URAL1081[Binary Lexicographic Sequence]

恩，先递推f[i][0]表示第i位为0且长度为i的合法串的数目，f[i][1]表示第i位为1且长度为i的合法串的数目。

然后f[0][0]=1，f[0][1]=0，f[i][0]=f[i-1][0]+f[i-1][1]，f[i][1]=f[i-1][0]。

最后，用这些信息来判断每一位该是0还是1。具体看代码。

CODE:

/*

PROGRAM: $PROGRAM

AUTHOR: Su Jiao

DATE: 2010-4-11

DESCRIPTION:

$DESCRIPTION

*/

#include <iostream>

using std::cin;

using std::cout;

#include <fstream>

using std::ifstream;

using std::ofstream;

#include <sstream>

using std::stringstream;

using std::endl;

#include <vector>

using std::vector;

#include <string>

using std::string;

#include <stack>

using std::stack;

#include <queue>

using std::queue;

using std::priority_queue;

#include <set>

using std::set;

#include <map>

using std::map;

using std::pair;

using std::make_pair;

#include <algorithm>

using std::sort;

#include <cassert>

//using std::assert;

 

class Application

{

      int N,K;

      public:

      Application()

      {

                   cin>>N>>K;

      }

      int run()

      {

          vector<vector<long long int> > f(N+1,vector<long long int>(2));

          f[0][0]=1;

          f[0][1]=0;

          for (int i=1;i<=N;i++)

          {

              f[i][0]=f[i-1][0]+f[i-1][1];

              f[i][1]=f[i-1][0];

          }

          bool noanswer=false;

          string output;

          output.resize(N);

          for (int i=N;i>=1;i–)

          {

              if (K>f[i][1]+f[i][0])

              {

                 noanswer=true;

                 break;

              }

              if (K>f[i][0])

              {

                 K-=f[i][0];

                 output[N-i]=’1′;

              }

              else

              {

                 output[N-i]=’0′;

              }

          }

          if (noanswer) cout<<-1<<endl;

          else cout<<output<<endl;

          return 0;

      }

};

 

int main()

{

    Application app;

    return app.run();

}