分治法求解最近点对.txt

分治法求解最近点对问题 求最近点对的分治算法实现,输入点对

分治法求解最近点对问题 

  
/**************求最近点对的分治算法实现,输入点对，输出最近点对的距离**************/
#include <iostream>
#include<cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
using namespace std;
const int N = 100005;
const double MAX = 10e100;
const double eps = 0.00001;
typedef struct TYPE
{
    double x, y;
    int index;
} Point;
Point a[N], b[N], c[N];
double closest(Point *, Point *, Point *, int, int);
double dis(Point, Point);
int cmp_x(const void *, const void*);
int cmp_y(const void *, const void*);
int merge(Point *, Point *, int, int, int);
inline double min(double, double);

int main()
{
    int n, i;
    double d;
    scanf("%d", &n);
    while (n)
    {
        for (i = 0; i < n; i++)
            scanf("%lf%lf", &(a[i].x), &(a[i].y));
        qsort(a, n, sizeof(a[0]), cmp_x);
        for (i = 0; i < n; i++)
            a[i].index = i;
        memcpy(b, a, n *sizeof(a[0]));
        qsort(b, n, sizeof(b[0]), cmp_y);
        d = closest(a, b, c, 0, n - 1);
        printf("%.2lf\n", d);
        scanf("%d", &n);
    }
    return 0;
}

double closest(Point a[], Point b[], Point c[], int p, int q)
{
    if (q - p == 1)
        return dis(a[p], a[q]);
    if (q - p == 2)
    {
        double x1 = dis(a[p], a[q]);
        double x2 = dis(a[p + 1], a[q]);
        double x3 = dis(a[p], a[p + 1]);
        if (x1 < x2 && x1 < x3)
            return x1;
        else if (x2 < x3)
            return x2;
        else
            return x3;
    }
    int m = (p + q) / 2;
    int i, j, k;
    double d1, d2;
    for (i = p, j = p, k = m + 1; i <= q; i++)
        if (b[i].index <= m)
            c[j++] = b[i];
    //数组c左半部保存划分后左部的点, 且对y是有序的.
    else
        c[k++] = b[i];
    d1 = closest(a, c, b, p, m);
    d2 = closest(a, c, b, m + 1, q);
    double dm = min(d1, d2);
    merge(b, c, p, m, q); //数组c左右部分分别是对y坐标有序的, 将其合并到b.
    for (i = p, k = p; i <= q; i++)
        if (fabs(b[i].x - b[m].x) < dm)
            c[k++] = b[i];
    //找出离划分基准左右不超过dm的部分, 且仍然对y坐标有序.
    for (i = p; i < k; i++)
    for (j = i + 1; j < k && c[j].y - c[i].y < dm; j++)
    {
        double temp = dis(c[i], c[j]);
        if (temp < dm)
            dm = temp;
    }
    return dm;
}

double dis(Point p, Point q)
{
    double x1 = p.x - q.x, y1 = p.y - q.y;
    return sqrt(x1 *x1 + y1 * y1);
}

int merge(Point p[], Point q[], int s, int m, int t)
{
    int i, j, k;
    for (i = s, j = m + 1, k = s; i <= m && j <= t;)
    {
        if (q[i].y > q[j].y)
            p[k++] = q[j], j++;
        else
            p[k++] = q[i], i++;
    }
    while (i <= m)
        p[k++] = q[i++];
    while (j <= t)
        p[k++] = q[j++];
    memcpy(q + s, p + s, (t - s + 1) *sizeof(p[0]));
    return 0;
}

int cmp_x(const void *p, const void *q)
{
    double temp = ((Point*)p)->x - ((Point*)q)->x;
    if (temp > 0)
        return 1;
    else if (fabs(temp) < eps)
        return 0;
    else
        return  - 1;
}

int cmp_y(const void *p, const void *q)
{
    double temp = ((Point*)p)->y - ((Point*)q)->y;
    if (temp > 0)
        return 1;
    else if (fabs(temp) < eps)
        return 0;
    else
        return  - 1;
}

inline double min(double p, double q)
{
    return (p > q) ? (q): (p);
}