hdu 1007_平面最近点对模板

最新推荐文章于 2025-06-24 15:51:49 发布

iteye_21202

最新推荐文章于 2025-06-24 15:51:49 发布

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文章标签： php

本文介绍了两种计算近点对距离的方法，一种是基于排序和二分查找的O(n log n)复杂度算法，另一种是使用分治策略的O(n log n * log n)复杂度算法，适用于解决点集中的最短距离问题。

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简单题目,直接模板上

http://acm.hdu.edu.cn/showproblem.php?pid=1007 Quoit Design

复杂度O( n * log(n) )

#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <string>
#include <set>
#include <stack>
#include <map>
#include <cmath>
#include <vector>
#include <iostream>
#include <algorithm>
#include <bitset>
#include <fstream>
using namespace std;


//LOOP
#define FF(i, a, b) for(int i = (a); i < (b); ++i)
#define FE(i, a, b) for(int i = (a); i <= (b); ++i)
#define FED(i, b, a) for(int i = (b); i>= (a); --i)
#define REP(i, N) for(int i = 0; i < (N); ++i)
#define CLR(A,value) memset(A,value,sizeof(A))
#define FC(it, c) for(__typeof((c).begin()) it = (c).begin(); it != (c).end(); it++)


//OTHER
#define SZ(V) (int)V.size()
#define PB push_back
#define MP make_pair
#define all(x) (x).begin(),(x).end()


//INPUT
#define RI(n) scanf("%d", &n)
#define RII(n, m) scanf("%d%d", &n, &m)
#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)
#define RIV(n, m, k, p) scanf("%d%d%d%d", &n, &m, &k, &p)
#define RV(n, m, k, p, q) scanf("%d%d%d%d%d", &n, &m, &k, &p, &q)
#define RS(s) scanf("%s", s)


//OUTPUT
#define WI(n) printf("%d\n", n)
#define WS(n) printf("%s\n", n)


//debug
//#define online_judge
#ifndef online_judge
#define debugt(a) cout << (#a) << "=" << a << " ";
#define debugI(a) debugt(a) cout << endl
#define debugII(a, b) debugt(a) debugt(b) cout << endl
#define debugIII(a, b, c) debugt(a) debugt(b) debugt(c) cout << endl
#define debugIV(a, b, c, d) debugt(a) debugt(b) debugt(c) debugt(d) cout << endl
#else
#define debugI(v)
#define debugII(a, b)
#define debugIII(a, b, c)
#define debugIV(a, b, c, d)
#endif

#define sqr(x) (x) * (x)
typedef long long LL;
typedef unsigned long long ULL;
typedef vector <int> VI;
const int INF = 0x3f3f3f3f;
const double EPS = 1e-10;
const int MOD = 100000007;
const int MAXN = 100010;
const double PI = acos(-1.0);

inline int dcmp(double x)
{
    if(fabs(x) < EPS) return 0;
    else return x < 0 ? -1 : 1;
}
struct Point
{
    double x, y;
    Point(double x=0, double y=0):x(x),y(y) { }
    inline void read()
    {
        scanf("%lf%lf", &x, &y);
    }
};




Point p[MAXN];
int px[MAXN], py[MAXN], ty[MAXN];
inline int cmpx(Point a, Point b)
{
    return a.x < b.x;
}
inline int cmpy(int a, int b)
{
    return p[a].y < p[b].y;
}
inline double min(double a, double b)
{
    return a < b ? a : b;
}
inline double dist2(Point a, Point b)
{
    return sqr(a.x - b.x) + sqr(a.y - b.y);
}
double min_dis = 1e100;
//返回最小距离的平方
double mindist(int* X, int* Y, int size)
{
    if(size <= 3)
    {
        if(size == 2)
            return dist2(p[X[0]], p[X[1]]);
        REP(i, size)
            min_dis = min(min_dis, dist2(p[X[i]], p[X[(i + 1) % size]]));
        return min_dis;
    }
    int pr = size >> 1, pl = size - pr;
    int l1 = 0, l2 = pl;
    REP(i, size)
        if(Y[i] < X[pl])
            ty[l1++] = Y[i];
        else
            ty[l2++] = Y[i];
    REP(i, size)
        Y[i] = ty[i];
    min_dis = min(mindist(X, Y, pl), mindist(X + pl, Y + pl, pr));
    l1 = 0;
    REP(i, size)
        if(sqr(p[Y[i]].x - p[X[pl - 1]].x) <= min_dis)
            ty[l1++] = Y[i];
    REP(i, l1)
        for(int j = 1; j < 6 && i + j < l1; j++)
            if((ty[i] - X[pl]) * (ty[i + j] - X[pl]) <= 0)
                min_dis = min(min_dis, dist2(p[ty[i]], p[ty[i + j]]));
    return min_dis;
}

