2016年江西理工大学C语言程序设计竞赛（高级组）

问题 A: jxust

解法：争议的问题（是输入整行还是输入字符串），这里倾向输入字符串，然后判断是否含有jxust就行

#include<bits/stdc++.h>
using namespace std;
string s;
int num;
//jxust
int t;
class P
{
public:
    int cmd(string s)
    {
        num=;
        for(int i=; i<s.length()-; i++)
        {
            if(s[i]=='j'&&s[i+]=='x'&&s[i+]=='u'&&s[i+]=='s'&&s[i+]=='t')
            {
                num++;
            }
        }
        return num;
    }
};
int main()
{
    P sovle;
    cin>>t;
    while(t--)
    {
       num=;
       cin>>s;
       cout<<sovle.cmd(s)<<endl;
    }
    return ;
}

问题 B: 开房

解法：贪心，不过首先判断是不是可以花完，题目可以知道价格都是100的倍数，那么除以100判断就好

#include<bits/stdc++.h>
using namespace std;
string s;
int num;
int t;
class P
{
public:

};
int main()
{
    int t;
    int n;
    int sum=;
    cin>>t;
    while(t--)
    {
        sum=;
        cin>>n;
        if(n%)
        {
            cout<<"-1"<<endl;
            continue;
        }
        sum+=(n/);
        n%=;
        sum+=(n/);
        n%=;
        sum+=(n/);
        n%=;
        sum+=(n/);
        cout<<sum<<endl;
    }
    return ;
}

问题 C: 回文

解法：dp，i表示左边的位置，j表示右边的位置，转移方程s[i] == s[j]？dp[i][j] = dp[i+1][j-1]：dp[i][j] = min({dp[i+1][j-1]+2, dp[i+1][j]+1, dp[i][j-1]+1})

include<bits/stdc++.h>
using namespace std;
int dp[][];
int t;
string s;
class P
{
public:

};
int main()
{
    cin>>t;
    while(t--)
    {
        cin>>s;
        for(int i=s.length()-; i>=; i--)
        {
            for(int j=i+; j<s.length(); j++)
            {
                if(s[i] == s[j])
                {
                    dp[i][j] = dp[i+][j-];
                }
                else
                {
                    dp[i][j] = min({dp[i+][j-]+, dp[i+][j]+, dp[i][j-]+});
                }
            }
        }
        cout<<dp[][s.length()-]<<endl;
    }
    return ;
}

问题 D: 豆豆的字符串

解法：KMP

#include<bits/stdc++.h>
using namespace std;
char a[];
char a1[];
char s[];
int Next[];
char pos;

void cmd(int M)
{
    int i=,j=-;
    Next[i] = -;
    while(i<M)
    {
        if(j==-||s[i]==s[j])Next[++i] = ++j;
        else j=Next[j];
    }
}
int kmp(int pos,int n,int m)
{
    int i = pos, j = ,ans = ;
    while(i<n)
    {
        if(a1[i]==s[j]||j==-)i++,j++;
        else j=Next[j];
        if(j==m)
        {
            ans++;
            j=Next[j-];
            i--;
        }
    }
    return ans;
}
int main()
{
    int n,m;
    char x;
    int c=;
    int cot=;
    scanf("%s",a);
    for(int i=; i<strlen(a); i++)
    {
        if(a[i]>=''&&a[i]<='')
        {
            c=(a[i]-'')+c*;
            continue;
        }
        else
        {
            for(int j=; j<=c; j++)
            {
                a1[cot++]=a[i];
            }
            c=;
        }
    }
   // cout<<a1<<endl;
    scanf("%s",s);
    cmd(strlen(s));
    cout<<kmp(,strlen(a1),strlen(s))<<endl;
    return ;
}

问题 F: 兽兽大神

解法：先用几何模版算法符合要求的方框，再用并查集求个数

#include <bits/stdc++.h>
using namespace std;

struct Point
{
    double x, y;
    Point(double x = , double y = ) : x(x), y(y) {}
};

typedef Point Vector;

