SRM 547

Brief description:

Problem 250. Pillars
。。要在兩面牆之間架一個梯子,兩面牆高度皆為整數,均勻選自 [1, A] 和 [1, B] 之間。
。中間距離為 w,問梯子期望的長度。
(。。1 ≤ A, B ≤ 100, 000 。。。)

Problem 500. RectangularSum
給定一個逐行逐列依次填 {0, 1, 2, 3, 4, … nm-1} 的 n × m 矩陣。。
。。。問所有和等於 S 的子矩陣中,面積最小的是多少。
(。。1 ≤ n, m ≤ 100, 000 。。。1 ≤ S ≤ 100, 000, 000, 000。。。)

Problem 1000. MaximalTriangle
問正 n 邊形的三角剖分中,有多少種剖分是可以產生一個面積最大的大三角形的。
(。。3 ≤ n ≤ 444 。。。)

Analysis:

Problem 250. Pillars
分組計數,枚舉高度差。

Problem 500. RectangularSum
。。這題的難點主要在 O(1) 時間內實現一個名為 bool check(x, y); 的函數; 來判斷長寬為 x, y ,和為 S 的子矩陣是否存在。。
這個先把整個子矩陣移動到最上角。。然後通過判斷位移是否合法就行了。。
。。。然後外圍用一個堆。。維護一堆下標。。這樣貌似複雜度是 O(n^2logn)。。然後隨便加了點剪枝就過掉了。。

Problem 1000. MaximalTriangle
。。沒什麼好的想法。。基本思想只能是先離散化三角形面積。然後枚舉中間的大三角形。。然後產生三個方向的遞歸?。。
。。f(i, s) 表示一個 i 個定點的子區域中,所有不包含面積大於等於 s 的三角形的剖分數。。。。。。
貌似總的複雜度 O(n4) 。。(共 O(n3) 種狀態。。轉移。O(n)。。。。
(不過好像大家都是這樣過的。。就是加常數優化。。 /$:o~o

DB sqr(DB x){
    return x * x;
}

class Pillars {
public:
	double getExpectedLength(int w, int x, int y) {

        DB q = min(x, y), p = w * q, pp, qq;
        
        REP_1_C(i, max(x, y)){
            qq = min(x, max(0, y - i)), pp = sqrt(sqr(w) +  sqr(i)) * qq;
            p += pp, q += qq;
            qq = min(max(0, x - i), y), pp = sqrt(sqr(w) +  sqr(i)) * qq;
            p += pp, q += qq;
        }
        
        return p / q;
	}
};
LL w, h, S; bool flag;

bool check(LL x, LL y){

    flag = false;
    LL A = x * y, B = A * (y - 1), C = x*(x-1) * (y*w);
    LL S = ::S - B - C; if (S < 0) return false; flag = true;
    LL d = S / (A*2); if (d * (A*2) != S) return false;
    LL up = (h - x + 1) * w;
    return d < up && d % w <= w - y;
}

class RectangularSum {
public:
	long long minimalArea(LL h, LL w, LL S) {
	    ::h = h, ::w = w, ::S = S, ::S <<= 1;

		priority_queue<PLI, vector<PLI>, greater<PLI> > Q;
		REP_1(i, h) Q.push(MP((LL)i, i));

#define s first
#define x second

		while (!Q.empty()){
		    PLI cur = Q.top(); LL y = cur.s / cur.x; Q.pop();
		    if (check(cur.x, y)) return cur.s;
		    if (y < w && flag) Q.push(MP(cur.s + cur.x, cur.x));
		}

		return -1;
	}
};
#define LOCAL

/** ` Micro Mezzo Macro Flation -- Overheated Economy ., **/

#include <algorithm>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <cstring>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>

using namespace std;

#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_C(i, n) for (int n____=int(n),i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=int(b),i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=int(a),i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_C(i, n) for (int n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=int(a),i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)
#define REP_C_N(i, n) for (n____=int(n),i=0;i<n____;++i)
#define FOR_C_N(i, a, b) for (b____=int(b),i=a;i<b____;++i)
#define DWN_C_N(i, b, a) for (a____=int(a),i=b-1;i>=a____;--i)
#define REP_1_C_N(i, n) for (n____=int(n),i=1;i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (b____=int(b),i=a;i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (a____=int(a),i=b;i>=a____;--i)

