Question

356. Line Reflection

中文文档

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

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)

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;
  }
}

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;
  }
};

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
}