hdu 1007_平面最近点对模板

淩亂°似流年 2022-05-14 13:49 165阅读 0赞

简单题目,直接模板上

[http://acm.hdu.edu.cn/showproblem.php?pid=1007][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;
    }

[http_acm.hdu.edu.cn_showproblem.php_pid_1007]: http://acm.hdu.edu.cn/showproblem.php?pid=1007