Self Crossing.py

'''
You are given an array x of n positive numbers. You start at point (0,0) and moves x[0] metres to the north, then x[1] metres to the west, x[2] metres to the south, x[3] metres to the east and so on. In other words, after each move your direction changes counter-clockwise.

Write a one-pass algorithm with O(1) extra space to determine, if your path crosses itself, or not.

 

Example 1:

┌───┐
│   │
└───┼──>
    │

Input: [2,1,1,2]
Output: true
Example 2:

┌──────┐
│      │
│
│
└────────────>

Input: [1,2,3,4]
Output: false 
Example 3:

┌───┐
│   │
└───┼>

Input: [1,1,1,1]
Output: true 
'''

class Solution:
    def isSelfCrossing(self, x: List[int]) -> bool:
        a = b = c = d = e = None
        for f in x:
            if c is not None and (d <= f and e <= c):

                return True
            if b is not None and (e == c and f + b >= d):

                return True
            if a is not None and (b <= d and 0 <= d - f <= b and 0 <= c - e <= a):

                return True
            
            a, b, c, d, e = b, c, d, e, f
            
        return False