World Last Hope .. .

.. .

Brief description :

給定一副 點權 Ei、邊權 Ci 的無向圖,現在要求對每條邊,對應一個收益函數 Fi,
要求滿足限制條件 Fi <= Ci && Gi <= Ei.. 其中 Gi 為覆蓋、某點的所有 Fi 的權值和。 最大化 |F| 。。。

Analysis :

… 這題題目比較長,而且有很多佔星學術語。。很多拉丁語的名詞之類。。.. (看來出題人和我有同樣的趣味。。。么?)
另一方面,一些常見單詞可能需要額外辨視。。例如,”aspect” 在這題中得含義是:

【天文學、占星術】

  • (太陽系的星體相對於太陽的)視位置;
  • 恆星(或行星)的相互位置
  • 占星術認為會影響人事禍福的運氣

..
所以首先要把題意梳理清楚。。。值得一題的是這題中得圖。。畫的非常漂亮!。。

之後就抽象成了 Brief description 中所述的圖論問題,yy 了 30 分鐘各種網路流建模但是無果。。於是。。。
。。搜索剪枝吧。。。

。。(強烈膜拜 First Blood 是數據結構的數據結構帝 cwj 。。)。。

/** ` 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 <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 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(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 **/

const int MOD = 360;
const int INF = 0x7fffffff;
const DB PI = acos(-1.0);
const DB EPS = 1e-6;
const DB OO = 1e15;

// <<= ` 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 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 int _1(int i){return 1<<i;}
inline int _U(int i){return _1(i) - 1;};

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;
}

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;
}

// <<= ` 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;}


// <<= ' 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';

}

int ____Case;
template<class T> inline void OT(const T &x){
    //cout << x << endl;
    printf("%d\n", x);
    //printf("%.2lf\n", x);
    //printf("Case %d: %d\n", ++____Case, x);
}


#define For_each(it, A) for (SII::iterator it = A.begin(); it != A.end(); ++it)

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

const int N = 10, M = N * N;

map<string, int> Star, Sign;

struct Vertex{
    int e, c, p;
} V[N];

struct Edge{
    int x, y, c;
    int cc(){
        return min(c, V[x].e, V[y].e);
    }
} E[M];

int ans, cur;
int m;


void Init(){
    Star["Sun"] = 0, Star["Moon"] = 1, Star["Mercury"] = 2, Star["Venus"] = 3;
    Star["Mars"] = 4, Star["Jupiter"] = 5, Star["Saturn"] = 6, Star["Uranus"] = 7;
    Star["Neptune"] = 8, Star["Pluto"] = 9;

    Sign["Aries"] = 0, Sign["Taurus"] = 1, Sign["Gemini"] = 2, Sign["Cancer"] = 3,
    Sign["Leo"] = 4, Sign["Virgo"] = 5, Sign["Libra"] = 6, Sign["Scorpio"] = 7,
    Sign["Sagittarius"] = 8, Sign["Capricorn"] = 9, Sign["Aquarius"] = 10, Sign["Pisces"] = 11;
}

void Build_Graph(){

    string star, sign;
    int a, b, d;

    DO_C(N){
        cin >> star >> sign >> d; a = Star[star], b = Sign[sign];

        V[a].e = 5, V[a].c = 3, V[a].p = b * 30 + d;

        // Star State: Rise, Fall, Exalt && Debilitate

#define Rise V[a].e += 3
#define Fall V[a].e -= 3
#define Exalt V[a].c += 2
#define Debilitate V[a].c -= 2

