[构造 哈密顿路径] SRM 704 div1 HamiltonianConstruction

构造一个图使得1到n的哈密尔顿路径恰好为k。
k<=100000, 要求点数不超过20。

广为流传的做法是

1<-2<-…<-18一条路径，然后1-18都向编号比它大的节点连边。这样的话往回走就只有唯一的路径，所以假如说我当前在i，走到了j，j>i，那么就需要立刻从j到j-1直到i+1，然后再往后走。这样就相当于每个节点有选或不选两种状态，如果选的话就是从前面第一个比它小的选的节点跳过来，不选的话就是从i+1过来。所以如果有0->i，就相当于贡献了218−i−1（1≤i<18)（因为18是必选的，19不能回到18）。

当然还有瞎搞的做法

传送门

dls的做法

// BEGIN CUT HERE  #include<conio.h>#include<sstream>// END CUT HERE  #include<cstdio>#include<cstdlib>#include<cstring>#include<cmath>#include<iostream>#include<algorithm>#include<vector>#include<map>#include<string>#include<set>#define cl(x) memset(x,0,sizeof(x))using namespace std;typedef long long ll;class HamiltonianConstruction{public:  vector <string> construct(int k){    int n=20;    vector<string> ans(n,string(n,'N'));    for (int i=2;i<=n-2;i++) ans[i][i-1]='Y';    for(int i=1;i<n;i++)      for(int j=i+1;j<n;j++)    ans[i][j]='Y';    for (int i=0;i<=17;i++,k>>=1)      if (k&1)    ans[0][18-i-1]='Y';    return ans;  }  // BEGIN CUT HEREpublic:  void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) 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() { int Arg0 = 1; string Arr1[] = {"NY", "NN" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); verify_case(0, Arg1, construct(Arg0)); }  void test_case_1() { int Arg0 = 3; string Arr1[] = {"NYYNY", "YNYYY", "YYNYY", "YNYNY", "YYYYN" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); verify_case(1, Arg1, construct(Arg0)); }  void test_case_2() { int Arg0 = 720; string Arr1[] = {"NYYYYYYY", "YNYYYYYY", "YYNYYYYY", "YYYNYYYY", "YYYYNYYY", "YYYYYNYY", "YYYYYYNY", "YYYYYYYN" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); verify_case(2, Arg1, construct(Arg0)); }  void test_case_3() { int Arg0 = 288; string Arr1[] = {"NYYYYNYY", "YNYYYYYY", "YYNYYYNY", "YYYNYYYY", "YNYYNYYY", "YYYYYNYN", "YYNYYYNY", "YYYYYNNN" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); verify_case(3, Arg1, construct(Arg0)); }  // END CUT HERE};// BEGIN CUT HEREint main(){  HamiltonianConstruction ___test;  ___test.run_test(-1);  getch() ;  return 0;}// END CUT HERE