.length;
    removeElements(arr, n);

</script>

10 12 13 14

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

Algorithm:

Step 1: Initialize a variable i to 1 to keep track of the index of the sorted array.
Step 2: Loop through the array arr from index 1 to n-1.
             a. If the current element at index i is greater than or equal to the last element of the sorted array arr[i-1], then insert the element at index i                    to the sorted array arr at index l and increment i by 1.
Step 3: Print the sorted array arr from index 0 to i-1.

Method 2: Instead of using an extra array, store them in the same array  

// C++ implementation of the approach

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

// Function to sort the array
// by removing misplaced elements
void removeElements(int arr[], int n)
{

    // l stores the index
    int l = 1;
    for (int i = 1; i < n; i++) {
        if (arr[l - 1] <= arr[i]) {
            arr[l] = arr[i];
            l++;
        }
    }

    // Print the sorted array
    for (int i = 0; i < l; i++)
        cout << arr[i] << " ";
}

// Driver code
int main()
{
    int arr[] = { 10, 12, 9, 10, 2, 13, 14 };
    int n = sizeof(arr) / sizeof(arr[0]);
    removeElements(arr, n);

    return 0;
}

// Java implementation of the approach
class GFG{

// Function to sort the array
// by removing misplaced elements
static void removeElements(int arr[], int n)
{
    
    // l stores the index
    int l = 1;
    for(int i = 1; i < n; i++) 
    {
        if (arr[l - 1] <= arr[i]) 
        {
            arr[l] = arr[i];
            l++;
        }
    }

    // Print the sorted array
    for(int i = 0; i < l; i++)
        System.out.print(arr[i] + " ");
}

// Driver code
public static void main(String[] args)
{
    int arr[] = { 10, 12, 9, 10, 2, 13, 14 };
    int n = arr.length;
    
    removeElements(arr, n);
}
}

// This code is contributed by shikhasingrajput 

# Python3 implementation of the approach

# Function to sort the array
# by removing misplaced elements
def removeElements(arr, n):
    
    # l stores the index
    l = 1
    for i in range(1, n):
        if (arr[l - 1] <= arr[i]):
            arr[l] = arr[i]
            l += 1
        
    # Print the sorted array
    for i in range(l):
        print(arr[i], end = " ")

# Driver code
if __name__ == "__main__" :

    arr = [ 10, 12, 9, 10, 2, 13, 14 ]
    n = len(arr)
    
    removeElements(arr, n)

# This code is contributed by Surbhi Tyagi.

// C# implementation of the approach
using System;

class GFG{

// Function to sort the array
// by removing misplaced elements
public static void removeElements(int []arr, int n)
{
    
    // l stores the index
    int l = 1;
    for(int i = 1; i < n; i++) 
    {
        if (arr[l - 1] <= arr[i])
        {
            arr[l] = arr[i];
            l++;
        }
    }

    // Print the sorted array
    for(int i = 0; i < l; i++)
        Console.Write( arr[i] + " ");
}

// Driver code
public static void Main(string []args)
{
    int []arr = { 10, 12, 9, 10, 2, 13, 14 };
    int n = arr.Length;
    
    removeElements(arr, n);
}
}

// This code is contributed by importantly

<script>

    // Javascript implementation of the approach
    
    // Function to sort the array
    // by removing misplaced elements
    function removeElements(arr, n)
    {

        // l stores the index
        let l = 1;
        for (let i = 1; i < n; i++) {
            if (arr[l - 1] <= arr[i]) {
                arr[l] = arr[i];
                l++;
            }
        }

        // Print the sorted array
        for (let i = 0; i < l; i++)
            document.write(arr[i] + " ");
    }
    
    let arr = [ 10, 12, 9, 10, 2, 13, 14 ];
    let n = arr.length;
    removeElements(arr, n);

</script>

10 12 13 14

Time Complexity: O(n)
Auxiliary Space: O(1)