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)
4th line may cross with 1st line, and so on: 5th with 2nd, ...etc
5th line may cross with 1st line, and so on: 6th with 2nd, ...etc
6th line also may cross with 1st line, and so on: 7th with 2nd, ...etc
However, if 7th line also cross with 1st line, either of the following cases should definitely happens:
a. 7th line cross with 2nd line
1 public class Solution {
2 public boolean isSelfCrossing(int[] x) {
3 if (x.length <= 3) return false;
4 for (int i=3; i<x.length; i++) {
5 //check if 4th line cross with the first line and so on
6 if (x[i]>=x[i-2] && x[i-1]<=x[i-3]) return true;
7
8 //check if 5th line cross with the first line and so on
9 if (i >= 4) {
10 if (x[i-1]==x[i-3] && x[i]+x[i-4]>=x[i-2]) return true;
11 }
12
13 //check if 6th line cross with the first line and so on
14 if (i >= 5) {
15 if (x[i-2]>=x[i-4] && x[i]>=x[i-2]-x[i-4] && x[i-1]<=x[i-3] && x[i-1]>=x[i-3]-x[i-5]) return true;
16 }
17 }
18 return false;
19 }
20 }