#define ECH(it, A) for (typeof(A.begin()) it=A.begin(); it != A.end(); ++it)
#define DO(n) while(n--)
#define DO_C(n) int n____ = n; while(n____--)
#define TO(i, a, b) int s_=a<b?1:-1,b_=b+s_;for(int i=a;i!=b_;i+=s_)
#define TO_1(i, a, b) int s_=a<b?1:-1,b_=b;for(int i=a;i!=b_;i+=s_)
#define SQZ(i, j, a, b) for (int i=int(a),j=int(b)-1;i<j;++i,--j)
#define SQZ_1(i, j, a, b) for (int i=int(a),j=int(b);i<=j;++i,--j)
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)

#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define BSC(A, X) find(ALL(A), X) // != A.end()
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int(A.size())
#define PB push_back
#define MP(A, B) make_pair(A, B)

#define Rush int T____; RD(T____); DO(T____)
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define Ruby system("ruby main.rb")
#define Haskell system("runghc main.hs")
#define Pascal system("fpc main.pas")

typedef long long LL;
typedef double DB;
typedef unsigned UINT;
typedef unsigned long long ULL;

typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VD;
typedef set<int> SI;
typedef set<string> SS;
typedef set<LL> SL;
typedef set<DB> SD;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef map<LL, int> MLI;
typedef map<DB, int> MDI;
typedef map<int, bool> MIB;
typedef map<string, bool> MSB;
typedef map<LL, bool> MLB;
typedef map<DB, bool> MDB;
typedef pair<int, int> PII;
typedef pair<int, bool> PIB;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
typedef set<PII> SII;
typedef map<PII, int> MPIII;
typedef map<PII, bool> MPIIB;

/** I/O Accelerator **/

/* ... :" We are I/O Accelerator ... Use us at your own risk ;) ... " .. */

template<class T> inline void RD(T &);
template<class T> inline void OT(const T &);

inline int RD(){ int x; RD(x); return x;}
template<class T> inline T& _RD(T &x){ RD(x); return x;}
inline void RC(char &c){scanf(" %c", &c);}
inline void RS(char *s){scanf("%s", s);}

template<class T0, class T1> inline void RD(T0 &x0, T1 &x1){RD(x0), RD(x1);}
template<class T0, class T1, class T2> inline void RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2);}
template<class T0, class T1, class T2, class T3> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);}
template<class T0, class T1> inline void OT(T0 &x0, T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(T0 &x0, T1 &x1, T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}

template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}


template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){
    while (!Q.empty()) Q.pop();
}

template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){
    while (!Q.empty()) Q.pop();
}

template<class T> inline void CLR(T &A){A.clear();}
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2){FLC(A0), FLC(A1), FLC(A2);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3){FLC(A0), FLC(A1), FLC(A2), FLC(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5), FLC(A6);}

template<class T> inline void SRT(T &A){sort(ALL(A));}
template<class T, class C> inline void SRT(T &A, C B){sort(ALL(A), B);}

/** Add - On **/

int MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const LL INF_64 = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-11;
const DB OO = 1e15;
const DB PI = 3.14159265358979323846264; //M_PI;

// <<= ` 0. Daily Use .,

template<class T> inline void checkMin(T &a,const T b){if (b<a) a=b;}
template<class T> inline void checkMax(T &a,const T b){if (b>a) a=b;}
template <class T, class C> inline void checkMin(T& a, const T b, C c){if (c(b,a)) a = b;}
template <class T, class C> inline void checkMax(T& a, const T b, C c){if (c(a,b)) a = b;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(min(a, b), max(c, d));}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
int Ceil(int x, int y){return (x - 1) / y + 1;}

