topcoder srm 550

div1 250pt:

　　题意：有个机器人，从某一点出发，他只有碰到地形边缘或者碰到走过的点时才会改变运动方向，然后接着走，现在给出他的运动轨迹，判断他的运动是否合法，如果合法的话，那么整个地形的最小面积是多少。

　　解法：先随便设定一个起点，然后模拟机器人走的路线，先确定出来运动的大致范围，然后判断运动轨迹是否合法，也就是出了最后一步可以手动终止之外，看其他的时候，它转变方向是不是合法。。。。

 // BEGIN CUT HERE

 // END CUT HERE
 #line 5 "RotatingBot.cpp"
 #include<cstdio>
 #include<sstream>
 #include<cstring>
 #include<cstdlib>
 #include<ctime>
 #include<cmath>
 #include<cassert>
 #include<iostream>
 #include<string>
 #include<vector>
 #include<map>
 #include<set>
 #include<queue>
 #include<stack>
 #include<algorithm>
 using namespace std;
 typedef long long ll;
 typedef pair<int,int> pii;
 int vis[][];
 int dir[][] = {,,,,-,,,-};
 class RotatingBot
 {
     public:
     int minArea(vector <int> moves){
     //$CARETPOSITION$
         memset(vis,-,sizeof(vis));
         int cur_d = ;
         int cur_x = ,cur_y = ;
         vis[cur_x][cur_y] = ;
         for(int i = ;i < moves.size();i++){
             int len = moves[i];
             while(len > ){
                 cur_x += dir[cur_d][];
                 cur_y += dir[cur_d][];
                 if(vis[cur_x][cur_y] != -)return -;
                 vis[cur_x][cur_y] = i;
                 len --;
             }
             cur_d = (cur_d + ) % ;
         }
      //   cout << "done" <<endl;
         int left = ,right = ,top = ,bottom = ;
         for(int i = ;i < ;i++)
             for(int j = ;j < ;j++){
                 if(vis[i][j] != -){
                     left = min(left,i);
                     right = max(right,i);
                     top = max(top,j);
                     bottom = min(bottom,j);
                 }
             }
     //    cout <<"left: "<<left<<" right: "<<right <<" top: "<<top<<" bottom:"<<bottom<<endl;
         cur_x = ,cur_y = ;cur_d = ;
         for(int i = ;i < moves.size();i++){
             int len = moves[i];
             while(len > ){
                 cur_x += dir[cur_d][];
                 cur_y += dir[cur_d][];
                 len --;
             }
             if(i == moves.size() - )continue;
             int next_x = cur_x + dir[cur_d][];
             int next_y = cur_y + dir[cur_d][];
             if(next_x >= left && next_x <= right && next_y >= bottom && next_y <= top){
                 if(vis[next_x][next_y] == -)return -;
                 if(vis[next_x][next_y] > i)return -;
             }
             cur_d = (cur_d + ) % ;
         }
         return (right - left + ) * (top - bottom + );

     }

 // 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(); if ((Case == -) || (Case == )) test_case_5(); if ((Case == -) || (Case == )) test_case_6(); if ((Case == -) || (Case == )) test_case_7(); }
     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 int &Expected, const int &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() { int Arr0[] = {}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = ; verify_case(, Arg1, minArea(Arg0)); }
     void test_case_1() { int Arr0[] = {,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = ; verify_case(, Arg1, minArea(Arg0)); }
     void test_case_2() { int Arr0[] = {,,,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = -; verify_case(, Arg1, minArea(Arg0)); }
     void test_case_3() { int Arr0[] = {,,,,,,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = ; verify_case(, Arg1, minArea(Arg0)); }
     void test_case_4() { int Arr0[] = {,,,,,,,,,,,,,,,,,,,,,,,,,,,,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = ; verify_case(, Arg1, minArea(Arg0)); }
     void test_case_5() { int Arr0[] = {,,,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = -; verify_case(, Arg1, minArea(Arg0)); }
     void test_case_6() { int Arr0[] = {,,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = ; verify_case(, Arg1, minArea(Arg0)); }
     void test_case_7() { int Arr0[] = {,,,,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = ; verify_case(, Arg1, minArea(Arg0)); }

 // END CUT HERE

 };
 // BEGIN CUT HERE
 int main(){
     RotatingBot ___test;
     ___test.run_test(-);
     return ;
 }
 // END CUT HERE

250pt

div1 500pt:

　　题意:两个人在一个无限大的格子里涂色，第一个人先在(0,0)涂色，然后接下来的每一轮，对于所有的点(x,y)，如果(x-1,y-1)和(x-2,y)中有且只有一个点被涂色了，那么就把这个点也涂了，问经过t轮之后，某个区域的染色情况。

