self-crossing.py

# -*- coding:utf-8 -*-


# 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:
#
#
# ┌──────┐
# │      │
# │
# │
# └────────────>
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# Input: [1,2,3,4]
# Output: false 
#
#
# Example 3:
#
#
# ┌───┐
# │   │
# └───┼>
#
# Input: [1,1,1,1]
# Output: true 
#
#


class Solution(object):
    def isSelfCrossing(self, x):
        """
        :type x: List[int]
        :rtype: bool
        """
        n = len(x)
        x.append(0.5)        # let x[-1] = 0.5
        if n < 4: return False
        grow = x[2] > x[0]
            
        for i in range(3,n):
            if not grow and x[i] >= x[i-2]: return True
            if grow and x[i] <= x[i-2]:
                grow = False
                if x[i] + x[i-4] >= x[i-2]:
                    x[i-1] -= x[i-3]
        return False