LeetCode Q335: Self Crossing (hard)

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)

Credits:
Special thanks to @dietpepsi for adding this problem and creating all test cases.

Solution:

There are only three cases where the line will intersect itself.

where red point is the start point.

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

view raw Q335.cpp hosted with ❤ by GitHub