Line Reflection in C++

Suppose we have n points on a 2D plane, we have to check whether there is any line parallel to y-axis that reflect the given points symmetrically, in other words, check whether there exists a line that after reflecting all points over the given line the set of the original points is the same that the reflected ones.

So, if the input is like points = [[1,1],[-1,1]]

then the output will be true

To solve this, we will follow these steps −

• Define one set ok

• n := size of points

• minVal := inf

• maxVal := -inf

• for initialize i := 0, when i < n, update (increase i by 1), do −

  • minVal := minimum of minVal and points[i, 0]

  • maxVal := maximum of maxVal and points[i, 0]

  • insert points[i] into ok

• mid := maxVal + minVal

• for initialize i := 0, when i < n, update (increase i by 1), do −

  • x := points[i, 0]

  • y := points[i, 1]

  • x := mid - x

  • if { x, y } is not in ok, then −

    • return false

• return true

Example 

Let us see the following implementation to get better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
   bool isReflected(vector<vector<int<>& points) {
      set<vector<int< > ok;
      int n = points.size();
      int minVal = INT_MAX;
      int maxVal = INT_MIN;
      for (int i = 0; i < n; i++) {
         minVal = min(minVal, points[i][0]);
         maxVal = max(maxVal, points[i][0]);
         ok.insert(points[i]);
      }
      int mid = maxVal + minVal;
      for (int i = 0; i < n; i++) {
         int x = points[i][0];
         int y = points[i][1];
         x = mid - x;
         if (!ok.count({ x, y }))
            return false;
      }
      return true;
   }
};
main(){
   Solution ob;
   vector<vector<int<> v = {{1,1},{-1,1}};
   cout << (ob.isReflected(v));
}

Input

{{1,1},{-1,1}}

Output

1