# Source to destination in 2-D path with fixed sized jumps

Given the source point and the destination point of the path and two integers **x** and **y**. The task is to check whether it is possible to move from source to the destination with the below moves, If current position is **(a, b)** then the valid moves are:

**(a + x, b + y)****(a – x, b + y)****(a + x, b – y)****(a – x, b – y)**

**Examples:**

Input:Sx = 0, Sy = 0, Dx = 0, Dy = 6, x = 2, y = 3

Output:Yes

(0, 0) -> (2, 3) -> (0, 6)

Input:Sx = 1, Sy = 1, Dx = 3, Dy = 6, x = 1, y = 5

Output:No

**Approach:** Let’s approach this problem as if the steps were (a, b) -> (a + x, 0) or (a, b) -> (a – x, 0) or (a, b) -> (0, b + y) or (a, b) -> (0, b – y). Then the answer is **Yes** if **|Sx – Dx| mod x = 0** and **|Sy – Dy| mod y = 0**.

It’s easy to see that if the answer to this problem is NO then the answer to the original problem is also NO.

Let’s return to the original problem and take a look at some sequence of steps. It ends in some point **(x _{e}, y_{e})**. Define

**cnt**as

_{x}**|x**and

_{e}– Sx| / x**cnt**as

_{y}**|y**. The parity of

_{e}– Sy| / y**cnt**is the same as the parity of

_{x}**cnt**because every type of move changes the parity of both

_{y}**cnt**and

_{x}**cnt**.

_{y}So the answer is **Yes** if **|Sx – Dx| mod x = 0**, **|Sy – Dy| mod y = 0** and **|Sx – Dx| / x mod 2 = |Sy – Dy| / y mod 2**.

Below is the implementation of the above approach.

## C++

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function that returns true if ` `// it is possible to move from source ` `// to the destination with the given moves ` `bool` `isPossible(` `int` `Sx, ` `int` `Sy, ` `int` `Dx, ` `int` `Dy, ` `int` `x, ` `int` `y) ` `{ ` ` ` `if` `(` `abs` `(Sx - Dx) % x == 0 ` ` ` `and ` `abs` `(Sy - Dy) % y == 0 ` ` ` `and (` `abs` `(Sx - Dx) / x) % 2 == (` `abs` `(Sy - Dy) / y) % 2) ` ` ` `return` `true` `; ` ` ` ` ` `return` `false` `; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `Sx = 0, Sy = 0, Dx = 0, Dy = 0; ` ` ` `int` `x = 3, y = 4; ` ` ` ` ` `if` `(isPossible(Sx, Sy, Dx, Dy, x, y)) ` ` ` `cout << ` `"Yes"` `; ` ` ` `else` ` ` `cout << ` `"No"` `; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java implementation of the approach ` `import` `java .io.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Function that returns true if ` `// it is possible to move from source ` `// to the destination with the given moves ` `static` `boolean` `isPossible(` `int` `Sx, ` `int` `Sy, ` `int` `Dx, ` ` ` `int` `Dy, ` `int` `x, ` `int` `y) ` `{ ` ` ` `if` `(Math.abs(Sx - Dx) % x == ` `0` `&& ` ` ` `Math.abs(Sy - Dy) % y == ` `0` `&& ` ` ` `(Math.abs(Sx - Dx) / x) % ` `2` `== ` ` ` `(Math.abs(Sy - Dy) / y) % ` `2` `) ` ` ` `return` `true` `; ` ` ` ` ` `return` `false` `; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `Sx = ` `0` `, Sy = ` `0` `, Dx = ` `0` `, Dy = ` `0` `; ` ` ` `int` `x = ` `3` `, y = ` `4` `; ` ` ` ` ` `if` `(isPossible(Sx, Sy, Dx, Dy, x, y)) ` ` ` `System.out.println(` `"Yes"` `); ` ` ` `else` ` ` `System.out.println(` `"No"` `); ` `} ` `} ` ` ` `// This code is contributed by inder_verma.. ` |

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## Python3

# Python3 implementation of the approach

# Function that returns true if it is

# possible to move from source to the

# destination with the given moves

def isPossible(Sx, Sy, Dx, Dy, x, y):

if (abs(Sx – Dx) % x == 0 and

abs(Sy – Dy) % y == 0 and

(abs(Sx – Dx) / x) % 2 ==

(abs(Sy – Dy) / y) % 2):

return True;

return False;

# Driver code

Sx = 0;

Sy = 0;

Dx = 0;

Dy = 0;

x = 3;

y = 4;

if (isPossible(Sx, Sy, Dx, Dy, x, y)):

print(“Yes”);

else:

print(“No”);

# This code is contributed by mits

## C#

`// C# implementation of the approach ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function that returns true if ` `// it is possible to move from source ` `// to the destination with the given moves ` `static` `bool` `isPossible(` `int` `Sx, ` `int` `Sy, ` `int` `Dx, ` ` ` `int` `Dy, ` `int` `x, ` `int` `y) ` `{ ` ` ` `if` `(Math.Abs(Sx - Dx) % x == 0 && ` ` ` `Math.Abs(Sy - Dy) % y == 0 && ` ` ` `(Math.Abs(Sx - Dx) / x) % 2 == ` ` ` `(Math.Abs(Sy - Dy) / y) % 2) ` ` ` `return` `true` `; ` ` ` ` ` `return` `false` `; ` `} ` ` ` `// Driver code ` `static` `void` `Main() ` `{ ` ` ` `int` `Sx = 0, Sy = 0, Dx = 0, Dy = 0; ` ` ` `int` `x = 3, y = 4; ` ` ` ` ` `if` `(isPossible(Sx, Sy, Dx, Dy, x, y)) ` ` ` `Console.WriteLine(` `"Yes"` `); ` ` ` `else` ` ` `Console.WriteLine(` `"No"` `); ` `} ` `} ` ` ` `// This code is contributed by chandan_jnu ` |

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## PHP

`<?php ` `// PHP implementation of the approach ` ` ` `// Function that returns true if ` `// it is possible to move from source ` `// to the destination with the given moves ` `function` `isPossible(` `$Sx` `, ` `$Sy` `, ` `$Dx` `, ` ` ` `$Dy` `, ` `$x` `, ` `$y` `) ` `{ ` ` ` `if` `(` `abs` `(` `$Sx` `- ` `$Dx` `) % ` `$x` `== 0 && ` ` ` `abs` `(` `$Sy` `- ` `$Dy` `) % ` `$y` `== 0 && ` ` ` `(` `abs` `(` `$Sx` `- ` `$Dx` `) / ` `$x` `) % 2 == ` ` ` `(` `abs` `(` `$Sy` `- ` `$Dy` `) / ` `$y` `) % 2) ` ` ` `return` `true; ` ` ` ` ` `return` `false; ` `} ` ` ` `// Driver code ` `$Sx` `= 0; ` `$Sy` `= 0; ` `$Dx` `= 0; ` `$Dy` `= 0; ` `$x` `= 3; ` `$y` `= 4; ` ` ` `if` `(isPossible(` `$Sx` `, ` `$Sy` `, ` `$Dx` `, ` ` ` `$Dy` `, ` `$x` `, ` `$y` `)) ` ` ` `echo` `(` `"Yes"` `); ` `else` ` ` `echo` `(` `"No"` `); ` ` ` `// This code is contributed ` `// by Code_Mech ` `?> ` |

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**Output:**

Yes

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