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:
Given x = [2, 1, 1, 2]
,
┌───┐
│ │
└───┼──>
│
Return true (self crossing)
Example 2:
Given x = [1, 2, 3, 4]
,
┌──────┐
│ │
│
│
└────────────>
Return false (not self crossing)
Example 3:
Given x = [1, 1, 1, 1]
,
┌───┐
│ │
└───┼>
Return true (self crossing)
Solution:
There are only three cases where the line will intersect itself.