SRM 446(1-250pt, 1-500pt)

嗯。。。。今天的500确实比较好

DIV1 250

　　模拟。。。略

 // BEGIN CUT HERE
 /*
  * Author:  plum rain
  * score :
  */
 /*

  */
 // END CUT HERE
 #line 11 "CubeWalking.cpp"
 #include <sstream>
 #include <stdexcept>
 #include <functional>
 #include <iomanip>
 #include <numeric>
 #include <fstream>
 #include <cctype>
 #include <iostream>
 #include <cstdio>
 #include <vector>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <cstdlib>
 #include <set>
 #include <queue>
 #include <bitset>
 #include <list>
 #include <string>
 #include <utility>
 #include <map>
 #include <ctime>
 #include <stack>

 using namespace std;

 #define clr0(x) memset(x, 0, sizeof(x))
 #define clr1(x) memset(x, -1, sizeof(x))
 #define pb push_back
 #define sz(v) ((int)(v).size())
 #define all(t) t.begin(),t.end()
 #define zero(x) (((x)>0?(x):-(x))<eps)
 #define out(x) cout<<#x<<":"<<(x)<<endl
 #define tst(a) cout<<a<<" "
 #define tst1(a) cout<<#a<<endl
 #define CINBEQUICKER std::ios::sync_with_stdio(false)

 typedef vector<int> vi;
 typedef vector<string> vs;
 typedef vector<double> vd;
 typedef pair<int, int> pii;
 typedef long long int64;

 const double eps = 1e-;
 const double PI = atan(1.0)*;
 const int inf =  / ;
 int temp[][] = {{, -}, {, }, {, }, {-, }};

 class CubeWalking
 {
     public:
         string finalPosition(string mov){
             int n = sz(mov);
             int x = , y = , dic = ;
             for (int i = ; i < n; ++ i){
                 if (mov[i] == 'L') dic = (dic + ) % ;
                 else if (mov[i] == 'R') dic = (dic + ) % ;
                 if (mov[i] == 'W') x = (x + temp[dic][] + ) % , y = (y + temp[dic][] + ) % ;
             }
             if (x ==  && y == ) return "GREEN";
             if (!x && y == ) return "BLUE";
             if (!y && x == ) return "BLUE";
             if (y ==  && x == ) return "BLUE";
             if (x ==  && y == ) return "BLUE";
             return "RED";
         }

 // BEGIN CUT HERE
     public:
     void run_test(int Case) { if ((Case == -) || (Case == )) test_case_0(); if ((Case == -) || (Case == )) test_case_1(); if ((Case == -) || (Case == )) test_case_2(); if ((Case == -) || (Case == )) test_case_3(); }
     private:
     template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
     void verify_case(int Case, const string &Expected, const string &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
     void test_case_0() { string Arg0 = "LLRR"; string Arg1 = "GREEN"; verify_case(, Arg1, finalPosition(Arg0)); }
     void test_case_1() { string Arg0 = "WWWWWWWWWWWW"; string Arg1 = "GREEN"; verify_case(, Arg1, finalPosition(Arg0)); }
     void test_case_2() { string Arg0 = "WLWRW"; string Arg1 = "RED"; verify_case(, Arg1, finalPosition(Arg0)); }
     void test_case_3() { string Arg0 = "WWLLWRWLWLLRWW"; string Arg1 = "BLUE"; verify_case(, Arg1, finalPosition(Arg0)); }

 // END CUT HERE

 };

 // BEGIN CUT HERE
 int main()
 {
 //    freopen( "a.out" , "w" , stdout );
     CubeWalking ___test;
     ___test.run_test(-);
        return ;
 }
 // END CUT HERE

DIV1 500

题意：给定一个有n个点的带权图，有一个蚂蚁要从点0到点1，它每秒走stp步，最多能走tim秒，走的时间可以少于tim秒，但一定要是整数秒。问，若蚂蚁得分为它通过的边权之和(通过某边两次则得两次分)，则求最大得分，若不能用整数秒走到1并停下，输出IMPOSSIBLE。

　　　n <= 50, stp <= 100, tim <= 10^9。

解法：首先，如果要求一定要走tim，那就很简单了，用矩阵乘法快速幂可以解决。

　　　至于走的时间可以少于tim，处理方法就是加一条1到1，长度为1s，边权为0的自环。

　　　然后，首先用矩阵乘法快速幂算出用时1s，从i点走到j点得分最高为多少。再赋值A[1][1] = max(A[1][1], 0)(若A[1][1]大于0则不用赋值)，然后再调用矩阵乘法快速幂即可。

tag:graph, matrix, 快速幂, good

 // BEGIN CUT HERE
 /*
  * Author:  plum rain
  * score :
  */
 /*

  */
 // END CUT HERE
 #line 11 "AntOnGraph.cpp"
 #include <sstream>
 #include <stdexcept>
 #include <functional>
 #include <iomanip>
 #include <numeric>
 #include <fstream>
 #include <cctype>
 #include <iostream>
 #include <cstdio>
 #include <vector>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <cstdlib>
 #include <set>
 #include <queue>
 #include <bitset>
 #include <list>
 #include <string>
 #include <utility>
 #include <map>
 #include <ctime>
 #include <stack>

 using namespace std;

