# 356 Line Reflection

### Problem:

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)?

Hint:

Find the smallest and largest x-value for all points. If there is a line then it should be at y = (minX + maxX) / 2. For each point, make sure that it has a reflected point in the opposite side.

### Solutions:

``````public class Solution {
public boolean isReflected(int[][] points) {
int min = Integer.MAX_VALUE;
int max = Integer.MIN_VALUE;
HashMap<Integer, HashSet<Integer>> ys = new HashMap<Integer, HashSet<Integer>>();
for (int i = 0; i < points.length; i ++) {
int x = points[i][0];
int y = points[i][1];
min = Math.min(min, x);
max = Math.max(max, x);
if (!ys.containsKey(x)) {
ys.put(x, new HashSet<Integer>());
}
}
int doublebar = (min + max);
for (int i = 0; i < points.length; i ++) {
int x = points[i][0];
int y = points[i][1];
int mx = doublebar - x;
if (!ys.containsKey(mx)) {
return false;
}
if (!ys.get(mx).contains(y)) {
return false;
}
}

return true;
}
}
``````
``````class Solution {
public boolean isReflected(int[][] points) {
int min = Integer.MAX_VALUE;
int max = Integer.MIN_VALUE;
HashMap<Integer, HashSet<Integer>> ys = new HashMap<Integer, HashSet<Integer>>();
for (int i = 0; i < points.length; i ++) {
int x = points[i][0];
int y = points[i][1];
min = Math.min(min, x);
max = Math.max(max, x);
if (!ys.containsKey(y)) {
ys.put(y, new HashSet<Integer>());
}
}
int doublebar = (min + max);
for (Integer y:ys.keySet()) {
for (Integer x:ys.get(y)) {
int mx = doublebar - x;
if (!ys.get(y).contains(mx)) {
return false;
}
}
}
return true;
}
}
``````