Vector operator + (Vector A, Vector B)
{
    return Vector(A.x + B.x, A.y + B.y);
}
Vector operator - (Vector A, Vector B)
{
    return Vector(A.x - B.x, A.y - B.y);
}
Vector operator * (Vector A, double p)
{
    return Vector(A.x*p, A.x*p);
}
Vector operator / (Vector A, double p)
{
    return Vector(A.x/p, A.x/p);
}

bool operator < (const Point& a, const Point b)
{
    return a.x < b.x || (a.x == b.x && a.y < b.y);
}

const double EPS = 1e-;

int dcmp(double x)
{
    if(fabs(x) < EPS) return ;
    else return x <  ? - : ;
}

bool operator == (const Point& a, const Point& b)
{
    return dcmp(a.x-b.x) ==  && dcmp(a.y-b.y);
}

//向量a的极角
double Angle(const Vector& v)
{
    return atan2(v.y, v.x);
}

//向量点积
double Dot(Vector A, Vector B)
{
    return A.x*B.x + A.y*B.y;
}

//向量长度\share\CodeBlocks\templates\wizard\console\cpp
double Length(Vector A)
{
    return sqrt(Dot(A, A));
}

//向量夹角
double Angle(Vector A, Vector B)
{
    return acos(Dot(A, B) / Length(A) / Length(B));
}

//向量叉积
double Cross(Vector A, Vector B)
{
    return A.x*B.y - A.y*B.x;
}

//三角形有向面积的二倍
double Area2(Point A, Point B, Point C)
{
    return Cross(B-A, C-A);
}

//向量逆时针旋转rad度(弧度)
Vector Rotate(Vector A, double rad)
{
    return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
}

//计算向量A的单位法向量。左转90°，把长度归一。调用前确保A不是零向量。
Vector Normal(Vector A)
{
    double L = Length(A);
    return Vector(-A.y/L, A.x/L);
}

/************************************************************************
使用复数类实现点及向量的简单操作

#include <complex>
typedef complex<double> Point;
typedef Point Vector;

double Dot(Vector A, Vector B) { return real(conj(A)*B)}
double Cross(Vector A, Vector B) { return imag(conj(A)*B);}
Vector Rotate(Vector A, double rad) { return A*exp(Point(0, rad)); }

*************************************************************************/

/****************************************************************************
* 用直线上的一点p0和方向向量v表示一条指向。直线上的所有点P满足P = P0+t*v;
* 如果知道直线上的两个点则方向向量为B-A, 所以参数方程为A+(B-A)*t;
* 当t 无限制时， 该参数方程表示直线。
* 当t > 0时， 该参数方程表示射线。
* 当 0 < t < 1时， 该参数方程表示线段。
*****************************************************************************/

//直线交点,须确保两直线有唯一交点。
Point GetLineIntersection(Point P, Vector v, Point Q, Vector w)
{
    Vector u = P - Q;
    double t = Cross(w, u)/Cross(v, w);
    return P+v*t;
}

//点到直线距离
double DistanceToLine(Point P, Point A, Point B)
{
    Vector v1 = B - A, v2 = P - A;
    return fabs(Cross(v1, v2) / Length(v1)); //不取绝对值，得到的是有向距离
}

//点到线段的距离
double DistanceToSegmentS(Point P, Point A, Point B)
{
    if(A == B) return Length(P-A);
    Vector v1 = B-A, v2 = P-A, v3 = P-B;
    if(dcmp(Dot(v1, v2)) < ) return Length(v2);
    else if(dcmp(Dot(v1, v3)) > ) return Length(v3);
    else return fabs(Cross(v1, v2)) / Length(v1);
}

//点在直线上的投影
Point GetLineProjection(Point P, Point A, Point B)
{
    Vector v = B - A;
    return A+v*(Dot(v, P-A)/Dot(v, v));
}

//线段相交判定，交点不在一条线段的端点
bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2)
{
    double c1 = Cross(a2-a1, b1-a1), c2 = Cross(a2-a1, b2-a1);
    double c3 = Cross(b2-b1, a1-b1), c4 = Cross(b2-b1, a2-b1);
    return dcmp(c1)*dcmp(c2) <  && dcmp(c3)*dcmp(c4) < ;
}

//判断点是否在点段上，不包含端点
bool OnSegment(Point P, Point a1, Point a2)
{
    return dcmp(Cross(a1-P, a2-P) ==  && dcmp((Dot(a1-P, a2-P)) < ));
}

