目录

C++ 的Lambda表达式

C++ 11 标准发布，各大编译器都开始支持里面的各种新特性，其中一项比较有意思的就是lambda表达式。

语法规则

C++ 11 Lambda表达式的四种声明方式

今年准备安安心心写一个协程库。一方面是觉得协程挺有意思，另一方面也是因为C/C++在这方面没有一个非常权威的解决方案。 按照我自己风格还是喜欢C++，所以协程库定名为 libcopp 。 源码托管在 github: https://github.com/owent/libcopp 镜像托管 http://git.oschina.net/owent/distinctionpp

C++11标准里有动态模板参数已经是众所周知的事儿了。但是当时还有个主流编译器还不支持。 但是现在，主要的编译器。VC(Windows),GCC(Windows,Linux),Clang(Mac,IOS)都已经支持了。所以就可以准备用于生产环境了。 type_traits没啥好说的。主要是一些静态检测。主要还是要看动态模板参数和他们两的结合使用上。 动态模版参数标准文档见: http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2242.pdf 和 http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2555.pdf 虽然贴出来了。估计是没人看得。所以就直接说重点。

用过std和boost的function对象和bind函数的童鞋们都知道这玩意用起来腰不酸了，腿不疼了，心情也舒畅了。先上一个简单得示例：

/**
 * 二维ACM计算几何模板
 * 注意变量类型更改和EPS
 * #include <cmath>
 * #include <cstdio>
 * By OWenT
 */

const double eps = 1e-8;
const double pi = std::acos(-1.0);
//点
class point
{
public:
    double x, y;
    point(){};
    point(double x, double y):x(x),y(y){};

    static int xmult(const point &ps, const point &pe, const point &po)
    {
        return (ps.x - po.x) * (pe.y - po.y) - (pe.x - po.x) * (ps.y - po.y);
    }

    //相对原点的差乘结果，参数：点[_Off]
    //即由原点和这两个点组成的平行四边形面积
    double operator *(const point &_Off) const
    {
        return x * _Off.y - y * _Off.x;
    }
    //相对偏移
    point operator - (const point &_Off) const
    {
        return point(x - _Off.x, y - _Off.y);
    }
    //点位置相同(double类型)
    bool operator == (const point &_Off) const
    {
        return std::fabs(_Off.x - x) < eps && std::fabs(_Off.y - y) < eps;
    }
    //点位置不同(double类型)
    bool operator != (const point &_Off) const
    {
        return ((*this) == _Off) == false;
    }
    //两点间距离的平方
    double dis2(const point &_Off) const
    {
        return (x - _Off.x) * (x - _Off.x) + (y - _Off.y) * (y - _Off.y);
    }
    //两点间距离
    double dis(const point &_Off) const
    {
        return std::sqrt((x - _Off.x) * (x - _Off.x) + (y - _Off.y) * (y - _Off.y));
    }
};

//两点表示的向量
class pVector
{
public:
    point s, e;//两点表示，起点[s]，终点[e]
    double a, b, c;//一般式,ax+by+c=0

    pVector(){}
    pVector(const point &s, const point &e):s(s),e(e){}

    //向量与点的叉乘,参数：点[_Off]
    //[点相对向量位置判断]
    double operator *(const point &_Off) const
    {
        return (_Off.y - s.y) * (e.x - s.x) - (_Off.x - s.x) * (e.y - s.y);
    }
    //向量与向量的叉乘,参数：向量[_Off]
    double operator *(const pVector &_Off) const
    {
        return (e.x - s.x) * (_Off.e.y - _Off.s.y) - (e.y - s.y) * (_Off.e.x - _Off.s.x);
    }
    //从两点表示转换为一般表示
    bool pton()
    {
        a = s.y - e.y;
        b = e.x - s.x;
        c = s.x * e.y - s.y * e.x;
        return true;
    }

    //-----------点和直线（向量）-----------
    //点在向量左边（右边的小于号改成大于号即可,在对应直线上则加上=号）
    //参数：点[_Off],向量[_Ori]
    friend bool operator<(const point &_Off, const pVector &_Ori)
    {
        return (_Ori.e.y - _Ori.s.y) * (_Off.x - _Ori.s.x)
            < (_Off.y - _Ori.s.y) * (_Ori.e.x - _Ori.s.x);
    }

    //点在直线上,参数：点[_Off]
    bool lhas(const point &_Off) const
    {
        return std::fabs((*this) * _Off) < eps;
    }
    //点在线段上,参数：点[_Off]
    bool shas(const point &_Off) const
    {
        return lhas(_Off)
            && _Off.x - std::min(s.x, e.x) > -eps && _Off.x - std::max(s.x, e.x) < eps
            && _Off.y - std::min(s.y, e.y) > -eps && _Off.y - std::max(s.y, e.y) < eps;
    }

    //点到直线/线段的距离
    //参数： 点[_Off], 是否是线段[isSegment](默认为直线)
    double dis(const point &_Off, bool isSegment = false)
    {
        //化为一般式
        pton();

        //到直线垂足的距离
        double td = (a * _Off.x + b * _Off.y + c) / sqrt(a * a + b * b);

        //如果是线段判断垂足
        if(isSegment)
        {
            double xp = (b * b * _Off.x - a * b * _Off.y - a * c) / ( a * a + b * b);
            double yp = (-a * b * _Off.x + a * a * _Off.y - b * c) / (a * a + b * b);
            double xb = std::max(s.x, e.x);
            double yb = std::max(s.y, e.y);
            double xs = s.x + e.x - xb;
            double ys = s.y + e.y - yb;
            if(xp > xb + eps || xp < xs - eps || yp > yb + eps || yp < ys - eps)
                td = std::min(_Off.dis(s), _Off.dis(e));
        }

        return fabs(td);
    }

    //关于直线对称的点
    point mirror(const point &_Off) const
    {
        //注意先转为一般式
        point ret;
        double d = a * a + b * b;
        ret.x = (b * b * _Off.x - a * a * _Off.x - 2 * a * b * _Off.y - 2 * a * c) / d;
        ret.y = (a * a * _Off.y - b * b * _Off.y - 2 * a * b * _Off.x - 2 * b * c) / d;
        return ret;
    }
    //计算两点的中垂线
    static pVector ppline(const point &_a, const point &_b)
    {
        pVector ret;
        ret.s.x = (_a.x + _b.x) / 2;
        ret.s.y = (_a.y + _b.y) / 2;
        //一般式
        ret.a = _b.x - _a.x;
        ret.b = _b.y - _a.y;
        ret.c = (_a.y - _b.y) * ret.s.y + (_a.x - _b.x) * ret.s.x;
        //两点式
        if(std::fabs(ret.a) > eps)
        {
            ret.e.y = 0.0;
            ret.e.x = - ret.c / ret.a;
            if(ret.e == ret. s)
            {
                ret.e.y = 1e10;
                ret.e.x = - (ret.c - ret.b * ret.e.y) / ret.a;
            }
        }
        else
        {
            ret.e.x = 0.0;
            ret.e.y = - ret.c / ret.b;
            if(ret.e == ret. s)
            {
                ret.e.x = 1e10;
                ret.e.y = - (ret.c - ret.a * ret.e.x) / ret.b;
            }
        }
        return ret;
    }

