Given a point (x, y), the task is to check if it is possible to reach from origin to (x, y) in exactly Z steps. From a given point (x, y) we can only moves in four direction left(x – 1, y), right(x + 1, y), up(x, y + 1) and down(x, y – 1).
Input: x = 5, y = 5, z = 11
Output: Not Possible
Input: x = 10, y = 15, z = 25
- The shortest path from origin to (x, y), is |x|+|y|.
- So, it is clear that if Z less than |x|+|y|, then we can’t reach (x, y) from origin in exactly Z steps.
- If the number of steps is not less than |x|+|y| then, we have to check below two conditions to check if we can reach to (x, y) or not:
- If Z ≥ |x| + |y|, and
- If (Z – |x| + |y|)%2 is 0.
- For the second conditions in the above step, if we reach (x, y), we can take two more steps such as (x, y)–>(x, y+1)–>(x, y) to come back to the same position (x, y). And this is possible only if different between them is even.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
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