　　解法：先在纸上模拟一下前几轮的情况，我们很容易发现，被涂色的区域就是{x>=0,y>=0并且x<=y}这部分区域，而且被涂色点的分布很像一个杨辉三角，其中被涂色的部分就是杨辉三角中奇数的点。。。于是问题就变成判断C(n,m)奇偶性的问题了，有个结论C(n,m)是奇数当且仅当n&m==n。。。

 // BEGIN CUT HERE

 // END CUT HERE
 #line 5 "CheckerExpansion.cpp"
 #include<cstdio>
 #include<sstream>
 #include<cstring>
 #include<cstdlib>
 #include<ctime>
 #include<cmath>
 #include<cassert>
 #include<iostream>
 #include<string>
 #include<vector>
 #include<map>
 #include<set>
 #include<queue>
 #include<stack>
 #include<algorithm>
 using namespace std;
 typedef long long ll;
 typedef pair<int,int> pii;
 class CheckerExpansion
 {
     public:
     vector <string> resultAfter(long long t, long long x0, long long y0, int w, int h){
     //$CARETPOSITION$
         vector<string> ret;
       //  t = 5;x0 = 0;y0 = 0;w = 10;h = 10;
         for(int i = ;i < h;i++){
             string tmp = "";
             for(int j = ;j < w;j++){
                 char will;
                 long long x = x0 + j;
                 long long y = y0 + h - i - ;
         //        if(x == y)cout <<"x : " <<x<<" y:"<<y<<endl;
                 if((x + y) %  == ){
                     if(x < y){
                         will = '.';
                     }else{
                         long long row = (x + y) / ;
                         long long column = abs(x - row);
                         if(row + > t){
                             will = '.';
                         }else if((row & column) == column){
                             if(row %  == ){
                                 will = 'A';
                             }else{
                                 will = 'B';
                             }
                         }else{
                             will = '.';
                         }
                     }
                 }else{
                     will = '.';
                 }
         //        if(x == y)cout<<will<<endl;
                 tmp += will;
             }
             ret.push_back(tmp);
         //    cout << tmp << endl;

         }
         return ret;

     }

 // 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 vector <string> &Expected, const vector <string> &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: " << print_array(Expected) << endl; cerr << "\tReceived: " << print_array(Received) << endl; } }
     void test_case_0() { long long Arg0 = 1LL; long long Arg1 = 0LL; long long Arg2 = 0LL; int Arg3 = ; int Arg4 = ; string Arr5[] = {"....", "....", "....", "A..." }; vector <string> Arg5(Arr5, Arr5 + (sizeof(Arr5) / sizeof(Arr5[]))); verify_case(, Arg5, resultAfter(Arg0, Arg1, Arg2, Arg3, Arg4)); }
     void test_case_1() { long long Arg0 = 5LL; long long Arg1 = 4LL; long long Arg2 = 1LL; int Arg3 = ; int Arg4 = ; string Arr5[] = {"A..", "...", "B..", ".B." }; vector <string> Arg5(Arr5, Arr5 + (sizeof(Arr5) / sizeof(Arr5[]))); verify_case(, Arg5, resultAfter(Arg0, Arg1, Arg2, Arg3, Arg4)); }
     void test_case_2() { long long Arg0 = 1024LL; long long Arg1 = 1525LL; long long Arg2 = 512LL; int Arg3 = ; int Arg4 = ; string Arr5[] = {"B...B...B...........", ".B.A.B.A.B.........." }; vector <string> Arg5(Arr5, Arr5 + (sizeof(Arr5) / sizeof(Arr5[]))); verify_case(, Arg5, resultAfter(Arg0, Arg1, Arg2, Arg3, Arg4)); }
     void test_case_3() { long long Arg0 = 53LL; long long Arg1 = 85LL; long long Arg2 = 6LL; int Arg3 = ; int Arg4 = ; string Arr5[] = {".....", ".....", "B....", ".B.A.", ".....", ".....", ".....", ".....", ".....", ".....", "B....", ".B...", "..B..", ".A.B." }; vector <string> Arg5(Arr5, Arr5 + (sizeof(Arr5) / sizeof(Arr5[]))); verify_case(, Arg5, resultAfter(Arg0, Arg1, Arg2, Arg3, Arg4)); }

 // END CUT HERE

 };
 // BEGIN CUT HERE
 int main(){
     CheckerExpansion ___test;
     ___test.run_test(-);
     return ;
 }
 // END CUT HERE

500pt