    //------------直线和直线（向量）-------------
    //直线重合,参数：直线向量[_Off]
    bool equal(const pVector &_Off) const
    {
        return lhas(_Off.e) && lhas(_Off.s);
    }
    //直线平行，参数：直线向量[_Off]
    bool parallel(const pVector &_Off) const
    {
        return std::fabs((*this) * _Off) < eps;
    }
    //两直线交点，参数：目标直线[_Off]
    point crossLPt(pVector _Off)
    {
        //注意先判断平行和重合
        point ret = s;
        double t = ((s.x - _Off.s.x) * (_Off.s.y - _Off.e.y) - (s.y - _Off.s.y) * (_Off.s.x - _Off.e.x))
                / ((s.x - e.x) * (_Off.s.y - _Off.e.y) - (s.y - e.y) * (_Off.s.x - _Off.e.x));
        ret.x += (e.x - s.x) * t;
        ret.y += (e.y - s.y) * t;
        return ret;
    }

    //------------线段和直线（向量）----------
    //线段和直线交
    //参数：线段[_Off]
    bool crossSL(const pVector &_Off) const
    {
        double rs = (*this) * _Off.s;
        double re = (*this) * _Off.e;
        return rs * re < eps;
    }

    //------------线段和线段（向量）----------
    //判断线段是否相交(注意添加eps)，参数：线段[_Off]
    bool isCrossSS(const pVector &_Off) const
    {
        //1.快速排斥试验判断以两条线段为对角线的两个矩形是否相交
        //2.跨立试验（等于0时端点重合）
        return (
            (std::max(s.x, e.x) >= std::min(_Off.s.x, _Off.e.x)) &&
            (std::max(_Off.s.x, _Off.e.x) >= std::min(s.x, e.x)) &&
            (std::max(s.y, e.y) >= std::min(_Off.s.y, _Off.e.y)) &&
            (std::max(_Off.s.y, _Off.e.y) >= std::min(s.y, e.y)) &&
            ((pVector(_Off.s, s) * _Off) * (_Off * pVector(_Off.s, e)) >= 0.0) &&
            ((pVector(s, _Off.s) * (*this)) * ((*this) * pVector(s, _Off.e)) >= 0.0)
            );
    }
};

class polygon
{
public:
    const static long maxpn = 100;
    point pt[maxpn];//点（顺时针或逆时针）
    long n;//点的个数

    point& operator[](int _p)
    {
        return pt[_p];
    }

    //求多边形面积，多边形内点必须顺时针或逆时针
    double area() const
    {
        double ans = 0.0;
        int i;
        for(i = 0; i < n; i ++)
        {
            int nt = (i + 1) % n;
            ans += pt[i].x * pt[nt].y - pt[nt].x * pt[i].y;
        }
        return std::fabs(ans / 2.0);
    }
    //求多边形重心，多边形内点必须顺时针或逆时针
    point gravity() const
    {
        point ans;
        ans.x = ans.y = 0.0;
        int i;
        double area = 0.0;
        for(i = 0; i < n; i ++)
        {
            int nt = (i + 1) % n;
            double tp = pt[i].x * pt[nt].y - pt[nt].x * pt[i].y;
            area += tp;
            ans.x += tp * (pt[i].x + pt[nt].x);
            ans.y += tp * (pt[i].y + pt[nt].y);
        }
        ans.x /= 3 * area;
        ans.y /= 3 * area;
        return ans;
    }
    //判断点在凸多边形内，参数：点[_Off]
    bool chas(const point &_Off) const
    {
        double tp = 0, np;
        int i;
        for(i = 0; i < n; i ++)
        {
            np = pVector(pt[i], pt[(i + 1) % n]) * _Off;
            if(tp * np < -eps)
                return false;
            tp = (std::fabs(np) > eps)?np: tp;
        }
        return true;
    }
    //判断点是否在任意多边形内[射线法]，O(n)
    bool ahas(const point &_Off) const
    {
        int ret = 0;
        double infv = 1e-10;//坐标系最大范围
        pVector l = pVector(_Off, point( -infv ,_Off.y));
        for(int i = 0; i < n; i ++)
        {
            pVector ln = pVector(pt[i], pt[(i + 1) % n]);
            if(fabs(ln.s.y - ln.e.y) > eps)
            {
                point tp = (ln.s.y > ln.e.y)? ln.s: ln.e;
                if(fabs(tp.y - _Off.y) < eps && tp.x < _Off.x + eps)
                    ret ++;
            }
            else if(ln.isCrossSS(l))
                ret ++;
        }
        return (ret % 2 == 1);
    }
    //凸多边形被直线分割,参数：直线[_Off]
    polygon split(pVector _Off)
    {
        //注意确保多边形能被分割
        polygon ret;
        point spt[2];
        double tp = 0.0, np;
        bool flag = true;
        int i, pn = 0, spn = 0;
        for(i = 0; i < n; i ++)
        {
            if(flag)
                pt[pn ++] = pt[i];
            else
                ret.pt[ret.n ++] = pt[i];
            np = _Off * pt[(i + 1) % n];
            if(tp * np < -eps)
            {
                flag = !flag;
                spt[spn ++] = _Off.crossLPt(pVector(pt[i], pt[(i + 1) % n]));
            }
            tp = (std::fabs(np) > eps)?np: tp;
        }
        ret.pt[ret.n ++] = spt[0];
        ret.pt[ret.n ++] = spt[1];
        n = pn;
        return ret;
    }

