Description
Given the coordinates of four points in 2D space p1
, p2
, p3
and p4
, return true
if the four points construct a square.
The coordinate of a point pi
is represented as [xi, yi]
. The input is not given in any order.
A valid square has four equal sides with positive length and four equal angles (90-degree angles).
Example 1:
Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
Output: true
Example 2:
Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12]
Output: false
Example 3:
Input: p1 = [1,0], p2 = [-1,0], p3 = [0,1], p4 = [0,-1]
Output: true
Constraints:
p1.length == p2.length == p3.length == p4.length == 2
-104 <= xi, yi <= 104
Solutions
Solution 1
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23 | class Solution:
def validSquare(
self, p1: List[int], p2: List[int], p3: List[int], p4: List[int]
) -> bool:
def check(a, b, c):
(x1, y1), (x2, y2), (x3, y3) = a, b, c
d1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)
d2 = (x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3)
d3 = (x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3)
return any(
[
d1 == d2 and d1 + d2 == d3 and d1,
d2 == d3 and d2 + d3 == d1 and d2,
d1 == d3 and d1 + d3 == d2 and d1,
]
)
return (
check(p1, p2, p3)
and check(p2, p3, p4)
and check(p1, p3, p4)
and check(p1, p2, p4)
)
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24 | class Solution {
public boolean validSquare(int[] p1, int[] p2, int[] p3, int[] p4) {
return check(p1, p2, p3) && check(p1, p3, p4) && check(p1, p2, p4) && check(p2, p3, p4);
}
private boolean check(int[] a, int[] b, int[] c) {
int x1 = a[0], y1 = a[1];
int x2 = b[0], y2 = b[1];
int x3 = c[0], y3 = c[1];
int d1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
int d2 = (x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3);
int d3 = (x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3);
if (d1 == d2 && d1 + d2 == d3 && d1 > 0) {
return true;
}
if (d1 == d3 && d1 + d3 == d2 && d1 > 0) {
return true;
}
if (d2 == d3 && d2 + d3 == d1 && d2 > 0) {
return true;
}
return false;
}
}
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19 | class Solution {
public:
bool validSquare(vector<int>& p1, vector<int>& p2, vector<int>& p3, vector<int>& p4) {
return check(p1, p2, p3) && check(p1, p3, p4) && check(p1, p2, p4) && check(p2, p3, p4);
}
bool check(vector<int>& a, vector<int>& b, vector<int>& c) {
int x1 = a[0], y1 = a[1];
int x2 = b[0], y2 = b[1];
int x3 = c[0], y3 = c[1];
int d1 = (x1
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