ClosestPairOfPointsNurlan.cpp

/***********

    Solution to Closest Pair of Points Problem. O(nlogn) Divide-and-Conquer.
    Tested on http://www.spoj.com/problems/CLOPPAIR/

***********/

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <algorithm>
#include <cmath>

using namespace std;

#define sqr(a) ((a)*(a))
const double inf = 1e100;
const int MAXN = 55000;


struct point {
    double x, y;
    int ind;
    void read() {
        scanf("%lf%lf", &x, &y);
    }
    double dist_to(point& r) {
        return sqrt(sqr(x - r.x) + sqr(y - r.y));
    }
    bool operator<(const point&r) const {
        return x < r.x || (x == r.x && y < r.y);
    }
};

point aux[MAXN], P[MAXN], v[MAXN]; int vn;

int a, b, n;
double ans = inf;

// ans contains closest distance, a, b - indices of points.
void closest_pair(point p[], int n) {
    if (n <= 1) return ;
    if (n == 2) {
        if (p[0].y > p[1].y)
            swap(p[0], p[1]);
        double d = p[0].dist_to(p[1]);
        if (d < ans)
            ans = d, a = p[0].ind, b = p[1].ind;
        return;
    }
    int m = n / 2;
    double x = p[m].x;
    closest_pair(p, m); // left
    closest_pair(p + m, n - m); //right

    int il = 0, ir = m, i = 0;
    while (il < m && ir < n) { // merging two halves
        if (p[il].y < p[ir].y) aux[i ++] = p[il ++];
        else aux[i ++] = p[ir ++];
    }
    while (il < m)
        aux[i ++] = p[il ++];
    while (ir < n)
        aux[i ++] = p[ir ++];

    vn = 0;
    for (int j = 0 ; j < n ; j ++) { // copying back into p
        p[j] = aux[j];
        if (fabs(p[j].x - x) < ans) // looking at the strip of width 2*ans
            v[vn ++] = p[j];
    }

    for (int j = 0 ; j < vn ; j ++) { // (2*ans) x (ans) box
        for (int k = j + 1 ; k < vn && v[k].y - v[j].y < ans ; k ++) {
            double d = v[j].dist_to(v[k]);
            if (ans > d) {
                ans = d;
                a = v[k].ind, b = v[j].ind;
            }
        }
    }
}

int main() {
    scanf("%d", &n);
    for (int i = 0 ; i < n ; i++) {
        P[i].read();
        P[i].ind = i;
    }
    sort(P, P + n);
    closest_pair(P, n);
    printf("%d %d %lf\n", min(a, b), max(a, b), ans);
    return 0;
}