uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1058

　　半平面交求面积最值。直接枚举C(20,8)的所有情况即可。

代码如下：

 #include <cstdio>

 #include <cstring>

 #include <iostream>

 #include <algorithm>

 #include <cmath>

 #include <vector>

 using namespace std;

 const int N = ;

 struct Point {

     double x, y;

     Point() {}

     Point(double x, double y) : x(x), y(y) {}

 } pt[N], poly[N];

 template<class T> T sqr(T x) { return x * x;}

 typedef Point Vec;

 Vec operator + (Vec a, Vec b) { return Vec(a.x + b.x, a.y + b.y);}

 Vec operator - (Vec a, Vec b) { return Vec(a.x - b.x, a.y - b.y);}

 Vec operator * (Vec a, double p) { return Vec(a.x * p, a.y * p);}

 Vec operator / (Vec a, double p) { return Vec(a.x / p, a.y / p);}

 const double EPS = 1e-;

 inline int sgn(double x) { return (x > EPS) - (x < -EPS);}

 inline double dotDet(Vec a, Vec b) { return a.x * b.x + a.y * b.y;}

 inline double crossDet(Vec a, Vec b) { return a.x * b.y - a.y * b.x;}

 inline double dotDet(Point o, Point a, Point b) { return dotDet(a - o, b - o);}

 inline double crossDet(Point o, Point a, Point b) { return crossDet(a - o, b - o);}

 inline double vecLen(Vec x) { return sqrt(dotDet(x, x));}

 inline Vec normal(Vec x) { return Vec(-x.y, x.x) / vecLen(x);}

 struct DLine {

     Point p;

     Vec v;

     double ang;

     DLine() {}

     DLine(Point p, Vec v) : p(p), v(v) { ang = atan2(v.y, v.x);}

     bool operator < (const DLine &L) const { return ang < L.ang;}

     DLine move(double x) { return DLine(p + normal(v) * x, v);}

 } dl[N];

 inline bool onLeft(DLine L, Point p) { return crossDet(L.v, p - L.p) > ;}

 inline Point dLineIntersect(DLine a, DLine b) { return a.p + a.v * (crossDet(b.v, a.p - b.p) / crossDet(a.v, b.v));}

 struct Poly {

     vector<Point> pt;

     Poly() { pt.clear();}

     ~Poly() {}

     Poly(vector<Point> &pt) : pt(pt) {}

     Point operator [] (int x) const { return pt[x];}

     int size() { return pt.size();}

     double area() {

         if (pt.size() < ) return 0.0;

         double ret = 0.0;

         for (int i = , sz = pt.size(); i < sz; i++)

             ret += crossDet(pt[i], pt[(i + ) % sz]);

         return fabs(ret / 2.0);

     }

 } ;

 Point p[N];

 DLine q[N];

 int halfPlane(DLine *L, int n) {

     sort(L, L + n);

     int fi, la;

     q[fi = la = ] = L[];

     for (int i = ; i < n; i++) {

         while (fi < la && !onLeft(L[i], p[la - ])) la--;

         while (fi < la && !onLeft(L[i], p[fi])) fi++;

         q[++la] = L[i];

         if (fabs(crossDet(q[la].v, q[la - ].v)) < EPS) {

             la--;

             if (onLeft(q[la], L[i].p)) q[la] = L[i];

         }

         if (fi < la) p[la - ] = dLineIntersect(q[la - ], q[la]);

     }

     while (fi < la && !onLeft(q[fi], p[la - ])) la--;

     if (la < fi) return ;

     p[la] = dLineIntersect(q[la], q[fi]);

     int ret = ;

     for (int i = fi; i <= la; i++) poly[ret++] = p[i];

     return ret;

 }

 //Poly halfPlane(DLine *L, int n) {

 //    Poly ret = Poly();

 //    sort(L, L + n);

 //    int fi, la;

 //    Point *p = new Point[n];

 //    DLine *q = new DLine[n];

 //    q[fi = la = 0] = L[0];

 //    for (int i = 1; i < n; i++) {

 //        while (fi < la && !onLeft(L[i], p[la - 1])) la--;

