DIV2 1000pt

题意：对于一个n*m的矩阵，每个格子都有一个颜色B或者W。对矩阵A执行以下程序后变成矩阵B。给出矩阵B，求A。(若有多种情况，输出字典序最小的)。(n,m <= 16)

  1.  For i =  to H-:
  2.      For j =  to W-:
  3.          //Get the current colors of cells (i,j) and (i,j+1)
  4.          A = Color(i,j) , B = Color(i,j+)
  5.  
  6.          If (A,B) == (White, White) Then:
  7.               Do nothing.
  8.          EndIf
  9.          If (A,B) == (Black, White) Then:
  10.               Repaint cells (i+,j) and (i+,j+) Black.
  11.          EndIf
  12.          If (A,B) == (White, Black) Then:
  13.               Repaint cells (i+,j) and (i+,j+) White.
  14.          EndIf
  15.          if (A,B) == (Black, Black) Then:
  16.               Swap the colors in cells (i+,j) and (i+,j+).
  17.          EndIf
  18.      EndFor
  19.  EndFor

解法：

　　　法一，水解：首先注意到两点，一是在读取矩阵A的第i行的时候，对其第i+1行进行操作，二是矩阵A和矩阵B的第一行必然相同。

　　　所以，直接暴力DFS即可。由于每行最多只有16个，所以可以压缩状态来做。

　　　法二：比较考查思维的方法。首先仍然要注意到，读第i行时处理第i+1行，所以每行可以单独分析。其次，在读i处理i+1行时，有两种操作，对i+1行的某两个格子染色或者交换他们的颜色。若在读i行时对i+1行的某两个格子染色，则他们之前(在A矩阵中的时候)是什么颜色就不影响了，考虑到要字典序最小，所以应该让他们颜色为'B'。而其他没有被染色的格子，他们需要与变换后的位置的相应元素相同。

