closestPair.cpp

#include <bits/stdc++.h>
using namespace std;
 
/* 
 * Point Declaration
 */
struct Point{
    int x, y;
};
 
/* 
 * sort array of points according to X coordinate
 */
int compareX(const void* a, const void* b){
    Point *p1 = (Point *)a, *p2 = (Point *)b;
    return (p1->x - p2->x);
}
/* 
 * sort array of points according to Y coordinate
 */
int compareY(const void* a, const void* b){
    Point *p1 = (Point *)a, *p2 = (Point *)b;
    return (p1->y - p2->y);
}
/* 
 * find the distance between two points
 */
float dist(Point p1, Point p2){
    return sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y));
}
/* 
 * return the smallest distance between two points
 */ 
float small_dist(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;
}
/* 
 * find the distance beween the closest points of strip of given size
 */
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;
}
/* 
 * find the smallest distance.
 */
float closestUtil(Point Px[], Point Py[], int n){
    if (n <= 3)
        return small_dist(Px, n);
    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));
}
/* 
 * finds the smallest distance
 */
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);
}
 
/*
 * Main
 */
int main(){
    Point P[] = {{2, 3}, {12, 30}, {40, 50}, {5, 1}, {12, 10}, {3, 4}};
    int n = sizeof(P) / sizeof(P[0]);
    cout << "The smallest distance is " << closest(P, n);
    return 0;
}