「学习笔记」杂项算法大礼包

平面最近点对。

#include <algorithm>
#include <cstdio>
#include <vector>
#include <cmath>
using namespace std;

#define fs first
#define sc second

typedef double db;
typedef pair<db, db> pa;

const int N = 2e5 + 10;
const db EPS = 1e-10;

int cmp1(pa a, pa b) { return a.fs - b.fs < -EPS; }
int cmp2(pa a, pa b) { return a.sc - b.sc < -EPS; }
int n, m;
pa a[N], arr[N];

db p(db x) { return x * x; }
db d(pa x, pa y) { return sqrt(p(x.fs - y.fs) + p(x.sc - y.sc)); }

db divide(int l, int r) {
    if(r - l <= 2) {
        db ans = 3e18;
        for(int i = l; i < r; i ++)
            for(int j = i + 1; j <= r; j ++)
                ans = min(ans, d(a[i], a[j]));
        sort(a + l, a + r + 1, cmp2);
        return ans;
    }
    int mid = (l + r) >> 1, p1 = l, p2 = mid + 1;
    db Mid = a[mid].fs, ans = min(divide(l, mid), divide(mid + 1, r));
    for(int i = l; i <= r; i ++) {
        if(p2 > r || (p1 <= mid && a[p1].sc - a[p2].sc < -EPS)) arr[i] = a[p1 ++];
        else arr[i] = a[p2 ++];
    }
    m = 0;
    for(int i = l; i <= r; i ++) a[i] = arr[i];
    for(int i = l; i <= r; i ++) if(fabs(a[i].fs - Mid) <= ans) arr[++ m] = a[i];
    for(int i = 1; i <= m; i ++)
        for(int j = i + 1; j <= i + 7 && j <= m; j ++) {
            db dis = d(arr[i], arr[j]);
            ans = min(ans, dis);
        }
    return ans;
}

int main() {
    while(~ scanf("%d", &n)) {
        for(int i = 1; i <= n; i ++)
            scanf("%lf%lf", &a[i].fs, &a[i].sc);
        sort(a + 1, a + n + 1, cmp1);
        printf("%.4lf\n", divide(1, n));
    }
    return 0;
}

来源：https://www.cnblogs.com/hongzy/p/11385391.html