// <<= ` 1. Bitwise Operation .,
inline bool _1(int x, int i){return x & 1<<i;}
inline bool _1(LL x, int i){return x & 1LL<<i;}
inline LL _1(int i){return 1LL<<i;}
//inline int _1(int i){return 1<<i;}
inline LL _U(int i){return _1(i) - 1;};
//inline int _U(int i){return _1(i) - 1;};


template<class T> inline T low_bit(T x) {
    return x & -x;
}

template<class T> inline T high_bit(T x) {
    T p = low_bit(x);
    while (p != x) x -= p, p = low_bit(x);
    return p;
}

inline int count_bits(int x){
    x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);
    x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);
    x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);
    x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);
    x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);
    return x;
}

inline int count_bits(LL x){
    x = (x & 0x5555555555555555LL) + ((x & 0xaaaaaaaaaaaaaaaaLL) >> 1);
    x = (x & 0x3333333333333333LL) + ((x & 0xccccccccccccccccLL) >> 2);
    x = (x & 0x0f0f0f0f0f0f0f0fLL) + ((x & 0xf0f0f0f0f0f0f0f0LL) >> 4);
    x = (x & 0x00ff00ff00ff00ffLL) + ((x & 0xff00ff00ff00ff00LL) >> 8);
    x = (x & 0x0000ffff0000ffffLL) + ((x & 0xffff0000ffff0000LL) >> 16);
    x = (x & 0x00000000ffffffffLL) + ((x & 0xffffffff00000000LL) >> 32);
    return x;
}

int reverse_bits(int x){
    x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
    x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
    x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
    x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
    x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
    return x;
}

LL reverse_bits(LL x){
    x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
    x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
    x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
    x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
    x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
    x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
    return x;
}

// <<= ` 2. Modular Arithmetic Basic .,

inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a  += MOD; return a;}
inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
inline int pdt(int a, int b){return (LL)a * b % MOD;}
inline int pdt(int a, int b, int c){return pdt(pdt(a, b), c);}
inline int sqr_M(int a){return pdt(a, a);}

inline int pow(int a, int b){
    int c = 1;
    while (b) {
        if (b&1) MUL(c, a);
        MUL(a, a), b >>= 1;
    }
    return c;
}

template<class T>
inline int pow(T a, int b){
    T c(1);
    while (b) {
        if (b&1) MUL(c, a);
        MUL(a, a), b >>= 1;
    }
    return c;
}

inline int _I(int b){
    int a = MOD, x1 = 0, x2 = 1, q;
    while (true){
        q = a / b, a %= b;
        if (!a) return (x2 + MOD) % MOD;
        DEC(x1, pdt(q, x2));

        q = b / a, b %= a;
        if (!b) return (x1 + MOD) % MOD;
        DEC(x2, pdt(q, x1));
    }
}

inline void DIV(int &a, int b){MUL(a, _I(b));}
inline int qtt(int a, int b){return pdt(a, _I(b));}

inline int sum(int a, int b, int MOD){
    a += b; if (a >= MOD) a -= MOD;
    return a;
}

inline int phi(int n){
    int res = n;
    for (int i=2;sqr(i)<=n;++i) if (!(n%i)){
        DEC(res, qtt(res, i));
        do{n /= i;} while(!(n%i));
    }
    if (n != 1)
        DEC(res, qtt(res, n));
    return res;
}

// <<= '9. Comutational Geometry .,

struct Po; struct Line; struct Seg;

inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
inline bool equ(DB x, DB y){return !sgn(x, y);}

struct Po{
    DB x, y;
    Po(DB _x = 0, DB _y = 0):x(_x), y(_y){}

    friend istream& operator >>(istream& in, Po &p){return in >> p.x >> p.y;}
    friend ostream& operator <<(ostream& out, Po p){return out << "(" << p.x << ", " << p.y << ")";}

    friend bool operator ==(Po, Po);
    friend bool operator !=(Po, Po);
    friend Po operator +(Po, Po);
    friend Po operator -(Po, Po);
    friend Po operator *(Po, DB);
    friend Po operator /(Po, DB);

    bool operator < (const Po &rhs) const{return sgn(x, rhs.x) < 0 || sgn(x, rhs.x) == 0 && sgn(y, rhs.y) < 0;}
    Po operator-() const{return Po(-x, -y);}
    Po& operator +=(Po rhs){x += rhs.x, y += rhs.y; return *this;}
    Po& operator -=(Po rhs){x -= rhs.x, y -= rhs.y; return *this;}
    Po& operator *=(DB k){x *= k, y *= k; return *this;}
    Po& operator /=(DB k){x /= k, y /= k; return *this;}

    DB length_sqr(){return sqr(x) + sqr(y);}
    DB length(){return sqrt(length_sqr());}

