Reaching Points
A move consists of taking a point (x, y)
and transforming it to either (x, x+y)
or (x+y, y)
.
Given a starting point (sx, sy)
and a target point (tx, ty)
, return True
if and only if a sequence of moves exists to transform the point (sx, sy)
to (tx, ty)
. Otherwise, return False
.
Examples:
Input: sx = 1, sy = 1, tx = 3, ty = 5
Output: True
Explanation:
One series of moves that transforms the starting point to the target is:
(1, 1) -> (1, 2)
(1, 2) -> (3, 2)
(3, 2) -> (3, 5)
Input: sx = 1, sy = 1, tx = 2, ty = 2
Output: False
Input: sx = 1, sy = 1, tx = 1, ty = 1
Output: True
Note:
sx, sy, tx, ty
will all be integers in the range[1, 10^9]
.
class Solution {
// Similar to GCD
public boolean helper(int sx, int sy, int tx, int ty) {
// Cannot go lower than sx
if (tx < sx)
return false;
else if (tx == sx)
return (ty >= sy && (ty - sy) % tx == 0);
else
// Always remove smaller number from bigger number
return helper(sy, sx, ty % tx, tx);
}
public boolean reachingPoints(int sx, int sy, int tx, int ty) {
if (tx > ty)
return helper(sy, sx, ty, tx);
else
return helper(sx, sy, tx, ty);
}
}
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