 #define clr0(x) memset(x, 0, sizeof(x))
 #define clr1(x) memset(x, -1, sizeof(x))
 #define pb push_back
 #define sz(v) ((int)(v).size())
 #define all(t) t.begin(),t.end()
 #define zero(x) (((x)>0?(x):-(x))<eps)
 #define out(x) cout<<#x<<":"<<(x)<<endl
 #define tst(a) cout<<a<<" "
 #define tst1(a) cout<<#a<<endl
 #define CINBEQUICKER std::ios::sync_with_stdio(false)

 typedef long long int64;
 typedef vector<int> vi;
 typedef vector<string> vs;
 typedef vector<double> vd;
 typedef pair<int, int> pii;
 typedef int64 mtx[][];

 const double eps = 1e-;
 const double PI = atan(1.0)*;
 const int inf =  / ;
 const int64 temp =  - (1LL<<);

 class AntOnGraph
 {
     public:
         int dit[], n;
         void mtx_eql(mtx &a, mtx b)
         {
             for (int i = ; i < n; ++ i) for (int j = ; j < n; ++ j) a[i][j] = b[i][j];
         }
         void mtx_mul(mtx &a, mtx b)
         {
             mtx ret;
             for (int i = ; i < n; ++ i)
                 for (int j = ; j < n; ++ j){
                     ret[i][j] = temp;
                     for (int k = ; k < n; ++ k)
                         if (a[i][k] != temp && b[k][j] != temp)
                             ret[i][j] = max(ret[i][j], a[i][k] + b[k][j]);
                 }

             mtx_eql(a, ret);
         }
         void mtx_pow(mtx &an, int64 num)
         {
             if (num == ) return;

             mtx ret; mtx_eql(ret, an);
             -- num;

             while (num){
                 if (num & ) mtx_mul(ret, an);
                 num >>= ;
                 mtx_mul(an, an);
             }

             mtx_eql(an, ret);
         }

         string gao(int64 x)
         {
             int len = ;
             bool u = ;
             if (x < ) x =  - x, u = ;

             while (x){
                 dit[len++] = x % ;
                 x /= ;
             }

             if (!len) return "";
             string ret; ret.clear();
             if (u) ret.pb ('-');
             for (int i = len-; i >= ; -- i) ret.pb (dit[i] + '');
             return ret;
         }
         string maximumBonus(vector <string> p0, vector <string> p1, vector <string> p2, int stp, int tim){
             n = sz(p1);
             int cnt = ;
             mtx an;
             for (int i = ; i < n; ++ i)
                 for (int j = ; j < n; ++ j){
                     cnt =  * (p0[i][j]-'') +  * (p1[i][j] - '') + p2[i][j] - '';
                     if (cnt == ) an[i][j] = temp;
                     else an[i][j] = cnt - ;
                 }

             mtx_pow(an, (int64)stp);
             if (an[][] < ) an[][] = ;

             mtx_pow(an, (int64)tim);
             if (an[][] == temp) return "IMPOSSIBLE";
             else return gao(an[][]);
         }

 // BEGIN CUT HERE
     public:
     void run_test(int Case) { if ((Case == -) || (Case == )) test_case_0(); if ((Case == -) || (Case == )) test_case_1(); if ((Case == -) || (Case == )) test_case_2(); if ((Case == -) || (Case == )) test_case_3(); if ((Case == -) || (Case == )) test_case_4(); }
     private:
     template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
     void verify_case(int Case, const string &Expected, const string &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
     void test_case_0() { string Arr0[] = {"",""}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"",""}; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); string Arr2[] = {"",""}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); int Arg3 = ; int Arg4 = ; string Arg5 = ""; verify_case(, Arg5, maximumBonus(Arg0, Arg1, Arg2, Arg3, Arg4)); }
     void test_case_1() { string Arr0[] = {"",""}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"",""}; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); string Arr2[] = {"",""}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); int Arg3 = ; int Arg4 = ; string Arg5 = "IMPOSSIBLE"; verify_case(, Arg5, maximumBonus(Arg0, Arg1, Arg2, Arg3, Arg4)); }
     void test_case_2() { string Arr0[] = {"","","",""}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"","","",""}; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); string Arr2[] = {"","","",""}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); int Arg3 = ; int Arg4 = ; string Arg5 = ""; verify_case(, Arg5, maximumBonus(Arg0, Arg1, Arg2, Arg3, Arg4)); }
     void test_case_3() { string Arr0[] = {"","","",""}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"","","",""}; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); string Arr2[] = {"","","",""}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); int Arg3 = ; int Arg4 = ; string Arg5 = "-5"; verify_case(, Arg5, maximumBonus(Arg0, Arg1, Arg2, Arg3, Arg4)); }
     void test_case_4() { string Arr0[] = {"","","",
  "","","",
  "","","",
  "","",""}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"","","",
  "","","",
  "","","",
  "","",""}; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); string Arr2[] = {"","","",
  "","","",
  "","","",
  "","",""}; vector <string> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[]))); int Arg3 = ; int Arg4 = ; string Arg5 = ""; verify_case(, Arg5, maximumBonus(Arg0, Arg1, Arg2, Arg3, Arg4)); }

 // END CUT HERE

 };

 // BEGIN CUT HERE
 int main()
 {
 //    freopen( "a.out" , "w" , stdout );
     AntOnGraph ___test;
     ___test.run_test(-);
        return ;
 }
 // END CUT HERE