335. Self Crossing

Description

You are given an array of integers distance.

You start at the point (0, 0) on an X-Y plane, and you move distance[0] meters to the north, then distance[1] meters to the west, distance[2] meters to the south, distance[3] meters to the east, and so on. In other words, after each move, your direction changes counter-clockwise.

Return true if your path crosses itself or false if it does not.

 

Example 1:

Input: distance = [2,1,1,2]
Output: true
Explanation: The path crosses itself at the point (0, 1).

Example 2:

Input: distance = [1,2,3,4]
Output: false
Explanation: The path does not cross itself at any point.

Example 3:

Input: distance = [1,1,1,2,1]
Output: true
Explanation: The path crosses itself at the point (0, 0).

 

Constraints:

• 1 <= distance.length <= 105
• 1 <= distance[i] <= 105

 

Solutions

Solution: Math

• Time complexity: O(n)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number[]} distance
 * @return {boolean}
 */
const isSelfCrossing = function (distance) {
  const situation1 = index => {
    const one = distance[index - 3];
    const two = distance[index - 2];
    const three = distance[index - 1];
    const four = distance[index];

    return one >= three && four >= two;
  };
  const situation2 = index => {
    if (index < 4) return false;
    const one = distance[index - 4];
    const two = distance[index - 3];
    const three = distance[index - 2];
    const four = distance[index - 1];
    const five = distance[index];

    return three >= one && two === four && five >= three - one;
  };
  const situation3 = index => {
    if (index < 5) return false;
    const one = distance[index - 5];
    const two = distance[index - 4];
    const three = distance[index - 3];
    const four = distance[index - 2];
    const five = distance[index - 1];
    const six = distance[index];

    return four >= two && three >= five && one >= three - five && six >= four - two;
  };

  for (let index = 3; index < distance.length; index++) {
    if (situation1(index)) return true;
    if (situation2(index)) return true;
    if (situation3(index)) return true;
  }
  return false;
};