Question Name:Mutual Smallest Distance

```
#include <iostream>
#include <float.h>
#include <stdlib.h>
#include <math.h>
#include <iomanip>

using namespace std;

struct Point
{
int x, y;
}point[10];

int compareX(const void* a, const void* b)
{
Point *p1 = (Point *)a,  *p2 = (Point *)b;
return (p1->x - p2->x);
}
int compareY(const void* a, const void* b)
{
Point *p1 = (Point *)a,   *p2 = (Point *)b;
return (p1->y - p2->y);
}

float dist(Point p1, Point p2)
{
return sqrt( (p1.x - p2.x)*(p1.x - p2.x) +
(p1.y - p2.y)*(p1.y - p2.y)
);
}

float bruteForce(Point P[], int n)
{
float min = FLT_MAX;
for (int i = 0; i < n; ++i)
for (int j = i+1; j < n; ++j)
if (dist(P[i], P[j]) < min)
min = dist(P[i], P[j]);
return min;
}

float min(float x, float y)
{
return (x < y)? x : y;
}

float stripClosest(Point strip[], int size, float d)
{
float min = d;

for (int i = 0; i < size; ++i)
for (int j = i+1; j < size && (strip[j].y - strip[i].y) < min; ++j)
if (dist(strip[i],strip[j]) < min)
min = dist(strip[i], strip[j]);

return min;
}

float closestUtil(Point Px[], Point Py[], int n)
{
if (n <= 3)
return bruteForce(Px, n);

// Find the middle point
int mid = n/2;
Point midPoint = Px[mid];

Point Pyl[mid+1];
Point Pyr[n-mid-1];
int li = 0, ri = 0;
for (int i = 0; i < n; i++)
{
if (Py[i].x <= midPoint.x)
Pyl[li++] = Py[i];
else
Pyr[ri++] = Py[i];
}

float dl = closestUtil(Px, Pyl, mid);
float dr = closestUtil(Px + mid, Pyr, n-mid);

float d = min(dl, dr);

Point strip[n];
int j = 0;
for (int i = 0; i < n; i++)
if (abs(Py[i].x - midPoint.x) < d)
strip[j] = Py[i], j++;

return min(d, stripClosest(strip, j, d) );
}

float closest(Point P[], int n)
{
Point Px[n];
Point Py[n];
for (int i = 0; i < n; i++)
{
Px[i] = P[i];
Py[i] = P[i];
}

qsort(Px, n, sizeof(Point), compareX);
qsort(Py, n, sizeof(Point), compareY);

return closestUtil(Px, Py, n);
}

int main()
{
int n,i;
float awm;
cin>>n;
for(i=0;i<n;i++) {
cin>>point[i].x>>point[i].y;
}
std::cout << std::fixed;

std:: cout<<std::setprecision(6);
cout<<closest(point, n);

return 0;
} ```

Problem Description

Given n points in d-dimensions, find two
whose mutual distance is smallest.

• Test Case 1

Input (stdin)

```4
10 20
5 1
2 10
3 4
```

Expected Output

`3.605551`
• Test Case 2

Input (stdin)

```6
2 3
12 30
40 50
5 1
12 10
3 4
```

Expected Output

`1.414214`