//计算凸多边形面积
double ConvexPolygonArea(Point *p, int n)
{
    double area = ;
    for(int i = ; i < n-; i++)
        area += Cross(p[i] - p[], p[i+] - p[]);
    return area/;
}

//计算多边形的有向面积
double PolygonArea(Point *p, int n)
{
    double area = ;
    for(int i = ; i < n-; i++)
        area += Cross(p[i] - p[], p[i+] - p[]);
    return area/;
}

/***********************************************************************
* Morley定理：三角形每个内角的三等分线，相交成的三角形是等边三角形。
* 欧拉定理：设平面图的定点数，边数和面数分别为V,E,F。则V+F-E = 2;
************************************************************************/

struct Circle
{
    Point c;
    double r;

    Circle(Point c, double r) : c(c), r(r) {}
    //通过圆心角确定圆上坐标
    Point point(double a)
    {
        return Point(c.x + cos(a)*r, c.y + sin(a)*r);
    }
};

struct Line
{
    Point p;
    Vector v;
    double ang;
    Line() {}
    Line(Point p, Vector v) : p(p), v(v) {}
    bool operator < (const Line& L) const
    {
        return ang < L.ang;
    }
};

//直线和圆的交点，返回交点个数，结果存在sol中。
//该代码没有清空sol。
int getLineCircleIntersecion(Line L, Circle C, double& t1, double& t2, vector<Point>& sol)
{
    double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;
    double e = a*a + c*c, f = *(a*b + c*d), g = b*b + d*d - C.r*C.r;
    double delta = f*f - *e*g;
    if(dcmp(delta) < ) return ; //相离
    if(dcmp(delta) == )          //相切
    {
        t1 = t2 = -f / (*e);
        sol.push_back(C.point(t1));
        return ;
    }
    //相交
    t1 = (-f - sqrt(delta)) / (*e);
    sol.push_back(C.point(t1));
    t2 = (-f + sqrt(delta)) / (*e);
    sol.push_back(C.point(t2));
    return ;
}

//两圆相交
int getCircleCircleIntersection(Circle C1, Circle C2, vector<Point>& sol)
{
    double d = Length(C1.c - C2.c);
    if(dcmp(d) == )
    {
        if(dcmp(C1.r - C2.r == )) return -;    //两圆完全重合
        return ;                                //同心圆，半径不一样
    }
    if(dcmp(C1.r + C2.r - d) < ) return ;
    if(dcmp(fabs(C1.r - C2.r) == )) return -;

    double a = Angle(C2.c - C1.c);               //向量C1C2的极角
    double da = acos((C1.r*C1.r + d*d - C2.r*C2.r) / (*C1.r*d));
    //C1C2到C1P1的角
    Point p1 = C1.point(a-da), p2 = C1.point(a+da);
    sol.push_back(p1);
    if(p1 == p2) return ;
    sol.push_back(p2);
    return ;
}

const double PI = acos(-);
//过定点做圆的切线
//过点p做圆C的切线，返回切线个数。v[i]表示第i条切线
int getTangents(Point p, Circle C, Vector* v)
{
    Vector u = C.c - p;
    double dist = Length(u);
    if(dist < C.r) return ;
    else if(dcmp(dist - C.r) == )
    {
        v[] = Rotate(u, PI/);
        return ;
    }
    else
    {
        double ang = asin(C.r / dist);
        v[] = Rotate(u, -ang);
        v[] = Rotate(u, +ang);
        return ;
    }
}