    DB atan(){
        return atan2(y, x);
    }

    void input(){
        scanf("%lf %lf", &x, &y);
    }
};

bool operator ==(Po a, Po b){return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;}
bool operator !=(Po a, Po b){return sgn(a.x - b.x) != 0 || sgn(a.y - b.y) != 0;}
Po operator +(Po a, Po b){return Po(a.x + b.x, a.y + b.y);}
Po operator -(Po a, Po b){return Po(a.x - b.x, a.y - b.y);}
Po operator *(Po a, DB k){return Po(a.x * k, a.y * k);}
Po operator *(DB k, Po a){return a * k;}
Po operator /(Po a, DB k){return Po(a.x / k, a.y / k);}

struct Line{
    Po a, b;
    Line(Po _a = Po(), Po _b = Po()):a(_a), b(_b){}
    Line(DB x0, DB y0, DB x1, DB y1):a(Po(x0, y0)), b(Po(x1, y1)){}
    Line(Seg);

    friend ostream& operator <<(ostream& out, Line p){return out << p.a << "-" << p.b;}
};

struct Seg{
    Po a, b;
    Seg(Po _a = Po(), Po _b = Po()):a(_a), b(_b){}
    Seg(DB x0, DB y0, DB x1, DB y1):a(Po(x0, y0)), b(Po(x1, y1)){}
    Seg(Line l);

    friend ostream& operator <<(ostream& out, Seg p){return out << p.a << "-" << p.b;}
    DB length(){return (b - a).length();}
};

Line::Line(Seg l):a(l.a), b(l.b){}
Seg::Seg(Line l):a(l.a), b(l.b){}

#define innerProduct dot
#define scalarProduct dot
#define dotProduct dot
#define outerProduct det
#define crossProduct det

inline DB dot(DB x1, DB y1, DB x2, DB y2){return x1 * x2 + y1 * y2;}
inline DB dot(Po a, Po b){return dot(a.x, a.y, b.x, b.y);}
inline DB dot(Po p0, Po p1, Po p2){return dot(p1 - p0, p2 - p0);}
inline DB dot(Line l1, Line l2){return dot(l1.b - l1.a, l2.b - l2.a);}
inline DB det(DB x1, DB y1, DB x2, DB y2){return x1 * y2 - x2 * y1;}
inline DB det(Po a, Po b){return det(a.x, a.y, b.x, b.y);}
inline DB det(Po p0, Po p1, Po p2){return det(p1 - p0, p2 - p0);}
inline DB det(Line l1, Line l2){return det(l1.b - l1.a, l2.b - l2.a);}

template<class T1, class T2> inline DB dist(T1 x, T2 y){return sqrt(dist_sqr(x, y));}

inline DB dist_sqr(Po a, Po b){return sqr(a.x - b.x) + sqr(a.y - b.y);}
inline DB dist_sqr(Po p, Line l){Po v0 = l.b - l.a, v1 = p - l.a; return sqr(fabs(det(v0, v1))) / v0.length_sqr();}
inline DB dist_sqr(Po p, Seg l){
    Po v0 = l.b - l.a, v1 = p - l.a, v2 = p - l.b;
    if (sgn(dot(v0, v1)) * sgn(dot(v0, v2)) <= 0) return dist_sqr(p, Line(l));
    else return min(v1.length_sqr(), v2.length_sqr());
}

inline DB dist_sqr(Line l, Po p){return dist_sqr(p, l);}
inline DB dist_sqr(Seg l, Po p){return dist_sqr(p, l);}

inline DB dist_sqr(Line l1, Line l2){
    if (sgn(det(l1, l2)) != 0) return 0;
    return dist_sqr(l1.a, l2);
}
inline DB dist_sqr(Line l1, Seg l2){
    Po v0 = l1.b - l1.a, v1 = l2.a - l1.a, v2 = l2.b - l1.a; DB c1 = det(v0, v1), c2 = det(v0, v2);
    return sgn(c1) != sgn(c2) ? 0 : sqr(min(fabs(c1), fabs(c2))) / v0.length_sqr();
}

bool isIntersect(Seg l1, Seg l2){

    //if (l1.a == l2.a || l1.a == l2.b || l1.b == l2.a || l1.b == l2.b) return true;

    return
        min(l1.a.x, l1.b.x) <= max(l2.a.x, l2.b.x) &&
        min(l2.a.x, l2.b.x) <= max(l1.a.x, l1.b.x) &&
        min(l1.a.y, l1.b.y) <= max(l2.a.y, l2.b.y) &&
        min(l2.a.y, l2.b.y) <= max(l1.a.y, l1.b.y) &&
    sgn( det(l1.a, l2.a, l2.b) ) * sgn( det(l1.b, l2.a, l2.b) ) <= 0 &&
    sgn( det(l2.a, l1.a, l1.b) ) * sgn( det(l2.b, l1.a, l1.b) ) <= 0;