　　　这样的方法很巧，而且倒着写比较好写。

tag:think, good

法一：

  1.  // BEGIN CUT HERE
  2.  /*
  3.   * Author:  plum rain
  4.   * score :
  5.   */
  6.  /*
  7.  
  8.   */
  9.  // END CUT HERE
  10.  #line 11 "Algrid.cpp"
  11.  #include <sstream>
  12.  #include <stdexcept>
  13.  #include <functional>
  14.  #include <iomanip>
  15.  #include <numeric>
  16.  #include <fstream>
  17.  #include <cctype>
  18.  #include <iostream>
  19.  #include <cstdio>
  20.  #include <vector>
  21.  #include <cstring>
  22.  #include <cmath>
  23.  #include <algorithm>
  24.  #include <cstdlib>
  25.  #include <set>
  26.  #include <queue>
  27.  #include <bitset>
  28.  #include <list>
  29.  #include <string>
  30.  #include <utility>
  31.  #include <map>
  32.  #include <ctime>
  33.  #include <stack>
  34.  
  35.  using namespace std;
  36.  
  37.  #define CLR(x) memset(x, 0, sizeof(x))
  38.  #define CLR1(x) memset(x, -1, sizeof(x))
  39.  #define PB push_back
  40.  #define SZ(v) ((int)(v).size())
  41.  #define zero(x) (((x)>0?(x):-(x))<eps)
  42.  #define out(x) cout<<#x<<":"<<(x)<<endl
  43.  #define tst(a) cout<<#a<<endl
  44.  #define CINBEQUICKER std::ios::sync_with_stdio(false)
  45.  
  46.  typedef vector<int> VI;
  47.  typedef vector<string> VS;
  48.  typedef vector<double> VD;
  49.  typedef long long int64;
  50.  
  51.  const double eps = 1e-;
  52.  const double PI = atan(1.0)*;
  53.  const int maxint = ;
  54.  
  55.  int n, all, len;
  56.  bool flag;
  57.  int a[], ans[];
  58.  
  59.  int change(int x, int y)
  60.  {
  61.      if (x == -) return -;
  62.  
  63.      int ta[], tb[];
  64.      int idxa = , idxb = ;
  65.      for (int i = ; i < len; ++ i){
  66.          ta[idxa++] = x & ;
  67.          x >>= ;
  68.          tb[idxb++] = y & ;
  69.          y >>= ;
  70.      }
  71.      for (int i = len-; i; -- i){
  72.          if (!ta[i] && ta[i-]) tb[i] = tb[i-] = ;
  73.          if (ta[i] && !ta[i-]) tb[i] = tb[i-] = ;
  74.          if (!ta[i] && !ta[i-]) swap(tb[i], tb[i-]);
  75.      }
  76.      int ret = ;
  77.      for (int i = len-; i >= ; -- i)
  78.          ret += (tb[i] << i);
  79.      return ret;
  80.  }
  81.  
  82.  void DFS (int x)
  83.  {
  84.      if (x == n){
  85.          flag = ;
  86.          return;
  87.      }
  88.  
  89.      for (int i = ; i < all; ++ i)
  90.          if (!flag && change(a[x-], i) == a[x]){
  91.              ans[x] = i;
  92.              DFS (x+);
  93.              if (!flag) ans[x] = -;
  94.          }
  95.  }
  96.  
  97.  class Algrid
  98.  {
  99.      public:
  100.          vector <string> makeProgram(vector <string> A){
  101.              len = A[].size();
  102.              n = A.size(); all =  << len;
  103.              for (int i = ; i < n; ++ i){
  104.                  int tmp = ;
  105.                  for (int j = len-, k = ; j >= ; -- j, ++ k)
  106.                      if (A[i][j] == 'W'){
  107.                          tmp += ( << k);
  108.                      }
  109.                  a[i] = tmp;
  110.              }
  111.  
  112.              CLR1 (ans);
  113.              ans[] = a[];
  114.  
  115.              flag = ;
  116.              DFS ();
  117.  
  118.              vector<string> ret; ret.clear();
  119.              string tmp;
  120.              for (int i = ; i < n; ++ i){
  121.                  if (ans[i] == -){
  122.                      ret.clear(); return ret;
  123.                  }
  124.  
  125.                  tmp.clear();
  126.                  for (int j = len-; j >= ; -- j){
  127.                      if (ans[i] & (<<j)) tmp.PB ('W');
  128.                      else tmp.PB('B');
  129.                  }
  130.                  ret.PB (tmp);
  131.              }
  132.              return ret;
  133.          }
  134.  
  135.  // BEGIN CUT HERE
  136.      public:
  137.      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(); }
  138.      //void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0();}
  139.      private:
  140.      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(); }
  141.      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; } }
  142.      void test_case_0() { string Arr0[] = {"WWBBB", "WBBBW"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"WWWWWWW", "WWWWWWB", "BBBBBBB" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); verify_case(, Arg1, makeProgram(Arg0)); }
  143.      void test_case_1() { string Arr0[] = {"BBBBB",
  144.   "WBWBW"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"BBBBB", "WWBWB" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); verify_case(, Arg1, makeProgram(Arg0)); }
  145.      void test_case_2() { string Arr0[] = {"BBBB",
  146.   "BBBB",
  147.   "BBWB",
  148.   "WWBB",
  149.   "BWBB"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = { }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); verify_case(, Arg1, makeProgram(Arg0)); }
  150.      void test_case_3() { string Arr0[] = {"WWBBBBW",
  151.   "BWBBWBB",
  152.   "BWBBWBW",
  153.   "BWWBWBB"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"WWBBBBW", "BBBBBWB", "BBBBBBB", "BBBWBBB" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); verify_case(, Arg1, makeProgram(Arg0)); }
  154.  
  155.  // END CUT HERE
  156.  
  157.  };
  158.  
  159.  // BEGIN CUT HERE
  160.  int main()
  161.  {
  162.  //    freopen( "a.out" , "w" , stdout );
  163.      Algrid ___test;
  164.      ___test.run_test(-);
  165.         return ;
  166.  }
  167.  // END CUT HERE