//两圆的公切线
//返回切线的个数，-1表示有无数条公切线。
//a[i], b[i] 表示第i条切线在圆A，圆B上的切点
int getTangents(Circle A, Circle B, Point *a, Point *b)
{
    int cnt = ;
    if(A.r < B.r)
    {
        swap(A, B);
        swap(a, b);
    }
    int d2 = (A.c.x - B.c.x)*(A.c.x - B.c.x) + (A.c.y - B.c.y)*(A.c.y - B.c.y);
    int rdiff = A.r - B.r;
    int rsum = A.r + B.r;
    if(d2 < rdiff*rdiff) return ;   //内含
    double base = atan2(B.c.y - A.c.y, B.c.x - A.c.x);
    if(d2 ==  && A.r == B.r) return -;   //无限多条切线
    if(d2 == rdiff*rdiff)           //内切一条切线
    {
        a[cnt] = A.point(base);
        b[cnt] = B.point(base);
        cnt++;
        return ;
    }
    //有外共切线
    double ang = acos((A.r-B.r) / sqrt(d2));
    a[cnt] = A.point(base+ang);
    b[cnt] = B.point(base+ang);
    cnt++;
    a[cnt] = A.point(base-ang);
    b[cnt] = B.point(base-ang);
    cnt++;
    if(d2 == rsum*rsum)    //一条公切线
    {
        a[cnt] = A.point(base);
        b[cnt] = B.point(PI+base);
        cnt++;
    }
    else if(d2 > rsum*rsum)       //两条公切线
    {
        double ang = acos((A.r + B.r) / sqrt(d2));
        a[cnt] = A.point(base+ang);
        b[cnt] = B.point(PI+base+ang);
        cnt++;
        a[cnt] = A.point(base-ang);
        b[cnt] = B.point(PI+base-ang);
        cnt++;
    }
    return cnt;
}

typedef vector<Point> Polygon;

//点在多边形内的判定
int isPointInPolygon(Point p, Polygon poly)
{
    int wn = ;
    int n = poly.size();
    for(int i = ; i < n; i++)
    {
        if(OnSegment(p, poly[i], poly[(i+)%n])) return -; //在边界上
        int k = dcmp(Cross(poly[(i+)%n]-poly[i], p-poly[i]));
        int d1 = dcmp(poly[i].y - p.y);
        int d2 = dcmp(poly[(i+)%n].y - p.y);
        if(k >  && d1 <=  && d2 > ) wn++;
        if(k <  && d2 <=  && d1 > ) wn++;
    }
    if(wn != ) return ;       //内部
    return ;                   //外部
}

//凸包
/***************************************************************
* 输入点数组p， 个数为p， 输出点数组ch。 返回凸包顶点数
* 不希望凸包的边上有输入点，把两个<= 改成 <
* 高精度要求时建议用dcmp比较
* 输入点不能有重复点。函数执行完以后输入点的顺序被破坏
****************************************************************/
int ConvexHull(Point *p, int n, Point* ch)
{
    sort(p, p+n);      //先比较x坐标，再比较y坐标
    int m = ;
    for(int i = ; i < n; i++)
    {
        while(m >  && Cross(ch[m-] - ch[m-], p[i]-ch[m-]) <= ) m--;
        ch[m++] = p[i];
    }
    int k = m;
    for(int i = n-; i >= ; i++)
    {
        while(m > k && Cross(ch[m-] - ch[m-], p[i]-ch[m-]) <= ) m--;
        ch[m++] = p[i];
    }
    if(n > ) m--;
    return m;
}

//用有向直线A->B切割多边形poly， 返回“左侧”。 如果退化，可能会返回一个单点或者线段
//复杂度O(n2);
Polygon CutPolygon(Polygon poly, Point A, Point B)
{
    Polygon newpoly;
    int n = poly.size();
    for(int i = ; i < n; i++)
    {
        Point C = poly[i];
        Point D = poly[(i+)%n];
        if(dcmp(Cross(B-A, C-A)) >= ) newpoly.push_back(C);
        if(dcmp(Cross(B-A, C-D)) != )
        {
            Point ip = GetLineIntersection(A, B-A, C, D-C);
            if(OnSegment(ip, C, D)) newpoly.push_back(ip);
        }
    }
    return newpoly;
}

//半平面交

//点p再有向直线L的左边。（线上不算）
bool Onleft(Line L, Point p)
{
    return Cross(L.v, p-L.p) > ;
}

