Check if Array can be sorted in non-decreasing order using given operations

Given an array arr[] of size N consisting of positive integers, the task is to check if the array can be sorted in non-decreasing order by performing the following operations:

• Select two adjacent elements.
• Swap the elements and invert their signs.
• All elements in the sorted array received at the end, must be positive.

Example:

Input: N = 4, arr[] = [4, 3, 2, 5]
Output: true
Explanation: In the given array, perform the following operations:
Swap arr[0] and arr[1] updated array: [-3, -4, 2, 5]
Swap arr[1] and arr[2] updated array: [-3, -2, 4, 5]
Swap arr[1] and arr[0] updated array: [2, 3, 4, 5]
The array is sorted in non-decreasing order and the elements are all positive.

Input: N = 4, arr[] = [3, 3, 2, 2]
Output: true
Explanation: In the given array, perform the following operations :
Swap arr[0] and arr[2] updated array: [-2, 3, -3, 2]
Swap arr[1] and arr[3] updated array: [-2, -2, -3, -3]
Swap arr[1] and arr[0] updated array: [2, 2, -3, -3]
Swap arr[2] and arr[3] updated array: [2, 2, 3, 3]
The array is sorted in non-decreasing order and the elements are all positive.

Input: N = 5, arr[] = [1, 2, 3, 5, 4]
Output: false
Explanation:  There is no way to sort the array such that it follows all the mentioned conditions.

Approach: The problem can be solved using the Greedy approach based on the following observation:

Each number needs to move an even distance because they should all be positive at the end. And a positive number remains positive only after even number of inversion of signs.
So the difference of distance for all array elements between the given one and the sorted array must be even.

Follow the below steps to solve this problem:

• Initialize an empty map (say ctr[2][]) to keep the frequency of an array element in even position and odd position.
• Iterate over an array arr and increment the ctr[i % 1][arr[i]] by 1 
• Sort the array arr[].
• Iterate over the array arr[] and decrement the ctr[i % 1][arr[i]] by 1.
• Iterate over the array arr[] and if ctr[1][a[i]] ≠ 0 or ctr[0][a[i]] ≠ 0 then return false.
• Otherwise, if the iteration is complete then return true.

Below is the implementation of the above approach:

C++

// C++ program for above approach

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

// Function to find if it is possible
// to sort the array in non-decreasing order
bool isItPossible(int n, vector<int>& a)
{
    // Initializing a map 'ctr'.
    map<int, int> ctr[2];

    // Iterating over an array and updating
    // the count for each occurrence
    for (int i = 0; i < n; i++) {
        ctr[i % 2][a[i]]++;
    }

    // Sorting out the array
    sort(a.begin(), a.end());

    // Updating count again according the
    // sorted array
    for (int i = 0; i < n; i++) {
        ctr[i % 2][a[i]]--;
    }

    // Iterating over array again and if the
    // count is not zero then returning false
    for (int i = 0; i < n; i++) {
        if (ctr[0][a[i]] != 0 || ctr[1][a[i]] != 0) {
            return false;
        }
    }
    return true;
}

// Driver code
int main()
{
    int N = 4;
    vector<int> arr = { 3, 3, 2, 2 };

    // Function call
    cout << boolalpha
         << isItPossible(N, arr);
    return 0;
}

Java

// Java program for above approach
import java.util.*;

class GFG
{

    // Function to find if it is possible
    // to sort the array in non-decreasing order
    public static boolean isItPossible(int n, int[] a)
    {

        // Initializing 2 maps 'ctr1' and 'ctr2'
        Map<Integer, Integer> ctr1 = new HashMap<Integer, Integer>();
        Map<Integer, Integer> ctr2 = new HashMap<Integer, Integer>();

        // Iterating over an array and updating
        // the count for each occurrence
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0)
            {
                if (ctr1.containsKey(a[i]))
                    ctr1.put(a[i], ctr1.get(a[i]) + 1);
                else
                    ctr1.put(a[i], 1);
            }
            else
            {
                if (ctr2.containsKey(a[i]))
                    ctr2.put(a[i], ctr2.get(a[i]) + 1);
                else
                    ctr2.put(a[i], 1);
            }
        }

        // Sorting out the array
        Arrays.sort(a);

        // Updating count again according the
        // sorted array
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0)
            {
                if (ctr1.containsKey(a[i]))
                    ctr1.put(a[i], ctr1.get(a[i]) - 1);
                else
                    ctr1.put(a[i],  -1);
            }
            else
            {
                if (ctr2.containsKey(a[i]))
                    ctr2.put(a[i], ctr2.get(a[i]) - 1);
                else
                    ctr2.put(a[i],  -1);
            }
        }