    //-------------凸包-------------
    //Graham扫描法，复杂度O(nlg(n)),结果为逆时针
    //#include <algorithm>
    static bool graham_cmp(const point &l, const point &r)//凸包排序函数
    {
        return l.y < r.y || (l.y == r.y && l.x < r.x);
    }
    polygon& graham(point _p[], int _n)
    {
        int i, len;
        std::sort(_p, _p + _n, polygon::graham_cmp);
        n = 1;
        pt[0] = _p[0], pt[1] = _p[1];
        for(i = 2; i < _n; i ++)
        {
            while(n && point::xmult(_p[i], pt[n], pt[n - 1]) >= 0)
                n --;
            pt[++ n] = _p[i];
        }
        len = n;
        pt[++ n] = _p[_n - 2];
        for(i = _n - 3; i >= 0; i --)
        {
            while(n != len && point::xmult(_p[i], pt[n], pt[n - 1]) >= 0)
                n --;
            pt[++ n] = _p[i];
        }
        return (*this);
    }

    //凸包旋转卡壳(注意点必须顺时针或逆时针排列)
    //返回值凸包直径的平方（最远两点距离的平方）
    double rotating_calipers()
    {
        int i = 1;
        double ret = 0.0;
        pt[n] = pt[0];
        for(int j = 0; j < n; j ++)
        {
            while(fabs(point::xmult(pt[j], pt[j + 1], pt[i + 1])) > fabs(point::xmult(pt[j], pt[j + 1], pt[i])) + eps)
                i = (i + 1) % n;
            //pt[i]和pt[j],pt[i + 1]和pt[j + 1]可能是对踵点
            ret = std::max(ret, std::max(pt[i].dis(pt[j]), pt[i + 1].dis(pt[j + 1])));
        }
        return ret;
    }

    //凸包旋转卡壳(注意点必须逆时针排列)
    //返回值两凸包的最短距离
    double rotating_calipers(polygon &_Off)
    {
        int i = 0;
        double ret = 1e10;//inf
        pt[n] = pt[0];
        _Off.pt[_Off.n] = _Off.pt[0];
        //注意凸包必须逆时针排列且pt[0]是左下角点的位置
        while(_Off.pt[i + 1].y > _Off.pt[i].y)
            i = (i + 1) % _Off.n;
        for(int j = 0; j < n; j ++)
        {
            double tp;
            //逆时针时为 >,顺时针则相反
            while((tp = point::xmult(pt[j], pt[j + 1], _Off.pt[i + 1]) - point::xmult( pt[j], pt[j + 1], _Off.pt[i])) > eps)
                i = (i + 1) % _Off.n;
            //(pt[i],pt[i+1])和(_Off.pt[j],_Off.pt[j + 1])可能是最近线段
            ret = std::min(ret, pVector(pt[j], pt[j + 1]).dis(_Off.pt[i], true));
            ret = std::min(ret, pVector(_Off.pt[i], _Off.pt[i + 1]).dis(pt[j + 1], true));
            if(tp > -eps)//如果不考虑TLE问题最好不要加这个判断
            {
                ret = std::min(ret, pVector(pt[j], pt[j + 1]).dis(_Off.pt[i + 1], true));
                ret = std::min(ret, pVector(_Off.pt[i], _Off.pt[i + 1]).dis(pt[j], true));
            }
        }
        return ret;
    }

    //-----------半平面交-------------
    //复杂度:O(nlog2(n))
    //#include <algorithm>
    //半平面计算极角函数[如果考虑效率可以用成员变量记录]
    static double hpc_pa(const pVector &_Off)
    {
        return atan2(_Off.e.y - _Off.s.y, _Off.e.x - _Off.s.x);
    }
    //半平面交排序函数[优先顺序: 1.极角 2.前面的直线在后面的左边]
    static bool hpc_cmp(const pVector &l, const pVector &r)
    {
        double lp = hpc_pa(l), rp = hpc_pa(r);
        if(fabs(lp - rp) > eps)
            return lp < rp;
        return point::xmult(l.s, r.e, r.s) < 0.0;
    }
    //用于计算的双端队列
    pVector dequeue[maxpn];
    //获取半平面交的多边形（多边形的核）
    //参数：向量集合[l]，向量数量[ln];(半平面方向在向量左边）
    //函数运行后如果n[即返回多边形的点数量]为0则不存在半平面交的多边形（不存在区域或区域面积无穷大）
    polygon& halfPanelCross(pVector _Off[], int ln)
    {
        int i, tn;
        n = 0;
        std::sort(_Off, _Off + ln, hpc_cmp);
        //平面在向量左边的筛选
        for(i = tn = 1; i < ln; i ++)
            if(fabs(hpc_pa(_Off[i]) - hpc_pa(_Off[i - 1])) > eps)
                _Off[tn ++] = _Off[i];
        ln = tn;
        int bot = 0, top = 1;
        dequeue[0] = _Off[0];
        dequeue[1] = _Off[1];
        for(i = 2; i < ln; i ++)
        {
            if(dequeue[top].parallel(dequeue[top - 1]) ||
                dequeue[bot].parallel(dequeue[bot + 1]))
                return (*this);
            while(bot < top &&
                point::xmult(dequeue[top].crossLPt(dequeue[top - 1]), _Off[i].e, _Off[i].s) > eps)
                top --;
            while(bot < top &&
                point::xmult(dequeue[bot].crossLPt(dequeue[bot + 1]), _Off[i].e, _Off[i].s) > eps)
                bot ++;
            dequeue[++ top] = _Off[i];
        }

        while(bot < top &&
            point::xmult(dequeue[top].crossLPt(dequeue[top - 1]), dequeue[bot].e, dequeue[bot].s) > eps)
            top --;
        while(bot < top &&
            point::xmult(dequeue[bot].crossLPt(dequeue[bot + 1]), dequeue[top].e, dequeue[top].s) > eps)
            bot ++;
        //计算交点(注意不同直线形成的交点可能重合)
        if(top <= bot + 1)
            return (*this);
        for(i = bot; i < top; i ++)
            pt[n ++] = dequeue[i].crossLPt(dequeue[i + 1]);
        if(bot < top + 1)
            pt[n ++] = dequeue[bot].crossLPt(dequeue[top]);
        return (*this);
    }
};
class circle
{
public:
    point c;//圆心
    double r;//半径
    double db, de;//圆弧度数起点， 圆弧度数终点(逆时针0-360)

    //-------圆---------

    //判断圆在多边形内
    bool inside(const polygon &_Off) const
    {
        if(_Off.ahas(c) == false)
            return false;
        for(int i = 0; i < _Off.n; i ++)
        {
            pVector l = pVector(_Off.pt[i], _Off.pt[(i + 1) % _Off.n]);
            if(l.dis(c, true) < r - eps)
                return false;
        }
        return true;
    }

