Self Crossing

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:

  1. Given x = [2, 1, 1, 2],
  2. ┌───┐
  3. │   │
  4. └───┼──>
  5.     │
  7. Return true (self crossing)

Example 2:

  1. Given x = [1, 2, 3, 4],
  2. ┌──────┐
  3. │      │
  4. │
  5. │
  6. └────────────>
  8. Return false (not self crossing)

Example 3:

  1. Given x = [1, 1, 1, 1],
  2. ┌───┐
  3. │   │
  4. └───┼>
  6. Return true (self crossing)