}

inline DB dist_sqr(Seg l1, Seg l2){
    if (isIntersect(l1, l2)) return 0;
    else return min(dist_sqr(l1.a, l2), dist_sqr(l1.b, l2), dist_sqr(l2.a, l1), dist_sqr(l2.b, l1));
}

inline bool isOnExtremePoint(const Po &p, const Seg &l){
    return p == l.a || p == l.b;
}

inline bool isOnseg(const Po &p, const Seg &l){

    //if (p == l.a || p == l.b) return false;

    return sgn(det(p, l.a, l.b)) == 0 &&
        sgn(l.a.x, p.x) * sgn(l.b.x, p.x) <= 0 && sgn(l.a.y, p.y) * sgn(l.b.y, p.y) <= 0;
}

inline Po intersect(const Line &l1, const Line &l2){
    return l1.a + (l1.b - l1.a) * (det(l2.a, l1.a, l2.b) / det(l2, l1));
}

// perpendicular foot
inline Po intersect(const Po & p, const Line &l){
    return intersect(Line(p, p + Po(l.a.y - l.b.y, l.b.x - l.a.x)), l);
}

inline Po rotate(Po p, DB alpha, Po o = Po()){
    p.x -= o.x, p.y -= o .y;
    return Po(p.x * cos(alpha) - p.y * sin(alpha), p.y * cos(alpha) + p.x * sin(alpha)) + o;
}

// <<= ' A. Random Event ..

inline int rand32(){return (bool(rand() & 1) << 30) | (rand() << 15) + rand();}
inline int random32(int l, int r){return rand32() % (r - l + 1) + l;}
inline int random(int l, int r){return rand() % (r - l + 1) + l;}
int dice(){return rand() % 6;}
bool coin(){return rand() % 2;}

// <<= ' 0. I/O Accelerator interface .,

template<class T> inline void RD(T &x){
    //cin >> x;
    scanf("%d", &x);
    //char c; for (c = getchar(); c < '0'; c = getchar()); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
    //char c; c = getchar(); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';
}

template<class T> inline void OT(const T &x){
    //printf("%d\n", x);
    cout << x << endl;
}

/* .................................................................................................................................. */

const int N = 495, AN = 17000;

Po P[N]; DB A[N][N]; int p[N][N]; VD L;
int cp[N], dp[N][AN];
int n;

DB area(int _a, int _b, int _c){

    //return abs(det(C[0], C[_a]) + det(C[_a], C[_b]) + det(C[_b], C[0]));

    DB a = dist(P[0], P[_a]), b = dist(P[0], P[_b]), c = dist(P[0], P[_c]);
    DB p = (a + b + c) / 2;
    return sqrt(p * (p - a) * (p - b) * (p - c));
}

int g(int len, int limit){

    if (len <= 1) return 1;

    int &res = dp[len][limit];

    if (res == -1){
        if (p[n-len][len/2] < limit){
            res = cp[len - 1];
        }
        else {
            LL buf = 0; for (int i=1;2*i<=len&&p[n-len][i]<limit;++i){
                buf += (LL) g(i, limit) * g(len - i, limit);
                if (buf >= INF_64) buf %= MOD;
            }
            buf %= MOD, res = buf, INC(res, res);
        }
    }

    return res;
}

int f(int a, int b){
    return pdt(g(a, p[a][b]), g(b, p[a][b]), g(n-a-b, p[a][b]));
}

class MaximalTriangle {
public:
	int howMany(int n, int z) {

	    MOD = z, RST(cp), cp[0] = 1 % z; REP_1(i, n){
	        REP_C(j, (i+1)/2) INC(cp[i], pdt(cp[j], cp[i-1-j])); INC(cp[i], cp[i]);
	        if (i&1) DEC(cp[i], sqr_M(cp[i/2]));
	    }