    //判断多边形在圆内（线段和折线类似）
    bool has(const polygon &_Off) const
    {
        for(int i = 0; i < _Off.n; i ++)
            if(_Off.pt[i].dis2(c) > r * r - eps)
                return false;
        return true;
    }

    //-------圆弧-------
    //圆被其他圆截得的圆弧，参数：圆[_Off]
    circle operator-(circle &_Off) const
    {
        //注意圆必须相交，圆心不能重合
        double d2 = c.dis2(_Off.c);
        double d = c.dis(_Off.c);
        double ans = std::acos((d2 + r * r - _Off.r * _Off.r) / (2 * d * r));
        point py = _Off.c - c;
        double oans = std::atan2(py.y, py.x);
        circle res;
        res.c = c;
        res.r = r;
        res.db = oans + ans;
        res.de = oans - ans + 2 * pi;
        return res;
    }
    //圆被其他圆截得的圆弧，参数：圆[_Off]
    circle operator+(circle &_Off) const
    {
        //注意圆必须相交，圆心不能重合
        double d2 = c.dis2(_Off.c);
        double d = c.dis(_Off.c);
        double ans = std::acos((d2 + r * r - _Off.r * _Off.r) / (2 * d * r));
        point py = _Off.c - c;
        double oans = std::atan2(py.y, py.x);
        circle res;
        res.c = c;
        res.r = r;
        res.db = oans - ans;
        res.de = oans + ans;
        return res;
    }

    //过圆外一点的两条切线
    //参数：点[_Off](必须在圆外),返回：两条切线(切线的s点为_Off,e点为切点)
    std::pair<pVector, pVector>  tangent(const point &_Off) const
    {
        double d = c.dis(_Off);
        //计算角度偏移的方式
        double angp = std::acos(r / d), ango = std::atan2(_Off.y - c.y, _Off.x - c.x);
        point pl = point(c.x + r * std::cos(ango + angp), c.y + r * std::sin(ango + angp)),
            pr = point(c.x + r * std::cos(ango - angp), c.y + r * std::sin(ango - angp));
        return std::make_pair(pVector(_Off, pl), pVector(_Off, pr));
    }

    //计算直线和圆的两个交点
    //参数：直线[_Off](两点式)，返回两个交点，注意直线必须和圆有两个交点
    std::pair<point, point> cross(pVector _Off) const
    {
        _Off.pton();
        //到直线垂足的距离
        double td = fabs(_Off.a * c.x + _Off.b * c.y + _Off.c) / sqrt(_Off.a * _Off.a + _Off.b * _Off.b);

        //计算垂足坐标
        double xp = (_Off.b * _Off.b * c.x - _Off.a * _Off.b * c.y - _Off.a * _Off.c) / ( _Off.a * _Off.a + _Off.b * _Off.b);
        double yp = (- _Off.a * _Off.b * c.x + _Off.a * _Off.a * c.y - _Off.b * _Off.c) / (_Off.a * _Off.a + _Off.b * _Off.b);

        double ango = std::atan2(yp - c.y, xp - c.x);
        double angp = std::acos(td / r);

        return std::make_pair(point(c.x + r * std::cos(ango + angp), c.y + r * std::sin(ango + angp)),
            point(c.x + r * std::cos(ango - angp), c.y + r * std::sin(ango - angp)));
    }
};

class triangle
{
public:
    point a, b, c;//顶点
    triangle(){}
    triangle(point a, point b, point c): a(a), b(b), c(c){}

    //计算三角形面积
    double area()
    {
        return fabs(point::xmult(a, b, c)) / 2.0;
    }

    //计算三角形外心
    //返回：外接圆圆心
    point circumcenter()
    {
        pVector u,v;
        u.s.x = (a.x + b.x) / 2;
        u.s.y = (a.y + b.y) / 2;
        u.e.x = u.s.x - a.y + b.y;
        u.e.y = u.s.y + a.x - b.x;
        v.s.x = (a.x + c.x) / 2;
        v.s.y = (a.y + c.y) / 2;
        v.e.x = v.s.x - a.y + c.y;
        v.e.y = v.s.y + a.x - c.x;
        return u.crossLPt(v);
    }

    //计算三角形内心
    //返回：内接圆圆心
    point incenter()
    {
        pVector u, v;
        double m, n;
        u.s = a;
        m = atan2(b.y - a.y, b.x - a.x);
        n = atan2(c.y - a.y, c.x - a.x);
        u.e.x = u.s.x + cos((m + n) / 2);
        u.e.y = u.s.y + sin((m + n) / 2);
        v.s = b;
        m = atan2(a.y - b.y, a.x - b.x);
        n = atan2(c.y - b.y, c.x - b.x);
        v.e.x = v.s.x + cos((m + n) / 2);
        v.e.y = v.s.y + sin((m + n) / 2);
        return u.crossLPt(v);
    }

    //计算三角形垂心
    //返回：高的交点
    point perpencenter()
    {
        pVector u,v;
        u.s = c;
        u.e.x = u.s.x - a.y + b.y;
        u.e.y = u.s.y + a.x - b.x;
        v.s = b;
        v.e.x = v.s.x - a.y + c.y;
        v.e.y = v.s.y + a.x - c.x;
        return u.crossLPt(v);
    }

    //计算三角形重心
    //返回：重心
    //到三角形三顶点距离的平方和最小的点
    //三角形内到三边距离之积最大的点
    point barycenter()
    {
        pVector u,v;
        u.s.x = (a.x + b.x) / 2;
        u.s.y = (a.y + b.y) / 2;
        u.e = c;
        v.s.x = (a.x + c.x) / 2;
        v.s.y = (a.y + c.y) / 2;
        v.e = b;
        return u.crossLPt(v);
    }

    //计算三角形费马点
    //返回：到三角形三顶点距离之和最小的点
    point fermentpoint()
    {
        point u, v;
        double step = fabs(a.x) + fabs(a.y) + fabs(b.x) + fabs(b.y) + fabs(c.x) + fabs(c.y);
        int i, j, k;
        u.x = (a.x + b.x + c.x) / 3;
        u.y = (a.y + b.y + c.y) / 3;
        while (step > eps)
        {
            for (k = 0; k < 10; step /= 2, k ++)
            {
                for (i = -1; i <= 1; i ++)
                {
                    for (j =- 1; j <= 1; j ++)
                    {
                        v.x = u.x + step * i;
                        v.y = u.y + step * j;
                        if (u.dis(a) + u.dis(b) + u.dis(c) > v.dis(a) + v.dis(b) + v.dis(c))
                            u = v;
                    }
                }
            }
        }
        return u;
    }
};

