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# Check if possible to move from given coordinate to desired coordinate

• Difficulty Level : Medium
• Last Updated : 19 May, 2021

Given two coordinates (x, y) and (a, b). Find if it is possible to reach (x, y) from (a, b).
Only possible moves from any coordinate (i, j) are

• (i-j, j)
• (i, i-j)
• (i+j, j)
• (i, i+j)

Given x, y, a, b can be negative.
Examples:

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```Input : (x, y) = (1, 1) and  (a, b) = (2, 3).
Output : Yes.
(1, 1) -> (2, 1) -> (2, 3).

Input : (x, y) = (2, 1) and  (a, b) = (2, 3).
Output : Yes.

Input : (x, y) = (35, 15) and  (a, b) = (20, 25).
Output : Yes.
(35, 15) -> (20, 15) -> (5, 15) -> (5, 10) -> (5, 5) ->
(10, 5) -> (15, 5) -> (20, 5) -> (20, 25)```

If we take a closer look at the problem, we can notice that the moves are similar steps of Euclidean algorithm for finding GCD. So, it is only possible to reach coordinate (a, b) from (x, y) if GCD of x, y is equal to GCD of a, b. Otherwise, it is not possible.
Let GCD of (x, y) be gcd. From (x, y), we can reach (gcd, gcd) and from this point, we can reach to (a, b) if and only if GCD of ‘a’ and ‘b’ is also gcd.
Below is the implementation of this approach:

C/C++

` `

## C++

 `// C++ program to check if it is possible to reach``// (a, b) from (x, y).``#include ``using` `namespace` `std;` `// Returns GCD of i and j``int` `gcd(``int` `i, ``int` `j)``{``    ``if` `(i == j)``        ``return` `i;` `    ``if` `(i > j)``        ``return` `gcd(i - j, j);``    ``return` `gcd(i, j - i);``}` `// Returns true if it is possible to go to (a, b)``// from (x, y)``bool` `ispossible(``int` `x, ``int` `y, ``int` `a, ``int` `b)``{``    ``// Find absolute values of all as sign doesn't``    ``// matter.``    ``x = ``abs``(x), y = ``abs``(y), a = ``abs``(a), b = ``abs``(b);` `    ``// If gcd is equal then it is possible to reach.``    ``// Else not possible.``    ``return` `(gcd(x, y) == gcd(a, b));``}` `// Driven Program``int` `main()``{``    ``// Converting coordinate into positive integer``    ``int` `x = 35, y = 15;``    ``int` `a = 20, b = 25;``    ``(ispossible(x, y, a, b)) ? (cout << ``"Yes"``) : (cout << ``"No"``);``    ``return` `0;``}`

## Java

 `// Java program to check if it is possible``// to reach (a, b) from (x, y).``class` `GFG {` `    ``// Returns GCD of i and j``    ``static` `int` `gcd(``int` `i, ``int` `j)``    ``{``        ``if` `(i == j)``            ``return` `i;` `        ``if` `(i > j)``            ``return` `gcd(i - j, j);``        ``return` `gcd(i, j - i);``    ``}` `    ``// Returns true if it is possible to go to (a, b)``    ``// from (x, y)``    ``static` `boolean` `ispossible(``int` `x, ``int` `y, ``int` `a, ``int` `b)``    ``{` `        ``// Find absolute values of all as``        ``// sign doesn't matter.``        ``x = Math.abs(x);``        ``y = Math.abs(y);``        ``a = Math.abs(a);``        ``b = Math.abs(b);` `        ``// If gcd is equal then it is possible to reach.``        ``// Else not possible.``        ``return` `(gcd(x, y) == gcd(a, b));``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{` `        ``// Converting coordinate into positive integer``        ``int` `x = ``35``, y = ``15``;``        ``int` `a = ``20``, b = ``25``;``        ``if` `(ispossible(x, y, a, b))``            ``System.out.print(``"Yes"``);``        ``else``            ``System.out.print(``"No"``);``    ``}``}``// This code is contributed by Anant Agarwal.`

