Find single Movement in a Matrix

Given four integers x1, y1 and x2, y2 which represent two locations in an infinite 2D-Matrix, the task is to find whether it is possible to move from (x1, y1) to (x2, y2) in a single move, either left, right, up or down. Note that the move will be repeated until the destination is reached. If it is impossible to reach (x2, y2) output -1.

Examples:

Input: x1 = 0, y1 = 0, x2 = 1, y2 = 0
Output: Down
Destination is just below the starting point.



Input: x1 = 0, y1 = 0, x2 = 1, y2 = 1
Output: -1
It is impossible to reach (1, 1) from (0, 0) in a single move.

Approach: Check if the coordinates are either in the same row or in the same column then only its possible to reach the final destination. Then print the move according to the direction of the destination.

Below is the implementation of the above approach:

C++

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#include <bits/stdc++.h>
using namespace std;
  
// Function that checks whether it is
// possible to move from
// (x1, y1) to (x2, y2)
void Robot_Grid(int x1, int y1, int x2, int y2)
{
    // Both locations are
    // in the same row
    if (x1 == x2) {
  
        // Destination is
        // at the right
        if (y1 < y2) {
            cout << "Right";
        }
        // Destination is
        // at the left
        else {
            cout << "Left";
        }
    }
  
    // Both locations are
    // in the same column
    else if (y1 == y2) {
  
        // Destination is below
        // the current row
        if (x1 < x2) {
            cout << "Down";
        }
  
        // Destination is above
        // the current row
        else {
            cout << "Up";
        }
    }
  
    // Impossible to get
    // to the destination
    else {
        cout << "-1";
    }
}
  
// Driver code
int main()
{
    int x1, x2, y1, y2;
    x1 = 0;
    y1 = 0;
    x2 = 0;
    y2 = 1;
  
    Robot_Grid(x1, y1, x2, y2);
    return 0;
}

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Java

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// Java implementation of the given above approach
  
public class GFG{
  
    // Function that checks whether it is 
    // possible to move from 
    // (x1, y1) to (x2, y2) 
    static void Robot_Grid(int x1, int y1, int x2, int y2) 
    
        // Both locations are 
        // in the same row 
        if (x1 == x2) { 
      
            // Destination is 
            // at the right 
            if (y1 < y2) { 
                System.out.print("Right"); 
            
            // Destination is 
            // at the left 
            else
                System.out.print("Left"); 
            
        
      
        // Both locations are 
        // in the same column 
        else if (y1 == y2) { 
      
            // Destination is below 
            // the current row 
            if (x1 < x2) { 
                System.out.print("Down");
            
      
            // Destination is above 
            // the current row 
            else
                System.out.println("Up"); 
            
        
      
        // Impossible to get 
        // to the destination 
        else
            System.out.print("-1"); 
        
    
      
    // Driver code 
     public static void main(String []args)
    
        int x1, x2, y1, y2; 
        x1 = 0
        y1 = 0
        x2 = 0
        y2 = 1
      
        Robot_Grid(x1, y1, x2, y2); 
  
// This code is contributed by Ryuga
}

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Python3

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# Function that checks whether it is
# possible to move from
# (x1, y1) to (x2, y2)
  
def Robot_Grid(x1, y1, x2, y2):
      
    # Both locations are in the same row
    if (x1 == x2):
          
        # Destination is at the right
        if (y1 < y2):
            print("Right")
  
        # Destination is at the left
        else:
            print("Left")
          
    # Both locations are in the same column
    elif (y1 == y2):
          
        # Destination is below the current row
        if (x1 < x2):
            print("Down")
  
        # Destination is above the current row
        else:
            print("Up")
  
    # Impossible to get to the destination
    else:
        print("-1")
  
# Driver code
if __name__ == '__main__':
    x1 = 0
    y1 = 0
    x2 = 0
    y2 = 1
  
    Robot_Grid(x1, y1, x2, y2)
  
# This code is contributed by
# Sanjit_Prasad

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C#

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// C# implementation of the given above approach
using System;
  
class GFG{
  
    // Function that checks whether it is 
    // possible to move from 
    // (x1, y1) to (x2, y2) 
    static void Robot_Grid(int x1, int y1, 
                           int x2, int y2) 
    
        // Both locations are 
        // in the same row 
        if (x1 == x2) 
        
      
            // Destination is 
            // at the right 
            if (y1 < y2) 
            
                Console.Write("Right"); 
            
            // Destination is 
            // at the left 
            else 
            
                Console.Write("Left"); 
            
        
      
        // Both locations are 
        // in the same column 
        else if (y1 == y2) 
        
      
            // Destination is below 
            // the current row 
            if (x1 < x2) 
            
                Console.Write("Down");
            
      
            // Destination is above 
            // the current row 
            else 
            
                Console.WriteLine("Up"); 
            
        
      
        // Impossible to get 
        // to the destination 
        else 
        
            Console.WriteLine("-1"); 
        
    
      
    // Driver code 
    public static void Main()
    
        int x1, x2, y1, y2; 
        x1 = 0; 
        y1 = 0; 
        x2 = 0; 
        y2 = 1; 
      
        Robot_Grid(x1, y1, x2, y2); 
    
}
  
// This code is contributed by 
// Mukul Singh

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PHP

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<?php
// PHP implementation of the above approach
  
// Function that checks whether it is
// possible to move from
// (x1, y1) to (x2, y2)
function Robot_Grid($x1, $y1, $x2, $y2)
{
    // Both locations are in the same row
    if ($x1 == $x2
    {
  
        // Destination is at the right
        if ($y1 < $y2)
        {
            echo "Right";
        }
          
        // Destination is at the left
        else
        {
            echo "Left";
        }
    }
  
    // Both locations are in the same column
    else if ($y1 == $y2)
    {
  
        // Destination is below the 
        // current row
        if ($x1 < $x2)
        {
            echo "Down";
        }
  
        // Destination is above the current row
        else
        {
            echo "Up";
        }
    }
  
    // Impossible to get to the destination
    else
    {
        echo "-1";
    }
}
  
// Driver code
$x1 = 0;
$y1 = 0;
$x2 = 0;
$y2 = 1;
  
Robot_Grid($x1, $y1, $x2, $y2);
  
// This code is contributed by ita_c
?>

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Output:

Right


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