solve Robot Bounded In Circle

Author: saubhik

problems/robot_bounded_in_circle.py

@@ -0,0 +1,35 @@
+class Solution:
+    # Time: O(n), One Pass!
+    # Space: O(1)
+    #
+    # After working out some examples, I found that the net direction should not be
+    # North. Or if it is North, then the robot should be in the same initial point after
+    # one full cycle.
+    #
+    # Extensive mathematical proof required.
+    # Two proofs required:
+    # 1. Bounded <=> Cycle. (Cycle => Bounded is trivial)
+    # 2. Cycle <=>  (final directions is not North OR final coordinate is not Origin)
+    def isRobotBounded(self, instructions: str) -> bool:
+        coordinate = (0, 0)
+        direction = (0, 1)
+        for instruction in instructions:
+            if instruction == "G":
+                coordinate = (
+                    coordinate[0] + direction[0],
+                    coordinate[1] + direction[1],
+                )
+            elif instruction == "L":
+                # 0,1 -> -1,0
+                # -1,0 -> 0,-1
+                # 0,-1 -> 1,0
+                # 1,0 -> 0,1
+                direction = (-1 * direction[1], direction[0])
+            elif instruction == "R":
+                # 0,1 -> 1,0
+                # 1,0 -> 0,-1
+                # 0,-1 -> -1,0
+                # -1,0 -> 0,1
+                direction = (direction[1], -1 * direction[0])
+
+        return direction != (0, 1) or coordinate == (0, 0)

tests/test_robot_bounded_in_circle.py

@@ -0,0 +1,14 @@
+import unittest
+
+from robot_bounded_in_circle import Solution
+
+
+class TestRobotBoundedInCircle(unittest.TestCase):
+    def test_example_1(self):
+        assert Solution().isRobotBounded(instructions="GGLLGG") is True
+
+    def test_example_2(self):
+        assert Solution().isRobotBounded(instructions="GG") is False
+
+    def test_example_3(self):
+        assert Solution().isRobotBounded(instructions="GL") is True