2849. Determine if a Cell Is Reachable at a Given Time
Description
You are given four integers sx
, sy
, fx
, fy
, and a non-negative integer t
.
In an infinite 2D grid, you start at the cell (sx, sy)
. Each second, you must move to any of its adjacent cells.
Return true
if you can reach cell (fx, fy)
after exactly t
seconds, or false
otherwise.
A cell's adjacent cells are the 8 cells around it that share at least one corner with it. You can visit the same cell several times.
Example 1:
Input: sx = 2, sy = 4, fx = 7, fy = 7, t = 6 Output: true Explanation: Starting at cell (2, 4), we can reach cell (7, 7) in exactly 6 seconds by going through the cells depicted in the picture above.
Example 2:
Input: sx = 3, sy = 1, fx = 7, fy = 3, t = 3 Output: false Explanation: Starting at cell (3, 1), it takes at least 4 seconds to reach cell (7, 3) by going through the cells depicted in the picture above. Hence, we cannot reach cell (7, 3) at the third second.
Constraints:
1 <= sx, sy, fx, fy <= 109
0 <= t <= 109
Solutions
Solution 1: Case Discussion
If the starting point and the destination are the same, then we can only reach the destination within the given time if $t \neq 1$.
Otherwise, we can calculate the difference in the x and y coordinates between the starting point and the destination, and then take the maximum value. If the maximum value is less than or equal to the given time, then we can reach the destination within the given time.
The time complexity is $O(1)$, and the space complexity is $O(1)$.
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