找到四个点，使它们形成一个正方形，其边平行于x和y轴

给定“ n”对点，任务是找到四个点，使它们形成一个正方形，其边平行于x和y轴，否则打印“无此正方形”。
如果可能有一个以上的正方形，则选择面积最大的正方形。

例子：

Input : n = 6, points = (1, 1), (4, 4), (3, 4), (4, 3), (1, 4), (4, 1)
Output :
side of the square is : 3, points of the square are 1, 1 4, 1 1, 4 4, 4
Explanation: The points 1, 1 4, 1 1, 4 4, 4 form a square of side 3

Input :n= 6, points= (1, 1), (4, 5), (3, 4), (4, 3), (7, 4), (3, 1)
Output :No such square

简单方法：用四个嵌套循环选择所有可能的点对，然后查看这些点是否形成与主轴平行的正方形。如果是，则检查该区域是否是到目前为止最大的正方形，并存储结果，然后在程序末尾显示结果。
时间复杂度： O(N ^ 4)

高效方法：为正方形的右上角和左下角创建一个嵌套循环，并用这两个点组成一个正方形，然后检查假定的其他两个点是否确实存在。要检查点是否存在，请创建地图并将点存储在地图中，以减少检查点是否存在的时间。另外，请检查到目前为止最大面积的正方形，并在最后打印。

下面是上述方法的实现：

CPP

// C++ implemenataion of the above approach
#include 
using namespace std;
  
// find the largest square
void findLargestSquare(long long int points[][2], int n)
{
    // map to store which points exist
    map, int> m;
  
    // mark the available points
    for (int i = 0; i < n; i++) {
        m[make_pair(points[i][0], points[i][1])]++;
    }
    long long int side = -1, x = -1, y = -1;
  
    // a nested loop to choose the opposite corners of square
    for (int i = 0; i < n; i++) {
  
        // remove the chosen point
        m[make_pair(points[i][0], points[i][1])]--;
        for (int j = 0; j < n; j++) {
  
            // remove the chosen point
            m[make_pair(points[j][0], points[j][1])]--;
  
            // check if the other two points exist
            if (i != j 
                  && (points[i][0]-points[j][0]) == (points[i][1]-points[j][1])){
                if (m[make_pair(points[i][0], points[j][1])] > 0
                     && m[make_pair(points[j][0], points[i][1])] > 0) {
  
                    // if the square is largest then store it
                    if (side < abs(points[i][0] - points[j][0]) 
                         || (side == abs(points[i][0] - points[j][0]) 
                            && ((points[i][0] * points[i][0] 
                                   + points[i][1] * points[i][1]) 
                                      < (x * x + y * y)))) {
                        x = points[i][0];
                        y = points[i][1];
                        side = abs(points[i][0] - points[j][0]);
                    }
                }
            }
  
            // add the removed point
            m[make_pair(points[j][0], points[j][1])]++;
        }
  
        // add the removed point
        m[make_pair(points[i][0], points[i][1])]++;
    }
  
    // display the largest square
    if (side != -1)
        cout << "Side of the square is : " << side
             << ", \npoints of the square are " << x << ", " << y
             << " "
             << (x + side) << ", " << y
             << " "
             << (x) << ", " << (y + side)
             << " "
             << (x + side) << ", " << (y + side) << endl;
    else
        cout << "No such square" << endl;
}
  
//Driver code
int main()
{
    int n = 6;
  
    // given points
    long long int points[n][2]
      = { { 1, 1 }, { 4, 4 }, { 3, 4 }, { 4, 3 }, { 1, 4 }, { 4, 1 } };
  
    // find the largest square
    findLargestSquare(points, n);
  
    return 0;
}

Python3

# Python3 implemenataion of the above approach
  
# find the largest square
def findLargestSquare(points,n):
      
    # map to store which points exist
    m = dict()
  
    # mark the available points
    for i in range(n):
        m[(points[i][0], points[i][1])] = \
        m.get((points[i][0], points[i][1]), 0) + 1
  
    side = -1
    x = -1
    y = -1
  
    # a nested loop to choose the opposite corners of square
    for i in range(n):
  
        # remove the chosen point
        m[(points[i][0], points[i][1])]-=1
        for j in range(n):
  
            # remove the chosen point
            m[(points[j][0], points[j][1])]-=1
  
            # check if the other two points exist
            if (i != j and (points[i][0]-points[j][0]) == \
                (points[i][1]-points[j][1])):
                if (m[(points[i][0], points[j][1])] > 0 and 
                    m[(points[j][0], points[i][1])] > 0):
  
                    # if the square is largest then store it
                    if (side < abs(points[i][0] - points[j][0])
                        or (side == abs(points[i][0] - points[j][0])
                            and ((points[i][0] * points[i][0]
                                + points[i][1] * points[i][1])
                                    < (x * x + y * y)))):
                        x = points[i][0]
                        y = points[i][1]
                        side = abs(points[i][0] - points[j][0])
  
            # add the removed point
            m[(points[j][0], points[j][1])] += 1
  
        # add the removed point
        m[(points[i][0], points[i][1])] += 1
  
    # display the largest square
    if (side != -1):
        print("Side of the square is : ",side
            ,", \npoints of the square are ",x,", ",y
            ," "
            ,(x + side),", ",y
            ," "
            ,(x),", ",(y + side)
            ," "
            ,(x + side),", ",(y + side))
    else:
        print("No such square")
  
# Driver code
n = 6
  
# given points
points=[[ 1, 1 ],[ 4, 4 ],[ 3, 4 ],[ 4, 3 ],[ 1, 4 ],[ 4, 1 ] ]
  
# find the largest square
findLargestSquare(points, n)
  
# This code is contributed by mohit kumar 29

输出：

Side of the square is : 3, 
points of the square are 1, 1 4, 1 1, 4 4, 4

时间复杂度： O(N ^ 2)

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