/**
 * 简易四则运算（栈实现）
 * #include <stack>
 * #include <cstring>
 */
std::stack<char> opr;
std::stack<double> num;
char oprPRI[256];
//初始化调用
void initCalc()
{
    //优先级设置
    char oprMap[7][2] = { {'+', 1}, {'-', 1}, {'*', 2}, {'/', 2}, {'^', 3}, {'(', 100}, {')', 0} };
    for(int i = 0; i < 7; i ++)
        oprPRI[oprMap[i][0]] = oprMap[i][1];
}
bool checkNum(char c)
{
    return c == '.' || (c >= '0' && c <= '9');
}
double calcOpr(double l, double r, char opr)
{
    switch(opr)
    {
        case '+': return l + r;
        case '-': return l - r;
        case '*': return l * r;
        case '/': return l / r;
        case '^': return ::pow(l, r);
    }
    return 0.0;
}
void calcStack()
{
    double cl, cr;
    cr = num.top();
    num.pop();
    cl = num.top();
    num.pop();
    num.push(::calcOpr(cl, cr, opr.top()));
    opr.pop();
}
double calc(const char str[])
{
    while(!opr.empty())
        opr.pop();
    while(!num.empty())
        num.pop();
    int i = 0, len = strlen(str);
    num.push(0.0);
    opr.push('(');
    while(i < len)
    {
        if(::checkNum(str[i]))
        {
            double l;
            ::sscanf(str + i, "%lf", &l);
            while(::checkNum(str[i]))
            i ++;
            num.push(l);
        }
        else
        {
            char c = str[i ++];
            if(c == ')')
            {
                while(opr.top() != '(')
                    calcStack();
                opr.pop();
            }
            else if(oprPRI[c] > oprPRI[opr.top()])
                opr.push(c);
            else
            {
                while(opr.top() != '(' && oprPRI[c] <= oprPRI[opr.top()])
                    calcStack();
                opr.push(c);
            }
        }
    }
    while(opr.size() > 1)
        calcStack();
    return num.top();
}

基础函数:

// 最大公约数,欧几里得定理
int gcd(int a, int b)
{
    return b?gcd(b, a % b): a;
}
// 拓展欧几里得定理
// 求解ax + by = gcd(a,b)
int ext_gcd(int a, int b, int &x, int &y)
{
    int tmp, ret;
    if(!b)
    {
        x = 1;
        y = 0;
        return a;
    }
    ret = ext_gcd(b, a % b, x, y);
    tmp = x;
    x = y;
    y = tmp - (a / b) * y;
    return ret;
}
//交换数值
void swap(int &a, int &b)
{
    a ^= b ^= a ^= b;
}

/**
 * a的b次方Mod c
 * 参数为整数
 * 使用时注意修改类型
 */
int PowerMod(int a, int b, int c)
{
    int tp = 1;
    while (b)
    {
        if (b & 1)
            tp = (tp * a) % c;
        a = (a * a) % c;
        b >>= 1;
    }
    return tp;
}

1.欧拉函数

Ψ（n） = 小于n且与n互质的数的个数

树状数组模块

ACM个人模板

POJ 2155 题目测试通过

/**
 * 树状数组模块
 * 下标从0开始
 */
typedef long DG_Ran;
typedef long DG_Num;
const DG_Num DG_MAXN = 1005;

//2^n
DG_Num LowBit(DG_Num n)
{
    return n & (-n);
}
//获取父节点索引
DG_Num DGFather(DG_Num n)
{
    return n + LowBit(n + 1);
}
//获取小的兄弟节点索引
DG_Num DGBrother(DG_Num n)
{
    return n - LowBit(n + 1);
}
//查找增加树状数组前pos项和
//参数(树状数组[in],索引[in],初始赋0即查找前n项和[out])
//复杂度:log(n)
void DGFind(DG_Ran *g,DG_Num pos,DG_Ran &sum)
{
    sum += *(g + pos);
    if(pos >= LowBit(pos + 1))
        DGFind(g, pos - LowBit(pos + 1), sum);
}
//查找对应线性数组元素
//参数(树状数组[in],索引[in]).
//返回值:对应线性数组元素log(n)
//复杂度:log(n)
DG_Ran DGFindEle(DG_Ran *g,DG_Num pos)
{
    DG_Ran a = 0 , b = 0;
    DGFind(g, pos, a);
    if(pos)
    {
        DGFind(g,pos - 1,b);
        return a - b;
    }
    else
        return a;
}
//树状数组,增加节点
//参数:树状数组[out],原数组大小[in],新增线性数组值[in]
//复杂度:log(n)
DG_Ran DGAdd(DG_Ran *g,DG_Num n,DG_Ran val)
{
    *(g + n) = val;
    DG_Num a = n;
    DG_Num b = 1;
    while((a & (~b)) != a)
    {
        *(g + n) += *(g + a - 1);
        a &= (~b);
        b <<= 1;
    }
    return n + 1;
}
//构建树状数组
//参数:线性数组[in],数组大小[in],树状数组[out]
//复杂度:nlog(n)
DG_Ran DGCreate(DG_Ran *g,DG_Num n,DG_Ran *tg)
{
    DG_Num i;
    *tg = *g;
    for(i = 1 ; i < n ; i ++)
        DGAdd(tg,i,*(g + i));
    return n;
}
//修改指定位置值
//参数:线性数组[in],数组位置[in],数组大小[in],新值[in]
//复杂度:log(n)
DG_Ran DGEdit(DG_Ran *g,DG_Num pos,DG_Num n,DG_Ran val)
{
    DG_Num f = DGFather(pos);
    DG_Ran o = *( g + pos );
    *( g + pos ) = val;
    if(f < n)
    {
        DG_Ran fv = val - o + *( g + f );
        DGEdit(g, f, n, fv);
    }
    return n;
}