        // Iterating over array again and if the
        // count is not zero then returning false
        for (int i = 0; i < n; i++) {
            if (ctr1.get(a[i]) != 0 || ctr2.get(a[i]) != 0) {
                return false;
            }
        }
        return true;
    }

    public static void main(String[] args) {
        int N = 4;
        int[] arr = { 3, 3, 2, 2 };

        // Function call
        System.out.println(isItPossible(N, arr));
    }
}

// This code is contributed by phasing17

Python3

# Python3 code for the above approach

# Function to find if it is possible
# to sort the array in non-decreasing order
def isItPossible(n, a):

    # Initializing a list of dicts 'ctr'.
    ctr = [dict(), dict()]

    # Iterating over an array and updating
    # the count for each occurrence
    for i in range(n):
        if a[i] in ctr[i % 2]:
            ctr[i % 2][a[i]] += 1
        else:
            ctr[i % 2][a[i]] = 1

    # sorting the array
    a.sort()

    # updating count again according
    # to the sorted array
    for i in range(n):
        if a[i] in ctr[i % 2]:
            ctr[i % 2][a[i]] -= 1

    # iterating over array again
    # and if the count is not zero
    # then returning false
    for i in range(n):
        if a[i] in ctr[0] and ctr[0][a[i]] != 0 or a[i] in ctr[1] and ctr[1][a[i]] != 0:
            return False

    return True

# Driver Code
N = 4
arr = [3, 3, 2, 2]

# Function Call
print(isItPossible(N, arr))

# This code is contributed by phasing17

C#

// C# program for above approach

// Include namespace system
using System;
using System.Collections.Generic;
using System.Linq;
using System.Collections;

public class GFG
{

    // Function to find if it is possible
    // to sort the array in non-decreasing order
    public static bool isItPossible(int n, int[] a)
    {

        // Initializing 2 maps 'ctr1' and 'ctr2'
        var ctr1 = new Dictionary<int, int>();
        var ctr2 = new Dictionary<int, int>();

        // Iterating over an array and updating
        // the count for each occurrence
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0) {
                if (ctr1.ContainsKey(a[i])) {
                    ctr1[a[i]] = ctr1[a[i]] + 1;
                }
                else {
                    ctr1[a[i]] = 1;
                }
            }
            else {
                if (ctr2.ContainsKey(a[i])) {
                    ctr2[a[i]] = ctr2[a[i]] + 1;
                }
                else {
                    ctr2[a[i]] = 1;
                }
            }
        }

        // Sorting out the array
        Array.Sort(a);

        // Updating count again according the
        // sorted array
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0) {
                if (ctr1.ContainsKey(a[i])) {
                    ctr1[a[i]] = ctr1[a[i]] - 1;
                }
                else {
                    ctr1[a[i]] = -1;
                }
            }
            else {
                if (ctr2.ContainsKey(a[i])) {
                    ctr2[a[i]] = ctr2[a[i]] - 1;
                }
                else {
                    ctr2[a[i]] = -1;
                }
            }
        }

        // Iterating over array again and if the
        // count is not zero then returning false
        for (int i = 0; i < n; i++) {
            if (ctr1[a[i]] != 0 || ctr2[a[i]] != 0) {
                return false;
            }
        }
        return true;
    }
    public static void Main(String[] args)
    {
        var N = 4;
        int[] arr = { 3, 3, 2, 2 };

        // Function call
        Console.WriteLine(GFG.isItPossible(N, arr));
    }
}

 // This code is contributed by mukulsomukesh

Javascript

    <script>
        // JavaScript program for above approach

        // Function to find if it is possible
        // to sort the array in non-decreasing order
        const isItPossible = (n, a) => {

            // Initializing a map 'ctr'.
            let ctr = [{}, {}];

            // Iterating over an array and updating
            // the count for each occurrence
            for (let i = 0; i < n; i++) {
                ctr[i % 2][a[i]] = a[i] in ctr[i % 2] ? ctr[i % 2][a[i]] + 1 : 1;
            }

            // Sorting out the array
            a.sort();

            // Updating count again according the
            // sorted array
            for (let i = 0; i < n; i++) {
                if (a[i] in ctr[i % 2])
                    ctr[i % 2][a[i]]--;
            }

            // Iterating over array again and if the
            // count is not zero then returning false
            for (let i = 0; i < n; i++) {
                if (a[i] in ctr[0] && ctr[0][a[i]] != 0 || a[i] in ctr[1] && ctr[1][a[i]] != 0) {
                    return false;
                }
            }
            return true;
        }

        // Driver code

        let N = 4;
        let arr = [3, 3, 2, 2];
s
        // Function call
        document.write(isItPossible(N, arr));

    // This code is contributed by rakeshsahni

    </script>

Output

true

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