 //        while (fi < la && !onLeft(L[i], p[fi])) fi++;

 //        q[++la] = L[i];

 //        if (fabs(crossDet(q[la].v, q[la - 1].v)) < EPS) {

 //            la--;

 //            if (onLeft(q[la], L[i].p)) q[la] = L[i];

 //        }

 //        if (fi < la) p[la - 1] = dLineIntersect(q[la - 1], q[la]);

 //    }

 //    while (fi < la && !onLeft(q[fi], p[la - 1])) la--;

 //    if (la < fi) return ret;

 //    p[la] = dLineIntersect(q[la], q[fi]);

 //    for (int i = fi; i <= la; i++) ret.pt.push_back(p[i]);

 //    return ret;

 //}

 double polyArea(Point *p, int n) {

     if (n < ) return 0.0;

     double sum = 0.0;

     p[n] = p[];

     Point O = Point(0.0, 0.0);

     for (int i = ; i < n; i++) sum += crossDet(O, p[i], p[i + ]);

     return fabs(sum / 2.0);

 }

 double work(int st, int n, double d) {

 //    cout << st << endl;

     for (int i = ; i < n; i++) dl[i] = DLine(pt[i], pt[i + ] - pt[i]).move((st & ( << i)) ==  ? 0.0 : d);

     int tmp = halfPlane(dl, n);

     return polyArea(poly, tmp);

 //    Poly tmp = halfPlane(dl, n);

 //    return tmp.area();

 }

 int cntBit(int x) {

     int cnt = ;

     while (x > ) {

         if (x & ) cnt++;

         x >>= ;

     }

     return cnt;

 }

 int main() {

 //    freopen("in", "r", stdin);

     int n, k;

     double d;

     while (~scanf("%d%d%lf", &n, &k, &d) && (n + k + d > EPS)) {

         for (int i = ; i < n; i++) scanf("%lf%lf", &pt[i].x, &pt[i].y);

         pt[n] = pt[];

         double ans = 0.0, area = polyArea(pt, n);

         for (int i = , end =  << n; i < end; i++) {

             if (cntBit(i) <= k) {

 //                cout << i << endl;

                 ans = max(ans, area - work(i, n, d));

             }

             if (sgn(ans - area) == ) break;

         }

         printf("%.2f\n", ans);

     }

     return ;

 }

能通过POJ的代码：

 #include <cstdio>

 #include <cstring>

 #include <iostream>

 #include <algorithm>

 #include <cmath>

 #include <vector>

 using namespace std;

 const int N = ;

 struct Point {

     double x, y;

     Point() {}

     Point(double x, double y) : x(x), y(y) {}

 } pt[N], poly[N];

 template<class T> T sqr(T x) { return x * x;}

 typedef Point Vec;

 Vec operator + (Vec a, Vec b) { return Vec(a.x + b.x, a.y + b.y);}

 Vec operator - (Vec a, Vec b) { return Vec(a.x - b.x, a.y - b.y);}

 Vec operator * (Vec a, double p) { return Vec(a.x * p, a.y * p);}

 Vec operator / (Vec a, double p) { return Vec(a.x / p, a.y / p);}

 const double EPS = 1e-;

 inline int sgn(double x) { return (x > EPS) - (x < -EPS);}

 inline double dotDet(Vec a, Vec b) { return a.x * b.x + a.y * b.y;}

 inline double crossDet(Vec a, Vec b) { return a.x * b.y - a.y * b.x;}

 inline double dotDet(Point o, Point a, Point b) { return dotDet(a - o, b - o);}

 inline double crossDet(Point o, Point a, Point b) { return crossDet(a - o, b - o);}

 inline double vecLen(Vec x) { return sqrt(dotDet(x, x));}

 inline Vec normal(Vec x) { return Vec(-x.y, x.x) / vecLen(x);}

 struct DLine {

     Point p;

     Vec v;

     double ang;