//树状数组的翻转(树状数组的应用)
//一维  复杂度log(n)
//小于等于指定位置的元素的翻转<=pos
void DGDown1(DG_Ran g[],DG_Num pos,DG_Ran av)
{
    while(pos >= 0)
        g[pos] += av , pos = DGBrother(pos);
}
//获取位置pos的元素翻转次数
DG_Ran DGCUp1(DG_Ran g[],DG_Num pos , DG_Num n)
{
    DG_Ran t = 0;
    while(pos < n)
        t += g[pos] , pos = DGFather(pos);
    return t;
}
//二维  复杂度(log(n))^2
//小于等于指定位置的元素的翻转(0,0)->(x,y)
void DGDown2(DG_Ran g[][DG_MAXN],DG_Num x ,DG_Num y,DG_Ran av)
{
    while(x >= 0)
    {
        DG_Num tmp = y;
        while (tmp >= 0)
        {
            g[x][tmp] += av;
            tmp = DGBrother(tmp);
        }
        x = DGBrother(x);
    }
}
//获取位置(x,y)的元素翻转次数
DG_Ran DGCUp2(DG_Ran g[][DG_MAXN],DG_Num x ,DG_Num y , DG_Num n)
{
    DG_Ran t = 0;
    while(x < n)
    {
        DG_Num tmp = y;
        while (tmp < n)
        {
            t += g[x][tmp];
            tmp = DGFather(tmp);
        }
        x = DGFather(x);
    }
    return t;
}

/**
 * 线性筛法求素数表
 * 复杂度: O(n)
 */
const long MAXP = 1000000;
long prime[MAXP] = {0},num_prime = 0;
int isNotPrime[MAXP] = {1, 1};
void GetPrime_Init()//初始化调用
{
    for(long i = 2 ; i <  MAXP ; i ++)
    {
        if(! isNotPrime[i])
            prime[num_prime ++]=i;
        for(long j = 0 ; j < num_prime && i * prime[j] <  MAXP ; j ++)
        {
            isNotPrime[i * prime[j]] = 1;
            if( !(i % prime[j]))
                break;
        }
    }
}

线性筛法,即是筛选掉所有合数,留下质数

/**
 * Hash模板
 * Based: 0
 * template<unsigned long _SZ,class _T, unsigned long *pFun(_T _Off)>
 * class _My_Hash_ToInt
 * 传入数据大小_SZ,传入类型_T,Hash函数
 * 传入类型_T必须重载 = 和 == 符号
 * 收录了ELFHash函数
 * 主要是为了判重的简化些的模板
 * Hash算法性能比较见 http://www.cnblogs.com/lonelycatcher/archive/2011/08/23/2150587.html
 */

const long hashsize = 51071; //Hash表大小(注意修改)
// 各种Hash算法
unsigned int SDBMHash(char *str)
{
    unsigned int hash = hashsize;

    while (*str)
    {
        // equivalent to: hash = 65599*hash + (*str++);
        hash = (*str++) + (hash << 6) + (hash << 16) - hash;
    }

    return (hash & 0x7FFFFFFF);
}

// RS Hash Function
unsigned int RSHash(char *str)
{
    unsigned int b = 378551;
    unsigned int a = 63689;
    unsigned int hash = hashsize;

    while (*str)
    {
        hash = hash * a + (*str++);
        a *= b;
    }

    return (hash & 0x7FFFFFFF);
}

// JS Hash Function
unsigned int JSHash(char *str)
{
    unsigned int hash = 1315423911;

    while (*str)
    {
        hash ^= ((hash << 5) + (*str++) + (hash >> 2));
    }

    return (hash & 0x7FFFFFFF);
}

// P. J. Weinberger Hash Function
unsigned int PJWHash(char *str)
{
    unsigned int BitsInUnignedInt = (unsigned int)(sizeof(unsigned int) * 8);
    unsigned int ThreeQuarters    = (unsigned int)((BitsInUnignedInt  * 3) / 4);
    unsigned int OneEighth        = (unsigned int)(BitsInUnignedInt / 8);
    unsigned int HighBits         = (unsigned int)(0xFFFFFFFF) << (BitsInUnignedInt - OneEighth);
    unsigned int hash             = hashsize;
    unsigned int test             = 0;

    while (*str)
    {
        hash = (hash << OneEighth) + (*str++);
        if ((test = hash & HighBits) != 0)
        {
            hash = ((hash ^ (test >> ThreeQuarters)) & (~HighBits));
        }
    }

    return (hash & 0x7FFFFFFF);
}

// ELF Hash Function
unsigned int ELFHash(char *str)
{
    unsigned int hash = hashsize;
    unsigned int x    = 0;

    while (*str)
    {
        hash = (hash << 4) + (*str++);
        if ((x = hash & 0xF0000000L) != 0)
        {
            hash ^= (x >> 24);
            hash &= ~x;
        }
    }

    return (hash & 0x7FFFFFFF);
}

// BKDR Hash Function
unsigned int BKDRHash(char *str)
{
    unsigned int seed = 131; // 31 131 1313 13131 131313 etc..
    unsigned int hash = hashsize;

    while (*str)
    {
        hash = hash * seed + (*str++);
    }

    return (hash & 0x7FFFFFFF);
}

// DJB Hash Function
unsigned int DJBHash(char *str)
{
    unsigned int hash = 5381;

    while (*str)
    {
        hash += (hash << 5) + (*str++);
    }

    return (hash & 0x7FFFFFFF);
}

// AP Hash Function
unsigned int APHash(char *str)
{
    unsigned int hash = hashsize;
    int i;

    for (i=0; *str; i++)
    {
        if ((i & 1) == 0)
        {
            hash ^= ((hash << 7) ^ (*str++) ^ (hash >> 3));
        }
        else
        {
            hash ^= (~((hash << 11) ^ (*str++) ^ (hash >> 5)));
        }
    }

    return (hash & 0x7FFFFFFF);
}

// 程序模板
template<typename _T>
class _My_Hash_ToInt_Data
{
public:
    _My_Hash_ToInt_Data()
    {
        times = 0;
        next = -1;
    }
    _T data;
    long times;
    long next;
};
template<long _SZ,class _T, unsigned long pFun(_T& _Off)>
class _My_Hash_ToInt
{
public:
    _My_Hash_ToInt()
    {
        memset(hash, -1, sizeof(hash));
        length = 0;
    };
    ~_My_Hash_ToInt(){};
    long find(_T _Off)
    {
        long pos = hash[pFun(_Off)];
        while(pos >= 0)
        {
            if(data[pos].data == _Off)
                return pos;
            else
                pos = data[pos].next;
        }
        return -1;
    }
    long insert(_T _Off)
    {
        long oldPos = pFun(_Off);
        long pos = hash[oldPos];
        while(pos >= 0)
        {
            if(data[pos].data == _Off)
            {
                data[pos].times ++;
                return pos;
            }
            else
                pos = data[pos].next;
        }
        data[length].data = _Off;
        data[length].times = 1;
        data[length].next = hash[oldPos];
        hash[oldPos] = length ;
        return length ++;
    }
    void clear()
    {
        length = 0;
        memset(hash, -1, sizeof(hash));
        memset(data, -1, sizeof(data));
    }
    //Member
    long length;
    _My_Hash_ToInt_Data<_T> data[_SZ];
    long hash[hashsize];
};

