Given an array 
of set of points in the X-Y plane. The task is to find the minimum area of a rectangle that can be formed from these points. The sides of the rectangle should be parallel to the X and Y axes. If a rectangle cannot be formed with the given points then print 
.
Examples:
Input: arr[][] = [[1, 1], [1, 3], [3, 1], [3, 3], [2, 2]]
Output: 4
The only rectangle possible will be formed with the points (1, 1), (1, 3), (3, 1) and (3, 3)Input: arr[][] = [[1, 1], [1, 3], [3, 1], [3, 3], [4, 1], [4, 3]]
Output: 2
Approach: Group the points by 
coordinates, so that points on straight vertical lines are grouped together. Then, for every pair of points in a group, for eg. coordinates (X, Y1) and (X, Y2), we check for the smallest rectangle with this pair of points as the rightmost edge of the rectangle to be formed. We can do this by keeping track of all other pairs of points we’ve visited before. Finally return the minimum possible area of the rectangle obtained.
Below is the implementation of the above approach:
CPP
// C++ Implementation of above approach #include <bits/stdc++.h> using namespace std; // function to find minimum area of Rectangle int minAreaRect(vector<vector<int>> A){ // creating empty columns map<int,vector<int>> columns; // fill columns with coordinates for(auto i:A) columns[i[0]].push_back(i[1]); map<pair<int,int>,int > lastx; int ans = INT_MAX; for (auto x:columns) { vector<int> column = x.second; sort(column.begin(), column.end()); for (int j = 0; j < column.size(); j++) { for (int i = 0; i < j; i++) { int y1 = column[i]; // check if rectangle can be formed if (lastx.find({y1, column[j]}) != lastx.end()) { ans = min(ans, (x.first - lastx[{y1, column[j]}]) * (column[j] - column[i])); } lastx[{y1, column[j]}] = x.first; } } } if (ans < INT_MAX) return ans; else return 0; } // Driver code int main() { vector<vector<int>> A = {{1, 1}, {1, 3}, {3, 1}, {3, 3}, {2, 2}}; cout << (minAreaRect(A)); return 0; } // This code is contributed by mohit kumar 29 |
Python
# Python Implementation of above approach import collections # function to find minimum area of Rectangle def minAreaRect(A): # creating empty columns columns = collections.defaultdict(list) # fill columns with coordinates for x, y in A: columns[x].append(y) lastx = {} ans = float('inf') for x in sorted(columns): column = columns[x] column.sort() for j, y2 in enumerate(column): for i in range(j): y1 = column[i] # check if rectangle can be formed if (y1, y2) in lastx: ans = min(ans, (x - lastx[y1, y2]) * (y2 - y1)) lastx[y1, y2] = x if ans < float('inf'): return ans else: return 0 # Driver code A = [[1, 1], [1, 3], [3, 1], [3, 3], [2, 2]] print(minAreaRect(A)) |
4
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