## Python

 `# Python program to check if it is possible to reach``# (a, b) from (x, y).``# Returns GCD of i and j``def` `gcd(i, j):``    ``if` `(i ``=``=` `j):``        ``return` `i`` ` `    ``if` `(i > j):``        ``return` `gcd(i ``-` `j, j)``    ``return` `gcd(i, j ``-` `i)`` ` `# Returns true if it is possible to go to (a, b)``# from (x, y)``def` `ispossible(x, y, a, b):``    ``# Find absolute values of all as sign doesn't``    ``# matter.``    ``x, y, a, b ``=` `abs``(x), ``abs``(y), ``abs``(a), ``abs``(b)`` ` `    ``# If gcd is equal then it is possible to reach.``    ``# Else not possible.``    ``return` `(gcd(x, y) ``=``=` `gcd(a, b))`` ` `# Driven Program``    ``# Converting coordinate into positive integer``x, y ``=` `35``, ``15``a, b ``=` `20``, ``25``if``(ispossible(x, y, a, b)):``    ``print` `"Yes"``else``:``    ``print` `"No"``# Contributed by Afzal Ansari`

## C#

 `// C# program to check if it is possible``// to reach (a, b) from (x, y).``using` `System;` `class` `GFG {` `    ``// Returns GCD of i and j``    ``static` `int` `gcd(``int` `i, ``int` `j)``    ``{``        ``if` `(i == j)``            ``return` `i;` `        ``if` `(i > j)``            ``return` `gcd(i - j, j);``        ``return` `gcd(i, j - i);``    ``}` `    ``// Returns true if it is possible``    ``// to go to (a, b) from (x, y)``    ``static` `bool` `ispossible(``int` `x, ``int` `y,``                           ``int` `a, ``int` `b)``    ``{` `        ``// Find absolute values of all as``        ``// sign doesn't matter.``        ``x = Math.Abs(x);``        ``y = Math.Abs(y);``        ``a = Math.Abs(a);``        ``b = Math.Abs(b);` `        ``// If gcd is equal then it is possible``        ``// to reach. Else not possible.``        ``return` `(gcd(x, y) == gcd(a, b));``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{` `        ``// Converting coordinate``        ``// into positive integer``        ``int` `x = 35, y = 15;``        ``int` `a = 20, b = 25;``        ` `        ``if` `(ispossible(x, y, a, b))``            ``Console.Write(``"Yes"``);``        ``else``            ``Console.Write(``"No"``);``    ``}``}` `// This code is contributed by nitin mittal.`

## PHP

 ` ``\$j``)``        ``return` `gcd(``\$i` `- ``\$j``, ``\$j``);``    ``return` `gcd(``\$i``, ``\$j` `- ``\$i``);``}` `// Returns true if it is``// possible to go to (a, b)``// from (x, y)``function` `ispossible(``\$x``, ``\$y``, ``\$a``, ``\$b``)``{``    ` `    ``// Find absolute values``    ``// of all as sign doesn't``    ``// matter.``    ``\$x` `= ``abs``(``\$x``);``    ``\$y` `= ``abs``(``\$y``);``    ``\$a` `= ``abs``(``\$a``);``    ``\$b` `= ``abs``(``\$b``);` `    ``// If gcd is equal then``    ``// it is possible to reach.``    ``// Else not possible.``    ``return` `(gcd(``\$x``, ``\$y``) == gcd(``\$a``, ``\$b``));``}` `// Driver Code``{``    ` `    ``// Converting coordinate``    ``// into positive integer``    ``\$x` `= 35; ``\$y` `= 15;``    ``\$a` `= 20; ``\$b` `= 25;``    ``if` `(ispossible(``\$x``, ``\$y``, ``\$a``, ``\$b``))``        ``echo``( ``"Yes"``);``    ``else``        ``echo``( ``"No"``);``    ``return` `0;``}` `// This code is contributed by nitin mittal.``?>`

## Javascript

 ``

Output:

`Yes`

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