//节点类（注意修改）
class node
{
public:
    char str[60];
    bool operator == (node &strin)
    {
        return !strcmp(str, strin.str);
    }
    node& operator = (node &strin)
    {
        strcpy(str, strin.str);
        return (*this);
    }
};
//扩展Hash函数（注意修改）
unsigned long ELFHashEx(node &strIn)
{
    return ELFHash(strIn.str);
}
_My_Hash_ToInt<10005, node, ELFHashEx>hash;//Hash类例子

//最长单调子序列 复杂度nlog(n)
//参数(原序列,序列长度,生成的序列),传入序列长度必须大于0
//返回值中lengthRecord中前k项表示长度为k的最小字序列
//LIScmp为关系函数,原函数表明lengthRecord为递增(不含等于)
typedef double LISTYPE;
#define LISMAXN 10000
int LIScmp(LISTYPE a,LISTYPE b)
{
    return a < b;
}
long LISLength(LISTYPE list[],long n,LISTYPE lengthRecord[])
{
    long length = 1,lth;
    LISTYPE lR[LISMAXN];
    lR[0] = list[0];

    for(int i = 1 ; i < n ; i ++)
    {
        //二分查找,复杂度 log(n)
        int b,e,m;
        b = 0;
        e = length - 1;
        while(b <= e && e >= 0)
        {
            m = (b + e) / 2;
            if(LIScmp(lR[m],list[i]))
                b = m + 1;
            else
                e = m - 1;
        }
        lR[b] = list[i];
        if(b >= length)
            length ++;
    }
    /*
    *计算序列部分
    *复杂度nlog(n)
    */
    lth = 1;
    for(int i = 1 ; i < n ; i ++)
    {
        //二分查找,复杂度 log(n)
        int b,e,m;
        b = 0;
        e = lth - 1;
        while(b <= e && e >= 0)
        {
            m = (b + e) / 2;
            if(LIScmp(lR[m],list[i]))
                b = m + 1;
            else
                e = m - 1;
        }
        lR[b] = list[i];
        if(b >= lth)
            lth ++;
        if(lth == length)
        {
            for(b = 0 ; b < length ; b ++)
                lengthRecord[b] = lR[b];
            break;
        }
    }
    //计算序列部分代码与之前的类似,可以直接Copy然后修改
    return length;
}

//Prime连通路模块
#define N 1000         //最大数据规模
#define MAXNUM 3000000   //最大路径长度
typedef double PrimeType;//路径类型

PrimeType PrimeRecord[N];
PrimeType dis[N][N];
int isLined[N] = {1,0};

PrimeType GetPrimeLength(const long n)
{
    PrimeType tmpLen = MAXNUM;
    long tmpPos = 0,left = n - 1;
    PrimeType sumLen = 0;

    for(long i = 1 ; i < n ; i ++)
        PrimeRecord[i] = dis[0][i];
    while(left --)
    {
        tmpLen = MAXNUM;
        for(long i = 1 ; i < n ; i ++)
            if(!isLined[i] && PrimeRecord[i] < tmpLen)
                tmpPos = i,tmpLen = PrimeRecord[i];

        sumLen += tmpLen;
        isLined[tmpPos] ++;
        for(long i = 1 ; i < n ; i ++)
            if(dis[tmpPos][i] < PrimeRecord[i])
                PrimeRecord[i] = dis[tmpPos][i];
    }

    return sumLen;
}

//MULDATATYPE为矩阵元素类型,MAXMAT为最大矩阵大小

typedef long MULDATATYPE;
#define MAXMAT 100
#define inf 1000000000

#define fabs(x) ((x)>0?(x):-(x))
#define zero(x) (fabs(x)<1e-10)

struct mat
{
    long n,m;
    MULDATATYPE data[MAXMAT][MAXMAT];
    void operator =(const mat& a);
    mat operator +(const mat& a);
    mat operator -(const mat& a);
    //0-1邻接矩阵
    mat operator &(const mat& a);
    mat operator |(const mat& a);
};

//c=a*b
//注意引用
int Mat_MulMode(mat& c,const mat& a,const mat& b,MULDATATYPE mod)
{
    long i,j,k;
    if (a.m != b.n)
        return 0;
    c.n = a.n , c.m = b.m;
    for (i = 0 ; i < c.n ; i ++)
        for (j = 0 ; j < c.m ; j ++)
            for (c.data[i][j] = k = 0 ; k  < a.m ; k ++)
                c.data[i][j] = (c.data[i][j] + a.data[i][k] * b.data[k][j]) % mod;
    return 1;
}
//c=a^b(其中必须满足b>0)
int Mat_PowMode(mat& c,mat a,long b,MULDATATYPE mod)
{
    c = a;
    b --;
    while(b)
    {
        mat tmp;
        if(b & 1)
        {
            tmp = c;
            Mat_MulMode(c,tmp,a,mod);
        }
        tmp = a;
        Mat_MulMode(a,tmp,tmp,mod);
        b = b>>1;
    }
    return 1;
}
//c=a+b
int Mat_AddMode(mat& c,const mat& a,const mat& b,MULDATATYPE mod)
{
    long i,j;
    if (a.n != b.n || a.m != b.m)
        return 0;
    c.n = a.n , c.m = b.m;
    for (i = 0 ; i < c.n ; i ++)
        for (j = 0 ; j < c.m ; j ++)
            c.data[i][j] = (a.data[i][j] + b.data[i][j]) % mod;
    return 1;
}
//c=a-b
int Mat_SubMode(mat& c,const mat& a,const mat& b,MULDATATYPE mod)
{
    long i,j;
    if (a.n != b.n || a.m != b.m)
        return 0;
    c.n = a.n , c.m = b.m;
    for (i = 0 ; i < c.n ; i ++)
        for (j = 0 ; j < c.m ; j ++)
            c.data[i][j] = (a.data[i][j] - b.data[i][j]) % mod;
    return 1;
}