        if (star == "Sun"){
            if (sign == "Leo") Rise;
            else if (sign == "Aquarius") Fall;
            else if (sign == "Aries") Exalt;
            else if (sign == "Libra") Debilitate;
        }
        else if (star == "Moon"){
            if (sign == "Cancer") Rise;
            else if (sign == "Capricorn") Fall;
            else if (sign == "Taurus") Exalt;
            else if (sign == "Scorpio") Debilitate;
        }
        else if (star == "Mercury"){
            if (sign == "Gemini" || sign == "Virgo") Rise;
            else if (sign == "Sagittarius" || sign == "Pisces") Fall;
            else if (sign == "Aquarius") Exalt;
            else if (sign == "Leo") Debilitate;
        }
        else if (star == "Venus"){
            if (sign == "Taurus" || sign == "Libra") Rise;
            else if (sign == "Scorpio" || sign == "Aries") Fall;
            else if (sign == "Pisces") Exalt;
            else if (sign == "Virgo") Debilitate;
        }
        else if (star == "Mars"){
            if (sign == "Aries" || sign == "Scorpio") Rise;
            else if (sign == "Libra" || sign == "Taurus") Fall;
            else if (sign == "Capricorn") Exalt;
            else if (sign == "Cancer") Debilitate;
        }
        else if (star == "Jupiter"){
            if (sign == "Sagittarius" || sign == "Pisces") Rise;
            else if (sign == "Gemini" || sign == "Virgo") Fall;
            else if (sign == "Cancer") Exalt;
            else if (sign == "Capricorn") Debilitate;
        }
        else if (star == "Saturn"){
            if (sign == "Capricorn" || sign == "Aquarius") Rise;
            else if (sign == "Cancer" || sign == "Leo") Fall;
            else if (sign == "Libra") Exalt;
            else if (sign == "Aries") Debilitate;
        }
        else if (star == "Uranus"){
            if (sign == "Aquarius") Rise;
            else if (sign == "Leo") Fall;
            else if (sign == "Scorpio") Exalt;
            else if (sign == "Taurus") Debilitate;
        }
        else if (star == "Neptune"){
            if (sign == "Pisces") Rise;
            else if (sign == "Virgo") Fall;
            else if (sign == "Sagittarius") Exalt;
            else if (sign == "Gemini") Debilitate;
        }
        else if (star == "Pluto"){
            if (sign == "Scorpio") Rise;
            else if (sign == "Taurus") Fall;
            else if (sign == "Virgo") Exalt;
            else if (sign == "Pisces") Debilitate;
        }
    }

    // Aspects: Sextile, Square, Trine && Opposite

#define Conjunct (Diff <= 0 + 5)
#define Sextile (60 - 3 <= Diff && Diff <= 60 + 3)
#define Square (90 - 4 <= Diff && Diff <= 90 + 4)
#define Trine (120 - 4 <= Diff && Diff <= 120 + 4)
#define Opposite (180 - 3 <= Diff && Diff <= 180)

    REP(i, N) FOR(j, i+1, N){

        int Diff = V[i].p - V[j].p; if (Diff < 0) Diff = -Diff; if (Diff > 180) Diff = 360 - Diff;

        if (Sextile) V[i].c += 1, V[j].c += 1;
        else if (Square) V[i].c += 2, V[j].c += 2, V[i].e -= 3, V[j].e -= 3;
        else if (Trine) V[i].e += 3, V[j].e += 3, V[i].c -= 2, V[j].c -= 2;
        else if (Opposite) V[i].e -= 1, V[j].e -= 1;
    }

    REP(i, N) checkMax(V[i].e, 0);

    m = 0;

    REP(i, N) FOR(j, i+1, N){

        int Diff = V[i].p - V[j].p; if (Diff < 0) Diff = -Diff; if (Diff > 180) Diff = 360 - Diff;

        if (Conjunct) E[m].c = INF, E[m].x = i, E[m++].y = j;
        else if (Sextile || Square || Trine || Opposite){
            E[m].c = max(0, V[i].c + V[j].c + 2);
            if (E[m].c) E[m].x = i, E[m++].y = j;
        }
    }
}

void dfs(int s = 0){

    int t = 0; FOR(i, s, m) t += E[i].cc();
    if (cur + t <= ans) return;

    if (s == m){
        ans = cur;
    }
    else {

        DWN_1_C(f, E[s].cc(), 0){

            cur += f;

            V[E[s].x].e -= f, V[E[s].y].e -= f;

            dfs(s + 1);

            V[E[s].x].e += f, V[E[s].y].e += f;

            cur -= f;
        }
    }

}

int main(){

    //freopen("in.txt", "r", stdin);
    //freopen("out.txt", "w", stdout);
    //ios::sync_with_stdio(false);

    Init(); Rush{
        Build_Graph(); cur = ans = 0; dfs();
        OT(ans * 2);
    }
}

External link:

http://acmicpc.info/archives/383
http://acm.hdu.edu.cn/showproblem.php?pid=4040
http://boj.me/onlinejudge/newoj/showProblem/show_problem.php?problem_id=211