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

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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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Output:

No


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Improved By : mohit kumar 29, AnkitRai01



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