Self Crossing

Problem Description

You are given an array of integers distance. You start at the point (0, 0) on an X-Y plane, and you move distance[0] meters to the north, then distance[1] meters to the west, distance[2] meters to the south, distance[3] meters to the east, and so on. Return true if your path crosses itself or false if it does not.

Key Insights

• The movement forms a square pattern where each move changes direction counter-clockwise.
• A crossing occurs when a segment of the path overlaps with a previous segment.
• The path can be represented as a series of line segments, and we need to check for intersections between these segments.
• The problem can be simplified by considering the relative positions of segments and their lengths.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To determine if the path crosses itself, we can simulate the movement on a coordinate plane and keep track of the segments formed by each move. The algorithm checks for potential crossings by examining the coordinates of the segments and using conditions based on their relative positions and distances.

1. Maintain the current position and direction of movement.
2. For each distance, calculate the new position and the segments formed.
3. Check if the new segment intersects with any of the previous segments based on defined geometric conditions.

Code Solutions