void mat::operator =(const mat& a)
{
    n = a.n;
    m = a.m;
    for(int i = 0 ; i < n ; i ++)
        for(int j = 0 ; j < m ; j ++)
            data[i][j] = a.data[i][j];
}
mat mat::operator +(const mat &a)
{
    long i,j;
    mat tmpMat;
    tmpMat.m = m;
    tmpMat.n = n;
    for(i = 0 ; i < n ; i ++)
        for(j = 0 ; j < m ; j ++)
            tmpMat.data[i][j] = data[i][j] + a.data[i][j];
    return tmpMat;
}
mat mat::operator -(const mat &a)
{
    long i,j;
    mat tmpMat;
    tmpMat.m = m;
    tmpMat.n = n;
    for(i = 0 ; i < n ; i ++)
        for(j = 0 ; j < m ; j ++)
            tmpMat.data[i][j] = data[i][j] - a.data[i][j];
    return tmpMat;
}
mat mat::operator &(const mat &a)
{
    long i,j;
    mat tmpMat;
    tmpMat.m = m;
    tmpMat.n = n;
    for(i = 0 ; i < n ; i ++)
        for(j = 0 ; j < m ; j ++)
            tmpMat.data[i][j] = data[i][j] & a.data[i][j];
    return tmpMat;
}
mat mat::operator |(const mat &a)
{
    long i,j;
    mat tmpMat;
    tmpMat.m = m;
    tmpMat.n = n;
    for(i = 0 ; i < n ; i ++)
        for(j = 0 ; j < m ; j ++)
            tmpMat.data[i][j] = data[i][j] | a.data[i][j];
    return tmpMat;
}

点到直线距离

// (x0,y0)到(x1,y1)和(x2,y2)确定的直线的距离

double disBetweenPointAndLine(double x0,double y0,double x1,double y1,double x2,double y2)
{
    //化为ax+by+c=0的形式
    double a = y1-y2;
    double b = x2-x1;
    double c = x1*y2-x2*y1;
    double d = (a*x0+b*y0+c)/sqrt(a*a+b*b);
    /*
    如果是线段判断垂足

    double xp = (b*b*x0-a*b*y0-a*c)/(a*a+b*b);
    double yp = (-a*b*x0+a*a*y0-b*c)/(a*a+b*b);
    double xb = (x1>x2)?x1:x2;
    double yb = (y1>y2)?y1:y2;
    double xs = x1+x2-xb;
    double ys = y1+y2-yb;
    if(xp > xb || xp < xs || yp > yb || yp < ys)
    {
        d = sqrt((x0 - x1) * (x0 - x1) + (y0 - y1) * (y0 - y1));
        if(d > sqrt((x0 - x2) * (x0 - x2) + (y0 - y2) * (y0 - y2)))
            d = sqrt((x0 - x2) * (x0 - x2) + (y0 - y2) * (y0 - y2));
    }
    */
    return fabs(d);
}

线段间最短距离

//n每个用例的点个数
//MAXN为最大点个数
//PTYPE为坐标值类型
#include<iostream>
#include<cmath>
using namespace std;

#define MAXN 1005
#define EPS 1e-10
typedef double PTYPE;

struct point
{
    PTYPE x,y;
};
struct node
{
    PTYPE k;
};
int cmp(const void * a, const void * b)
{
    return((*(PTYPE*)a-*(PTYPE*)b>0)?1:-1);
}
node numK[MAXN * MAXN / 2];
point pt[MAXN];
int main()
{

    int n , maxNum = 1 , tmpNum = 0;
    while(scanf("%d",&n),n)
    {
        for(int i = 0 ; i < n ; i ++)
            scanf("%lf %lf",&pt[i].x,&pt[i].y);
        for(int i = 0 ; i <  n ; i ++)
        {
            int pos = 0;
            for(int j = i + 1 ; j < n ; j ++)
                if((pt[i].x - pt[j].x) > EPS)
                    numK[pos ++].k = (pt[j].y - pt[i].y) / (pt[j].x - pt[i].x);
                else
                    numK[pos ++].k = 100000;

            qsort(numK,pos,sizeof(numK[0]),cmp);
            int tmpNum = 2;
            for(int j = 1 ; j < pos ; j ++)
            {
                if(numK[j].k == numK[j - 1].k)
                    tmpNum ++;
                else
                {
                    if(tmpNum > maxNum)
                        maxNum = tmpNum;
                    tmpNum = 2;
                }
            }
            if(tmpNum > maxNum)
                maxNum = tmpNum;
        }


        printf("%d\n",maxNum);
        maxNum = 1;
    }
    return 0;
}

//并查集
//注意类型匹配
const int maxn = 100002;
int DSet[maxn];
void init(int n) {
    for(int i = 0 ; i <= n ; i ++)
        DSet[i] = i;
}
int findP(int id) {
if(DSet[id] != id)
    DSet[id] = findP(DSet[id]);
    return DSet[id];
}
//返回根节点ID
int UnionEle(int a,int b) {
    a = findP(a);
    b = findP(b);
    if(a > b)
        a ^= b ^= a ^= b;
    DSet[b] = a;
    return a;
}

/**
 * KMP模式匹配
 * 算法复杂度O(m+n)
 * ACM 模板 
 *
 * @Author OWenT
 * @link http://www.owent.net
 */

// 最大字符串长度
const int maxLen = 10000;
// 前一个匹配位置,多次匹配注意要重新初始化
// 注：preMatch[i]表示0~preMatch[i-1]能和?~i匹配
int preMatch[maxLen]={0};

/**
 * kmp匹配算法
 * @param char[] source 查找源
 * @param char[] checked 查找目标
 * @return int 根据以下两个分支返回值分别表示不同的含义
 */
int kmp_match(char source[],char checked[]) {
    int i = 0, j = 0;
    memset(preMatch, 0, sizeof(preMatch));

    if(!checked[i]) // 被匹配串为空串，直接返回 0
        return 0;

    ++ i;
    while(checked[i]) {
        for(j = preMatch[i - 1]; checked[i] != checked[j] && j; j = preMatch[j - 1]);
        preMatch[i] = (checked[i] == checked[j])? j + 1 : 0 ;
        ++ i;
    }
    //计算匹配子串个数(子串间无重叠)(与以下一起二选一)
    int num = 0;//计数变量
    for(i = j = 0; source[i]; ++ i) {
        if(checked[j] == source[i])
            ++ j;
        else if(j)
            -- i, j = preMatch[j - 1];

        if(!checked[j])
            ++ num, j = 0;//如果要子串间重叠 则此句中j = 0 改成 j = preMatch[j - 1]
    }
    return num;

    //计算首个匹配子串位置(与以上一起二选一)
    for(i = j = 0; checked[j] && source[i]; ++ i) {
        if(checked[j] == source[i])
            ++ j;
        else if(j)
            -- i, j = preMatch[j - 1];
    }

    //返回匹配的串的第一个字符出现位置(从1开始计数,0表示无匹配)
    if(!checked[j])
        return i - j + 1;
    else
        return 0;

    return 0;
}