法二：

  1.  // BEGIN CUT HERE
  2.  /*
  3.   * Author:  plum rain
  4.   * score :
  5.   */
  6.  /*
  7.  
  8.   */
  9.  // END CUT HERE
  10.  #line 11 "Algrid.cpp"
  11.  #include <sstream>
  12.  #include <stdexcept>
  13.  #include <functional>
  14.  #include <iomanip>
  15.  #include <numeric>
  16.  #include <fstream>
  17.  #include <cctype>
  18.  #include <iostream>
  19.  #include <cstdio>
  20.  #include <vector>
  21.  #include <cstring>
  22.  #include <cmath>
  23.  #include <algorithm>
  24.  #include <cstdlib>
  25.  #include <set>
  26.  #include <queue>
  27.  #include <bitset>
  28.  #include <list>
  29.  #include <string>
  30.  #include <utility>
  31.  #include <map>
  32.  #include <ctime>
  33.  #include <stack>
  34.  
  35.  using namespace std;
  36.  
  37.  #define CLR(x) memset(x, 0, sizeof(x))
  38.  #define CLR1(x) memset(x, -1, sizeof(x))
  39.  #define PB push_back
  40.  #define SZ(v) ((int)(v).size())
  41.  #define zero(x) (((x)>0?(x):-(x))<eps)
  42.  #define out(x) cout<<#x<<":"<<(x)<<endl
  43.  #define tst(a) cout<<#a<<endl
  44.  #define CINBEQUICKER std::ios::sync_with_stdio(false)
  45.  
  46.  typedef vector<int> VI;
  47.  typedef vector<string> VS;
  48.  typedef vector<double> VD;
  49.  typedef long long int64;
  50.  
  51.  const double eps = 1e-;
  52.  const double PI = atan(1.0)*;
  53.  const int maxint = ;
  54.  
  55.  class Algrid
  56.  {
  57.      public:
  58.          vector <string> makeProgram(vector <string> opt){
  59.              vector<string> tmp; tmp.clear();
  60.              int n = opt.size(), m = opt[].size();
  61.              for (int i = n-; i >= ; -- i){
  62.                  for (int j = m-; j >= ; -- j){
  63.                      char a = opt[i][j], b = opt[i][j+];
  64.                      char &c = opt[i+][j], &d = opt[i+][j+];
  65.  
  66.                      if (a == 'B' && b == 'B')
  67.                          swap (c, d);
  68.                      if (a == 'B' && b == 'W'){
  69.                          if (c == 'W' || d == 'W') return tmp;
  70.                          else d = c = '?';
  71.                      }
  72.                      if (a == 'W' && b == 'B'){
  73.                          if (c == 'B' || d == 'B') return tmp;
  74.                          else c = d = '?';
  75.                      }
  76.                  }
  77.                  replace (opt[i+].begin(), opt[i+].end(), '?', 'B');
  78.              }
  79.              return opt;
  80.          }
  81.  
  82.  // BEGIN CUT HERE
  83.      public:
  84.      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(); }
  85.      private:
  86.      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(); }
  87.      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; } }
  88.      void test_case_0() { string Arr0[] = {"WWWWWWW",
  89.   "WWWWWWB",
  90.   "BBBBBWW"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"WWWWWWW", "WWWWWWB", "BBBBBBB" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); verify_case(, Arg1, makeProgram(Arg0)); }
  91.      void test_case_1() { string Arr0[] = {"BBBBB",
  92.   "WBWBW"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"BBBBB", "WWBWB" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); verify_case(, Arg1, makeProgram(Arg0)); }
  93.      void test_case_2() { string Arr0[] = {"BBBB",
  94.   "BBBB",
  95.   "BBWB",
  96.   "WWBB",
  97.   "BWBB"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = { }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); verify_case(, Arg1, makeProgram(Arg0)); }
  98.      void test_case_3() { string Arr0[] = {"WWBBBBW",
  99.   "BWBBWBB",
  100.   "BWBBWBW",
  101.   "BWWBWBB"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); string Arr1[] = {"WWBBBBW", "BBBBBWB", "BBBBBBB", "BBBWBBB" }; vector <string> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); verify_case(, Arg1, makeProgram(Arg0)); }
  102.  
  103.  // END CUT HERE
  104.  
  105.  };
  106.  
  107.  // BEGIN CUT HERE
  108.  int main()
  109.  {
  110.  //    freopen( "a.out" , "w" , stdout );
  111.      Algrid ___test;
  112.      ___test.run_test(-);
  113.         return ;
  114.  }
  115.  // END CUT HERE

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