Question
Given a set of points in the xy-plane, determine the minimum area of any rectangle formed from these points, with sides not necessarily parallel to the x and y axes.
If there isn't any rectangle, return 0.
Example 1:
Input: [[1,2],[2,1],[1,0],[0,1]] Output: 2.00000 Explanation: The minimum area rectangle occurs at [1,2],[2,1],[1,0],[0,1], with an area of 2.
Example 2:
Input: [[0,1],[2,1],[1,1],[1,0],[2,0]] Output: 1.00000 Explanation: The minimum area rectangle occurs at [1,0],[1,1],[2,1],[2,0], with an area of 1.
Example 3:
Input: [[0,3],[1,2],[3,1],[1,3],[2,1]] Output: 0 Explanation: There is no possible rectangle to form from these points.
Example 4:
Input: [[3,1],[1,1],[0,1],[2,1],[3,3],[3,2],[0,2],[2,3]] Output: 2.00000 Explanation: The minimum area rectangle occurs at [2,1],[2,3],[3,3],[3,1], with an area of 2.
Note:
1 <= points.length <= 50
0 <= points[i][0] <= 40000
0 <= points[i][1] <= 40000
- All points are distinct.
- Answers within
10^-5
of the actual value will be accepted as correct.
Difficulty:Medium
Category:Math, Geometry
Analyze
Solution
class Solution {
public:
double minAreaFreeRect(vector<vector<int>>& points) {
int n = points.size();
bool find = false;
double ans = INT_MAX;
vector<vector<int>>& P = points;
for (int a = 0; a < n; ++a)
for (int b = 0; b < n; ++b)
for (int c = 0; c < n; ++c)
for (int d = 0; d < n; ++d) {
if (a == b || a == c || a == d || b == c || b == d || c == d) continue;
if (P[a][0] - P[b][0] != P[d][0] - P[c][0]) continue;
// Deal with the parallel sides
if (P[a][1] - P[b][1] != P[d][1] - P[c][1]) continue;
double x1 = P[a][0] - P[b][0];
double x2 = P[c][0] - P[b][0];
double y1 = P[a][1] - P[b][1];
double y2 = P[c][1] - P[b][1];
if (x1 * x2 + y1 * y2 == 0) {
double area = abs(x1 * y2 - x2 * y1);
if (area > 0 && area < ans) {
find = true;
ans = area;
}
}
}
if (!find) return 0;
return ans;
}
};