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356. Line Reflection πŸ”’

Description

Given n points on a 2D plane, find if there is such a line parallel to the y-axis that reflects the given points symmetrically.

In other words, answer whether or not if there exists a line that after reflecting all points over the given line, the original points' set is the same as the reflected ones.

Note that there can be repeated points.

 

Example 1:

Input: points = [[1,1],[-1,1]]
Output: true
Explanation: We can choose the line x = 0.

Example 2:

Input: points = [[1,1],[-1,-1]]
Output: false
Explanation: We can't choose a line.

 

Constraints:

  • n == points.length
  • 1 <= n <= 104
  • -108 <= points[i][j] <= 108

 

Follow up: Could you do better than O(n2)?

Solutions

Solution 1

Thinking

Decide whether the points are symmetric about some vertical line. Trying every candidate axis is unnecessary: if one exists, it is the midpoint of the extreme \(x\)-coordinates.

Let \(s=\min x+\max x\). Every \((x,y)\) must have \((s-x,y)\) in the set. Load the points, then test once.

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class Solution:
    def isReflected(self, points: List[List[int]]) -> bool:
        min_x, max_x = inf, -inf
        point_set = set()
        for x, y in points:
            min_x = min(min_x, x)
            max_x = max(max_x, x)
            point_set.add((x, y))
        s = min_x + max_x
        return all((s - x, y) in point_set for x, y in points)

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class Solution {
    public boolean isReflected(int[][] points) {
        final int inf = 1 << 30;
        int minX = inf, maxX = -inf;
        Set<List<Integer>> pointSet = new HashSet<>();
        for (int[] p : points) {
            minX = Math.min(minX, p[0]);
            maxX = Math.max(maxX, p[0]);
            pointSet.add(List.of(p[0], p[1]));
        }
        int s = minX + maxX;
        for (int[] p : points) {
            if (!pointSet.contains(List.of(s - p[0], p[1]))) {
                return false;
            }
        }
        return true;
    }
}

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class Solution {
public:
    bool isReflected(vector<vector<int>>& points) {
        const int inf = 1 << 30;
        int minX = inf, maxX = -inf;
        set<pair<int, int>> pointSet;
        for (auto& p : points) {
            minX = min(minX, p[0]);
            maxX = max(maxX, p[0]);
            pointSet.insert({p[0], p[1]});
        }
        int s = minX + maxX;
        for (auto& p : points) {
            if (!pointSet.count({s - p[0], p[1]})) {
                return false;
            }
        }
        return true;
    }
};

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func isReflected(points [][]int) bool {
    const inf = 1 << 30
    minX, maxX := inf, -inf
    pointSet := map[[2]int]bool{}
    for _, p := range points {
        minX = min(minX, p[0])
        maxX = max(maxX, p[0])
        pointSet[[2]int{p[0], p[1]}] = true
    }
    s := minX + maxX
    for _, p := range points {
        if !pointSet[[2]int{s - p[0], p[1]}] {
            return false
        }
    }
    return true
}

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