Check if it is possible to move from (0, 0) to (X, Y) in exactly K steps

Given a point (X, Y) in a 2-D plane and an integer K, the task is to check whether it is possible to move from (0, 0) to the given point (X, Y) in exactly K moves. In a single move, the positions that are reachable from (X, Y) are (X, Y + 1), (X, Y – 1), (X + 1, Y) and (X – 1, Y).

Examples:

Input: X = 0, Y = 0, K = 2
Output: Yes
Move 1: (0, 0) -> (0, 1)
Move 2: (0, 1) -> (0, 0)

Input: X = 5, Y = 8, K = 20
Output: No

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: It is clear that the shortest path to reach (X, Y) from (0, 0) will be minMoves = (|X| + |Y|). So, if K < minMoves then it is impossible to reach (X, Y) but if K ≥ minMoves then after reaching (X, Y) in minMoves number of moves the remaining (K – minMoves) number of moves have to be even in order to remain at that point for the rest of the moves.
So it is possible to reach (X, Y) from (0, 0) only if K ≥ (|X| + |Y|) and (K – (|X| + |Y|)) % 2 = 0.

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 (0, 0) to 
// (x, y) in exactly k moves 
bool isPossible(int x, int y, int k) 
{ 
    // Minimum moves required 
    int minMoves = abs(x) + abs(y); 
  
    // If possible 
    if (k >= minMoves && (k - minMoves) % 2 == 0) 
        return true; 
  
    return false; 
} 
  
// Driver code 
int main() 
{ 
    int x = 5, y = 8, k = 20; 
  
    if (isPossible(x, y, k)) 
        cout << "Yes"; 
    else
        cout << "No"; 
  
    return 0; 
} 

Java

// Java implementation of the approach  
class GFG 
{ 
      
    // Function that returns true if it is  
    // possible to move from (0, 0) to  
    // (x, y) in exactly k moves  
    static boolean isPossible(int x, int y, int k)  
    {  
        // Minimum moves required  
        int minMoves = Math.abs(x) + Math.abs(y);  
      
        // If possible  
        if (k >= minMoves && (k - minMoves) % 2 == 0)  
            return true;  
      
        return false;  
    }  
      
    // Driver code  
    public static void main (String[] args)  
    {  
        int x = 5, y = 8, k = 20;  
      
        if (isPossible(x, y, k))  
            System.out.println("Yes");  
        else
            System.out.println("No");  
    }  
} 
  
// This code is contributed by AnkitRai01 

Python3

# Python3 implementation of the approach 
  
# Function that returns true if it is 
# possible to move from (0, 0) to 
# (x, y) in exactly k moves 
def isPossible(x, y, k): 
      
    # Minimum moves required 
    minMoves = abs(x) + abs(y) 
  
    # If possible 
    if (k >= minMoves and (k - minMoves) % 2 == 0): 
        return True
  
    return False
  
# Driver code 
x = 5
y = 8
k = 20
  
if (isPossible(x, y, k)): 
    print("Yes") 
else: 
    print("No") 
  
# This code is contributed by Mohit Kumar 

Output:

No

My Personal Notes

Suggest a Topic

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

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