//px的初始化
//每次调用时,两次排序,mid_dis赋值
int main()
{
    int n;
    REP(i, MAXN) px[i] = i;
    while(scanf("%d",&n)&&n)
    {
        REP(i, n)
        {
            p[i].read();
            py[i] = i;
        }
        sort(p, p + n, cmpx);
        sort(py, py + n, cmpy);
        min_dis = 1e100;
        printf("%.2f\n", sqrt(mindist(px, py, n)) / 2);
    }
    return 0;
}

O(n * log(n) *log(n))的复杂度

#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <string>
#include <set>
#include <stack>
#include <map>
#include <cmath>
#include <vector>
#include <iostream>
#include <algorithm>
#include <bitset>
#include <fstream>
using namespace std;


//LOOP
#define FF(i, a, b) for(int i = (a); i < (b); ++i)
#define FE(i, a, b) for(int i = (a); i <= (b); ++i)
#define FED(i, b, a) for(int i = (b); i>= (a); --i)
#define REP(i, N) for(int i = 0; i < (N); ++i)
#define CLR(A,value) memset(A,value,sizeof(A))
#define FC(it, c) for(__typeof((c).begin()) it = (c).begin(); it != (c).end(); it++)


//OTHER
#define SZ(V) (int)V.size()
#define PB push_back
#define MP make_pair
#define all(x) (x).begin(),(x).end()


//INPUT
#define RI(n) scanf("%d", &n)
#define RII(n, m) scanf("%d%d", &n, &m)
#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)
#define RIV(n, m, k, p) scanf("%d%d%d%d", &n, &m, &k, &p)
#define RV(n, m, k, p, q) scanf("%d%d%d%d%d", &n, &m, &k, &p, &q)
#define RS(s) scanf("%s", s)


//OUTPUT
#define WI(n) printf("%d\n", n)
#define WS(n) printf("%s\n", n)


//debug
//#define online_judge
#ifndef online_judge
#define debugt(a) cout << (#a) << "=" << a << " ";
#define debugI(a) debugt(a) cout << endl
#define debugII(a, b) debugt(a) debugt(b) cout << endl
#define debugIII(a, b, c) debugt(a) debugt(b) debugt(c) cout << endl
#define debugIV(a, b, c, d) debugt(a) debugt(b) debugt(c) debugt(d) cout << endl
#else
#define debugI(v)
#define debugII(a, b)
#define debugIII(a, b, c)
#define debugIV(a, b, c, d)
#endif

#define sqr(x) (x) * (x)
typedef long long LL;
typedef unsigned long long ULL;
typedef vector <int> VI;
const int INF = 0x3f3f3f3f;
const double EPS = 1e-10;
const int MOD = 100000007;
const int MAXN = 100010;
const double PI = acos(-1.0);


inline int dcmp(double x)
{
    if(fabs(x) < EPS) return 0;
    else return x < 0 ? -1 : 1;
}
struct Point
{
    double x, y;
    Point(double x=0, double y=0):x(x),y(y) { }
    inline void read()
    {
        scanf("%lf%lf", &x, &y);
    }
};



//最近点对
Point point[MAXN];
int tmpt[MAXN], Y[MAXN];

inline bool cmpxy(Point a, Point b)
{
    if(a.x != b.x)
        return a.x < b.x;
    return a.y < b.y;
}

inline bool cmpy(int a, int b)
{
    return point[a].y < point[b].y;
}

inline double dist(int x, int y)
{
    Point& a = point[x], &b = point[y];
    return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));
}

double Closest_Pair(int left, int right)
{
    double d = 1e100;
    if(left == right)
        return d;
    if(left + 1 == right)
        return dist(left, right);
    int mid = (left + right) >> 1;
    double d1 = Closest_Pair(left, mid);
    double d2 = Closest_Pair(mid + 1, right);
    d = min(d1, d2);
    int k = 0;
    //分离出宽度为d的区间
    FE(i, left, right)
    {
        if(fabs(point[mid].x - point[i].x) <= d)
            tmpt[k++] = i;
    }
    sort(tmpt, tmpt + k, cmpy);
    //线性扫描
    REP(i, k)
    {
        for(int j = i + 1; j < k && point[tmpt[j]].y-point[tmpt[i]].y < d; j++)
        {
            double d3 = dist(tmpt[i],tmpt[j]);
            if(d > d3)
                d = d3;
        }
    }
    return d;
}

int main()
{
    //freopen("input.txt", "r", stdin);
    int n;
    while (~RI(n) && n)
    {
        REP(i, n)
        {
            point[i].read();
        }
        sort(point, point + n, cmpxy);
        printf("%.2f\n", Closest_Pair(0, n - 1) / 2);
    }
    return 0;
}