	    ::n = n; REP(i, n) P[i] = Po(cos(2.0*PI*i/n), sin(2.0*PI*i/n));

	    CLR(L); FOR(i, 1, n) FOR(j, 1, n-i){
	        A[i][j] = area(i, j, n - i - j);
	        L.PB(A[i][j]);
        }

        SRT(L); L.resize(unique(ALL(L), equ) - L.begin());

        RST(p); FOR(i, 1, n) FOR(j, 1, n - i)
            p[i][j] = lower_bound(ALL(L), A[i][j] - EPS) - L.begin();

        int t[] = {(n / 3) % MOD, n % MOD, (LL) 2 * n % MOD};
        FLC(dp, -1); int res = 0; REP(a, n) FOR_1_C(b, a, (n - a) / 2){
            INC(res, pdt(f(a, b), t[(a != b) + (b != n - a - b)]));
        }

	    return res;
	}
};


// BEGIN CUT HERE
namespace moj_harness {
	int run_test_case(int);
	void run_test(int casenum = -1, bool quiet = false) {
		if (casenum != -1) {
			if (run_test_case(casenum) == -1 && !quiet) {
				cerr << "Illegal input! Test case " << casenum << " does not exist." << endl;
			}
			return;
		}

		int correct = 0, total = 0;
		for (int i=0;; ++i) {
			int x = run_test_case(i);
			if (x == -1) {
				if (i >= 100) break;
				continue;
			}
			correct += x;
			++total;
		}

		if (total == 0) {
			cerr << "No test cases run." << endl;
		} else if (correct < total) {
			cerr << "Some cases FAILED (passed " << correct << " of " << total << ")." << endl;
		} else {
			cerr << "All " << total << " tests passed!" << endl;
		}
	}

	int verify_case(int casenum, const int &expected, const int &received, clock_t elapsed) {
		cerr << "Example " << casenum << "... ";

		string verdict;
		vector<string> info;
		char buf[100];

		if (elapsed > CLOCKS_PER_SEC / 200) {
			sprintf(buf, "time %.2fs", elapsed * (1.0/CLOCKS_PER_SEC));
			info.push_back(buf);
		}

		if (expected == received) {
			verdict = "PASSED";
		} else {
			verdict = "FAILED";
		}

		cerr << verdict;
		if (!info.empty()) {
			cerr << " (";
			for (int i=0; i<(int)info.size(); ++i) {
				if (i > 0) cerr << ", ";
				cerr << info[i];
			}
			cerr << ")";
		}
		cerr << endl;

		if (verdict == "FAILED") {
			cerr << "    Expected: " << expected << endl;
			cerr << "    Received: " << received << endl;
		}

		return verdict == "PASSED";
	}

	int run_test_case(int casenum) {
		switch (casenum) {
		case 0: {
			int n                     = 428;
			int z                     = 900000005;
			int expected__            = 180276168;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}
		case 1: {
			int n                     = 5;
			int z                     = 100;
			int expected__            = 5;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}
		case 2: {
			int n                     = 6;
			int z                     = 1000003;
			int expected__            = 2;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}
		case 3: {
			int n                     = 10;
			int z                     = 1000000000;
			int expected__            = 1010;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}
		case 4: {
			int n                     = 15;
			int z                     = 1000000000;
			int expected__            = 714340;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}
		case 5: {
			int n                     = 100;
			int z                     = 987654321;
			int expected__            = 308571232;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}

		// custom cases

/*      case 6: {
			int n                     = ;
			int z                     = ;
			int expected__            = ;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}*/
/*      case 7: {
			int n                     = ;
			int z                     = ;
			int expected__            = ;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}*/
/*      case 8: {
			int n                     = ;
			int z                     = ;
			int expected__            = ;

			clock_t start__           = clock();
			int received__            = MaximalTriangle().howMany(n, z);
			return verify_case(casenum, expected__, received__, clock()-start__);
		}*/
		default:
			return -1;
		}
	}
}

int main(int argc, char *argv[]) {
	if (argc == 1) {
		moj_harness::run_test();
	} else {
		for (int i=1; i<argc; ++i)
			moj_harness::run_test(atoi(argv[i]));
	}
}
// END CUT HERE

External link:

http://apps.topcoder.com/wiki/display/tc/SRM+547
http://community.topcoder.com/stat?c=coder_room_stats&rd=14739&cr=22727863