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:
public class Solution {
public boolean isSelfCrossing(int[] x) {
for(int i=3; i<x.length; i++){
if(x[i]>=x[i-2] && x[i-3]>=x[i-1]) return true;
else if(i>3 && x[i-1]==x[i-3] && x[i]-x[i-2]+x[i-4]>=0) return true;
else if(i>4 && x[i-1]<=x[i-3] && x[i-2]>=x[i-4] && -x[i-4]+x[i-2]-x[i]<=0 && x[i-5]-x[i-3]+x[i-1]>=0) return true;
}
return false;
}
}