Self Crossing

To solve this coding challenge, it's crucial to understand how the movement happens on the X-Y plane and identify the conditions under which the path crosses itself. You need to monitor your position after every movement and check if any future move intersects with the previous path.

Explanation

The movement happens in a specific order: north, west, south, and east, which repeats. To track whether the path crosses itself, you can monitor the relative position changes and use logical conditions to check for intersections.

Breakdown of the Solution:

1. Monitoring Movements : Every move modifies the current position on the X-Y plane. Starting from (0, 0), move distance[0] steps north, distance[1] steps west, and so forth.
2. Direction Change : The direction changes counter-clockwise after each move—North, West, South, East, North, and so on.
3. Condition Identification :
• Fourth move and onwards : Check simple intersections by comparing the current distance with distances two steps and three steps before.
• Fifth move : Check if the current move coincides with previous movements that could form a loop.
• Sixth move : Check the more complex intersection where it could form a loop not immediately obvious.

Pseudocode Breakdown

Here is the pseudocode explained with detailed comments to illustrate how these checks are performed:

                                            
# Function to check if path crosses itself
function isSelfCrossing(distance):
# Iterate over the distance array starting from index 3
for i from 3 to length(distance):
# Case 1: Fourth move onward checking if it crosses a direct line segment before
if distance[i] >= distance[i-2] and distance[i-1] <= distance[i-3]:
# Path crosses itself
return True

# Case 2: Starting from the fifth move
if i >= 4:
# Check if the current move forms a square loop with fourth and first move
if distance[i-1] == distance[i-3] and distance[i] + distance[i-4] >= distance[i-2]:
# Path crosses itself
return True

# Case 3: Starting from the sixth move
if i >= 5:
# Check if movement forms a tighter spiral loop with previous sequences
if distance[i-2] >= distance[i-4] and distance[i] + distance[i-4] >= distance[i-2] and distance[i-1] <= distance[i-3] and distance[i-1] + distance[i-5] >= distance[i-3]:
# Path crosses itself
return True

# If none of the conditions met, path does not cross itself
return False

                                        

Step-by-Step Explanation

4. Initialize the Loop : The loop starts at index 3, since the first three moves cannot cross each other (minimum of four moves are required to form a crossing).
5. First Condition (i >= 3):
• This checks if the i-th move intersects the (i-3)-th line segment.
• if distance[i] >= distance[i-2] and distance[i-1] <= distance[i-3]
  : This ensures that the line segment from the current step
  i
  can potentially cross the line segment from step
  (i-2)
  if the relative distances meet certain spatial conditions.
6. Second Condition (i >= 4) :
• Verifies an intersection forming a special case where
  distance[i-1] == distance[i-3]
  ensures alignment, and the combination
  distance[i] + distance[i-4] >= distance[i-2]
  ensures overlap.
7. Third Condition (i >= 5):
• This handles more complex scenarios where earlier overlaps are involved:
• distance[i-2] >= distance[i-4] and distance[i] + distance[i-4] >= distance[i-2]
  : Ensures that the line segment from step
  (i-2)
  overlaps with the segment before it.
• distance[i-1] <= distance[i-3] and distance[i-1] + distance[i-5] >= distance[i-3]
  : Ensures the crossing with another earlier segment.

By evaluating these conditions at each step, the function will determine if and when the path crosses itself, ultimately returning

True

if it does and

False

otherwise.