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.
Question
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.
Solution
To solve this problem, you need to calculate the Manhattan distance between the starting point (sx, sy) and the final point (fx, fy). The Manhattan distance in a 2D grid is the sum of the absolute differences in the x and y coordinates.
Here are the steps to solve this problem:
- Calculate the Manhattan distance:
distance = abs(sx - fx) + abs(sy - fy). - If the distance is greater than
t(the total time), returnfalsebecause you cannot reach the final cell in time. - If the distance is equal to
t, returntruebecause you can reach the final cell exactly intseconds. - If the distance is less than
t, you need to check if the difference betweentand the distance is even. This is because you can only spend extra time by moving back and forth along the same path, which takes 2 seconds for each round trip. If(t - distance) % 2 == 0, returntrue. Otherwise, returnfalse.
Here is the Python code for the above steps:
def can_reach_in_time(sx, sy, fx, fy, t):
distance = abs(sx - fx) + abs(sy - fy)
if distance > t:
return False
elif distance == t:
return True
else:
return (t - distance) % 2 == 0
This function will return true if you can reach cell (fx, fy) after exactly t seconds, or false otherwise.
Similar Questions
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