//两直线交点，假定交点唯一存在
Point GetIntersection(Line a, Line b)
{
    Vector u = a.p - b.p;
    double t = Cross(b.v, u) / Cross(a.v, b.v);
    return a.p+a.v*t;
}

int HalfplaneIntersection(Line* L, int n, Point* poly)
{
    sort(L, L+n);               //按极角排序

    int first, last;            //双端队列的第一个元素和最后一个元素
    Point *p = new Point[n];    //p[i]为q[i]和q[i+1]的交点
    Line *q = new Line[n];      //双端队列
    q[first = last = ] = L[]; //队列初始化为只有一个半平面L[0]
    for(int i = ; i < n; i++)
    {
        while(first < last && !Onleft(L[i], p[last-])) last--;
        while(first < last && !Onleft(L[i], p[first])) first++;
        q[++last] = L[i];
        if(fabs(Cross(q[last].v, q[last-].v)) < EPS)
        {
            last--;
            if(Onleft(q[last], L[i].p)) q[last] = L[i];
        }
        if(first < last) p[last-] = GetIntersection(q[last-], q[last]);
    }
    while(first < last && !Onleft(q[first], p[last-])) last--;
    //删除无用平面
    if(last-first <= ) return ;   //空集
    p[last] = GetIntersection(q[last], q[first]);

    //从deque复制到输出中
    int m = ;
    for(int i = first; i <= last; i++) poly[m++] = p[i];
    return m;
}
int fa[];
int Find(int x)
{
    if(x!=fa[x]) fa[x]=Find(fa[x]);
    return fa[x];
}
double ShortgetLen(Point a,Point b,Point c,Point d)
{
    double len = DistanceToSegmentS(a,c,d);
    len = min(len,DistanceToSegmentS(b,c,d));
    return len;
}
int n;
double m;
int x,y,w,h;
struct P
{
   Point A,B,C,D;
}He[];
bool cmd(int i,int j){
    double shortlen=1000000000.0;
    shortlen = min({shortlen,ShortgetLen(He[i].D,He[i].A,He[j].A,He[j].B),ShortgetLen(He[i].C,He[i].D,He[j].C,He[j].D),ShortgetLen(He[i].C,He[i].D,He[j].A,He[j].B),ShortgetLen(He[i].B,He[i].C,He[j].C,He[j].D),ShortgetLen(He[i].A,He[i].B,He[j].D,He[j].A),ShortgetLen(He[i].B,He[i].C,He[j].A,He[j].B),ShortgetLen(He[i].B,He[i].C,He[j].B,He[j].C)});
    shortlen = min({shortlen,ShortgetLen(He[i].C,He[i].D,He[j].D,He[j].A),ShortgetLen(He[i].C,He[i].D,He[j].B,He[j].C),ShortgetLen(He[i].B,He[i].C,He[j].D,He[j].A),ShortgetLen(He[i].A,He[i].B,He[j].A,He[j].B),ShortgetLen(He[i].A,He[i].B,He[j].B,He[j].C),ShortgetLen(He[i].A,He[i].B,He[j].C,He[j].D)});
    shortlen = min({shortlen,ShortgetLen(He[i].D,He[i].A,He[j].D,He[j].A),ShortgetLen(He[i].D,He[i].A,He[j].B,He[j].C),ShortgetLen(He[i].D,He[i].A,He[j].C,He[j].D)});
    if(m-shortlen>=0.00) return true;
    else return false;
}

void init()
{
    for(int i=; i<=n; i++) fa[i]=i;
}
map<int,int>p;
map<int,int>::iterator it;
int ans;
int main()
{
    p.clear();
    cin>>n>>m;
    init();
    for(int i=; i<=n; i++)
    {

        scanf("%d%d%d%d",&x,&y,&w,&h);
        He[i].A.x = x;
        He[i].A.y = y;
        He[i].B.x = x+w;
        He[i].B.y = y;
        He[i].C.x = x+w;
        He[i].C.y = y+h;
        He[i].D.x = x;
        He[i].D.y = y+h;
    }
    for(int i=; i<=n; i++)
    {
        for(int j=i+; j<=n; j++)
        {
            if(cmd(i,j))
            {
                int a=Find(i);
                int b=Find(j);
                if(a!=b) fa[a]=b;
            }
        }
    }
    for(int i=; i<=n; i++)
    {
        fa[i]=Find(fa[i]);
    }
    for(int i=; i<=n; i++)
    {
        p[fa[i]]++;
    }
    for(it=p.begin();it!=p.end();it++)
    {
         ans++;
    }
    cout<<ans<<endl;
    return ;
}