Check whether we can sort two arrays by swapping A[i] and B[i]

Given two arrays, we have to check whether we can sort two arrays in strictly ascending order by swapping A[i] and B[i].

Examples:

Input : A[ ]={ 1, 4, 3, 5, 7}, B[ ]={ 2, 2, 5, 8, 9}
Output : True
After swapping A[1] and B[1], both the arrays are sorted.

Input : A[ ]={ 1, 4, 5, 5, 7}, B[ ]={ 2, 2, 5, 8, 9}
Output : False
It is not possible to make both the arrays sorted with any number of swaps.

We are given two arrays, we can swap A[i] with B[i] so that we can sort both the array in strictly ascending order so we have to sort the array in such a way that A[i] < A[i+1] and B[i] < B[i+1].
We will use a greedy approach and solve the problem.
We will get the minimum and maximum of A[i] and B[i] and assign minimum to B[i] and maximum to A[i].
Now, we will check that array A and array B is strictly increasing or not.

Let us consider our approach is incorrect, (there is possibility to arrange but our approach gives false), that means any one or more position is switched.
That means a[i-1] is not less than a[i] or a[i+1] is not greater than a[i] . Now if a[i] is not greater than a[i-1] we cannot switch a[i] with b[i] as b[i] is always less than a[i]. Now let us take a[i+1] is not greater than a[i] so we can switch a[i] with b[i] as a[i] > b[i], but as a[i] > b[i] and a[i+1]> b[i+1] and a[i]>a[i+1] so a[i] can never be less than b[i+1] so there is no possible switch. We can similarly prove for b[i].

So it is proved that there might be more possible combinations for arranging the array when the output is YES but there is no possible way of arranging the array according to constraints when output is NO.

Below is the implementation of the above approach:

C++

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// C++ implementation of above approach
#include <iostream>
using namespace std;
  
// Function to check whether both the array can be 
// sorted in (strictly increasing ) ascending order
bool IsSorted(int A[], int B[], int n)
{
    // Traverse through the array
    // and find out the min and max
    // variable at each position
    // make one array of min variables
    // and another of maximum variable
    for (int i = 0; i < n; i++) {
        int x, y;
  
        // Maximum and minimum variable
        x = max(A[i], B[i]);
        y = min(A[i], B[i]);
  
        // Assign min value to
        // B[i] and max value to A[i]
        A[i] = x;
        B[i] = y;
    }
  
    // Now check whether the array is
    // sorted or not
    for (int i = 1; i < n; i++) {
        if (A[i] <= A[i - 1] || B[i] <= B[i - 1])
            return false;
    }
  
    return true;
}
  
// Driver code
int main()
{
    int A[] = { 1, 4, 3, 5, 7 };
    int B[] = { 2, 2, 5, 8, 9 };
    int n = sizeof(A) / sizeof(int);
  
    cout << (IsSorted(A, B, n) ? "True" : "False");
  
    return 0;
}

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Java

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// Java implementation of above approach
import java.io.*;
  
class GFG
{
          
// Function to check whether both the array can be 
// sorted in (strictly increasing ) ascending order
static boolean IsSorted(int []A, int []B, int n)
{
    // Traverse through the array
    // and find out the min and max
    // variable at each position
    // make one array of min variables
    // and another of maximum variable
    for (int i = 0; i < n; i++)
    {
        int x, y;
  
        // Maximum and minimum variable
        x = Math.max(A[i], B[i]);
        y = Math.min(A[i], B[i]);
  
        // Assign min value to
        // B[i] and max value to A[i]
        A[i] = x;
        B[i] = y;
    }
  
    // Now check whether the array is
    // sorted or not
    for (int i = 1; i < n; i++) 
    {
        if (A[i] <= A[i - 1] || B[i] <= B[i - 1])
            return false;
    }
  
    return true;
}
  
// Driver code
public static void main (String[] args)
{
  
    int []A = { 1, 4, 3, 5, 7 };
    int []B = { 2, 2, 5, 8, 9 };
    int n = A.length;
  
    if(IsSorted(A, B, n) == true)
    {
        System.out.println("True");
    }
    else
    {
        System.out.println("False");
    }
}
}
  
// This code is contributed by ajit 

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Python3

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# Python3 implementation of above approach 
  
# Function to check whether both the array can be 
# sorted in (strictly increasing ) ascending order 
def IsSorted(A, B, n) : 
  
    # Traverse through the array 
    # and find out the min and max 
    # variable at each position 
    # make one array of min variables 
    # and another of maximum variable 
    for i in range(n) :
          
        # Maximum and minimum variable 
        x = max(A[i], B[i]); 
        y = min(A[i], B[i]); 
  
        # Assign min value to 
        # B[i] and max value to A[i] 
        A[i] = x; 
        B[i] = y; 
      
    # Now check whether the array is 
    # sorted or not 
    for i in range(1, n) :
        if (A[i] <= A[i - 1] or B[i] <= B[i - 1]) : 
            return False
  
    return True
  
  
# Driver code 
if __name__ == "__main__"
      
    A = [ 1, 4, 3, 5, 7 ]; 
    B = [ 2, 2, 5, 8, 9 ]; 
      
    n = len(A); 
  
    if (IsSorted(A, B, n)) :
        print(True)
    else :
        print(False
  
# This code is contributed by AnkitRai01

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C#

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// C# implementation of above approach
using System;
  
class GFG
{
      
// Function to check whether both the array can be 
// sorted in (strictly increasing ) ascending order
static bool IsSorted(int []A, int []B, int n)
{
    // Traverse through the array
    // and find out the min and max
    // variable at each position
    // make one array of min variables
    // and another of maximum variable
    for (int i = 0; i < n; i++) {
        int x, y;
  
        // Maximum and minimum variable
        x = Math.Max(A[i], B[i]);
        y = Math.Min(A[i], B[i]);
  
        // Assign min value to
        // B[i] and max value to A[i]
        A[i] = x;
        B[i] = y;
    }
  
    // Now check whether the array is
    // sorted or not
    for (int i = 1; i < n; i++) {
        if (A[i] <= A[i - 1] || B[i] <= B[i - 1])
            return false;
    }
  
    return true;
}
  
// Driver code
public static void Main()
{
    int []A = { 1, 4, 3, 5, 7 };
    int []B = { 2, 2, 5, 8, 9 };
    int n = A.Length;
  
    if(IsSorted(A, B, n) == true)
    {
        Console.Write("True");
    }
    else
    {
        Console.Write("False");
    }
}
}
  
// This code is contributed
// by Akanksha Rai

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Output:

True

Time Complexity : O(N)



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Second year Department of Information Technology Jadavpur University

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Improved By : AnkitRai01, Akanksha_Rai, jit_t



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