Axis-Parallel Rectangle
D - Axis-Parallel Rectangle
Time limit : 2sec / Memory limit : 256MB
Problem Statement
We have N points in a two-dimensional plane.
The coordinates of the i-th point (1≤i≤N) are (xi,yi).
Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.
Here, points on the sides of the rectangle are considered to be in the interior.
Find the minimum possible area of such a rectangle.
Constraints
- 2≤K≤N≤50
- −109≤xi,yi≤109(1≤i≤N)
- xi≠xj(1≤i<j≤N)
- yi≠yj(1≤i<j≤N)
- All input values are integers. (Added at 21:50 JST)
Input
Input is given from Standard Input in the following format:
N K
x1 y1
:
xN yN
Output
Print the minimum possible area of a rectangle that satisfies the condition.
Sample Input 1
4 4
1 4
3 3
6 2
8 1
Sample Output 1
21
One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).
Its area is (8−1)×(4−1)=21.
Sample Input 2
4 2
0 0
1 1
2 2
3 3
Sample Output 2
1
Sample Input 3
4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999
#include <bits/stdc++.h>
using namespace std;
#define MOD 998244353
#define INF 0x3f3f3f3f3f3f3f3f
#define LL long long
#define MX 55
struct Node
{
LL x, y;
bool operator < (const Node &b)const{
return x<b.x;
}
}pt[MX]; int k, n; int main()
{
scanf("%d%d",&n,&k);
for (int i=;i<=n;i++)
scanf("%lld%lld",&pt[i].x, &pt[i].y);
sort(pt+,pt++n);
LL area = INF;
for (int i=;i<=n;i++)
{
for (int j=i+;j<=n;j++)
{
LL miny = min(pt[i].y, pt[j].y);
LL maxy = max(pt[i].y, pt[j].y);
for (int q=;q<=n;q++)
{
if (pt[q].y>maxy||pt[q].y<miny) continue;
int tot = ;
for (int z=q;z<=n;z++)
{
if (pt[z].y>maxy||pt[z].y<miny) continue;
tot++;
if (tot>=k)
area = min(area, (maxy-miny)*(pt[z].x-pt[q].x));
}
}
}
}
printf("%lld\n",area);
return ;
}
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