Line Reflection -- LeetCode

Posted 2020-08-05 Coder and Writer

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

Example 1:

Given points = [[1,1],[-1,1]], return true.

Example 2:

Given points = [[1,1],[-1,-1]], return false.

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

思路：假设如果存在这样的一条对称轴，那么对于一对对称点，它们的X坐标之和应该是个定值。

我们找到所有点中X坐标的最小值和最大值，两者之和就是这个定值。

然后将所有点的坐标记录在set中，然后判断每个点的对称点是否在set中。

时间复杂度O(N)。

 1 class Solution {
 2 public:
 3     bool isReflected(vector<pair<int, int>>& points) {
 4         if (points.size() == 0) return true;
 5         unordered_set<string> p;
 6         int minX = INT_MAX, maxX = INT_MIN;
 7         for (int i = 0; i < points.size(); i++) {
 8             int x = points[i].first, y = points[i].second;
 9             minX = std::min(minX, x);
10             maxX = std::max(maxX, x);
11             string code = std::to_string(x) + "|" + std::to_string(y);
12             p.insert(code);
13         }
14         int sum = minX + maxX;
15         for (int i = 0; i < points.size(); i++) {
16             int x = sum - points[i].first, y = points[i].second;
17             string code = std::to_string(x) + "|" + std::to_string(y);
18             if (p.count(code) == 0) return false;
19         }
20         return true;
21     }
22 };