     DLine() {}

     DLine(Point p, Vec v) : p(p), v(v) { ang = atan2(v.y, v.x);}

     bool operator < (const DLine &L) const { return ang < L.ang;}

     DLine move(double x) { return DLine(p + normal(v) * x, v);}

 } dl[N];

 inline bool onLeft(DLine L, Point p) { return crossDet(L.v, p - L.p) > ;}

 inline Point dLineIntersect(DLine a, DLine b) { return a.p + a.v * (crossDet(b.v, a.p - b.p) / crossDet(a.v, b.v));}

 struct Poly {

     vector<Point> pt;

     Poly() { pt.clear();}

     ~Poly() {}

     Poly(vector<Point> &pt) : pt(pt) {}

     Point operator [] (int x) const { return pt[x];}

     int size() { return pt.size();}

     double area() {

         if (pt.size() < ) return 0.0;

         double ret = 0.0;

         for (int i = , sz = pt.size(); i < sz; i++)

             ret += crossDet(pt[i], pt[(i + ) % sz]);

         return fabs(ret / 2.0);

     }

 } ;

 Point p[N];

 DLine q[N], tmpDL[N];

 int halfPlane(DLine *L, int n) {

     for (int i = ; i < n; i++) tmpDL[i] = L[i];

     sort(L, L + n);

     int fi, la;

     q[fi = la = ] = L[];

     for (int i = ; i < n; i++) {

         while (fi < la && !onLeft(L[i], p[la - ])) la--;

         while (fi < la && !onLeft(L[i], p[fi])) fi++;

         q[++la] = L[i];

         if (fabs(crossDet(q[la].v, q[la - ].v)) < EPS) {

             la--;

             if (onLeft(q[la], L[i].p)) q[la] = L[i];

         }

         if (fi < la) p[la - ] = dLineIntersect(q[la - ], q[la]);

     }

     for (int i = ; i < n; i++) L[i] = tmpDL[i];

     while (fi < la && !onLeft(q[fi], p[la - ])) la--;

     if (la < fi) return ;

     p[la] = dLineIntersect(q[la], q[fi]);

     int ret = ;

     for (int i = fi; i <= la; i++) poly[ret++] = p[i];

     return ret;

 }

 double polyArea(Point *p, int n) {

     if (n < ) return 0.0;

     double sum = 0.0;

     p[n] = p[];

     Point O = Point(0.0, 0.0);

     for (int i = ; i < n; i++) sum += crossDet(O, p[i], p[i + ]);

     return fabs(sum / 2.0);

 }

 double work(int st, int n, double d) {

 //    cout << st << endl;

     for (int i = ; i < n; i++) dl[i] = DLine(pt[i], pt[i + ] - pt[i]).move((st & ( << i)) ==  ? 0.0 : d);

     int tmp = halfPlane(dl, n);

     return polyArea(poly, tmp);

 //    Poly tmp = halfPlane(dl, n);

 //    return tmp.area();

 }

 int cntBit(int x) {

     int cnt = ;

     while (x > ) {

         if (x & ) cnt++;

         x >>= ;

     }

     return cnt;

 }

 const double FINF = 1e100;

 double ans, d;

 void dfs(int id, int tt, int used, int k) {

     if (id >= tt) {

         int tmp = halfPlane(dl, tt);

         ans = min(ans, polyArea(poly, tmp));

         return ;

     }

     dl[id] = DLine(pt[id], pt[id + ] - pt[id]);

     dfs(id + , tt, used, k);

     if (used >= k) return ;

     dl[id] = DLine(pt[id], pt[id + ] - pt[id]).move(d);

     dfs(id + , tt, used + , k);

 }

 int main() {

 //    freopen("in", "r", stdin);

     int n, k;

     while (~scanf("%d%d%lf", &n, &k, &d) && (n + k + d > EPS)) {

         for (int i = ; i < n; i++) scanf("%lf%lf", &pt[i].x, &pt[i].y);

         pt[n] = pt[];

         double area = polyArea(pt, n);

         ans = FINF;

         dfs(, n, , k);

         printf("%.2f\n", area - ans);

     }

     return ;

 }

——written by Lyon

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