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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 1

Thinking

Walk north, west, south, east in turn and decide whether the polyline crosses itself. Storing coordinates and testing segments is \(O(n^2)\) for \(n\le 5\times 10^4\).

A crossing involves only the last few sides: the fourth meets the first, the fifth meets the second, or the sixth meets the third and first. Check these three local patterns for \(i\ge 3\); the full path is unnecessary.

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class Solution:
    def isSelfCrossing(self, distance: List[int]) -> bool:
        d = distance
        for i in range(3, len(d)):
            if d[i] >= d[i - 2] and d[i - 1] <= d[i - 3]:
                return True
            if i >= 4 and d[i - 1] == d[i - 3] and d[i] + d[i - 4] >= d[i - 2]:
                return True
            if (
                i >= 5
                and d[i - 2] >= d[i - 4]
                and d[i - 1] <= d[i - 3]
                and d[i] >= d[i - 2] - d[i - 4]
                and d[i - 1] + d[i - 5] >= d[i - 3]
            ):
                return True
        return False

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

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

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func isSelfCrossing(distance []int) bool {
    d := distance
    for i := 3; i < len(d); i++ {
        if d[i] >= d[i-2] && d[i-1] <= d[i-3] {
            return true
        }
        if i >= 4 && d[i-1] == d[i-3] && d[i]+d[i-4] >= d[i-2] {
            return true
        }
        if i >= 5 && d[i-2] >= d[i-4] && d[i-1] <= d[i-3] && d[i] >= d[i-2]-d[i-4] && d[i-1]+d[i-5] >= d[i-3] {
            return true
        }
    }
    return false
}

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

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