SRM 504(2-1000pt)

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)

 For i =  to H-:
     For j =  to W-:
         //Get the current colors of cells (i,j) and (i,j+1)
         A = Color(i,j) , B = Color(i,j+)

         If (A,B) == (White, White) Then:
              Do nothing.
         EndIf
         If (A,B) == (Black, White) Then:
              Repaint cells (i+,j) and (i+,j+) Black.
         EndIf
         If (A,B) == (White, Black) Then:
              Repaint cells (i+,j) and (i+,j+) White.
         EndIf
         if (A,B) == (Black, Black) Then:
              Swap the colors in cells (i+,j) and (i+,j+).
         EndIf
     EndFor
 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：

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

  */
 // END CUT HERE
 #line 11 "Algrid.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 CLR(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 zero(x) (((x)>0?(x):-(x))<eps)
 #define out(x) cout<<#x<<":"<<(x)<<endl
 #define tst(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 long long int64;

 const double eps = 1e-;
 const double PI = atan(1.0)*;
 const int maxint = ;

 int n, all, len;
 bool flag;
 int a[], ans[];

 int change(int x, int y)
 {
     if (x == -) return -;

     int ta[], tb[];
     int idxa = , idxb = ;
     for (int i = ; i < len; ++ i){
         ta[idxa++] = x & ;
         x >>= ;
         tb[idxb++] = y & ;
         y >>= ;
     }
     for (int i = len-; i; -- i){
         if (!ta[i] && ta[i-]) tb[i] = tb[i-] = ;
         if (ta[i] && !ta[i-]) tb[i] = tb[i-] = ;
         if (!ta[i] && !ta[i-]) swap(tb[i], tb[i-]);
     }
     int ret = ;
     for (int i = len-; i >= ; -- i)
         ret += (tb[i] << i);
     return ret;
 }

 void DFS (int x)
 {
     if (x == n){
         flag = ;
         return;
     }

     for (int i = ; i < all; ++ i)
         if (!flag && change(a[x-], i) == a[x]){
             ans[x] = i;
             DFS (x+);
             if (!flag) ans[x] = -;
         }
 }

 class Algrid
 {
     public:
         vector <string> makeProgram(vector <string> A){
             len = A[].size();
             n = A.size(); all =  << len;
             for (int i = ; i < n; ++ i){
                 int tmp = ;
                 for (int j = len-, k = ; j >= ; -- j, ++ k)
                     if (A[i][j] == 'W'){
                         tmp += ( << k);
                     }
                 a[i] = tmp;
             }

             CLR1 (ans);
             ans[] = a[];

             flag = ;
             DFS ();

             vector<string> ret; ret.clear();
             string tmp;
             for (int i = ; i < n; ++ i){
                 if (ans[i] == -){
                     ret.clear(); return ret;
                 }

                 tmp.clear();
                 for (int j = len-; j >= ; -- j){
                     if (ans[i] & (<<j)) tmp.PB ('W');
                     else tmp.PB('B');
                 }
                 ret.PB (tmp);
             }
             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(); }
     //void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0();}
     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() { 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)); }
     void test_case_1() { string Arr0[] = {"BBBBB",
  "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)); }
     void test_case_2() { string Arr0[] = {"BBBB",
  "BBBB",
  "BBWB",
  "WWBB",
  "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)); }
     void test_case_3() { string Arr0[] = {"WWBBBBW",
  "BWBBWBB",
  "BWBBWBW",
  "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)); }

 // END CUT HERE

 };

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

法二：

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

  */
 // END CUT HERE
 #line 11 "Algrid.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 CLR(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 zero(x) (((x)>0?(x):-(x))<eps)
 #define out(x) cout<<#x<<":"<<(x)<<endl
 #define tst(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 long long int64;

 const double eps = 1e-;
 const double PI = atan(1.0)*;
 const int maxint = ;

 class Algrid
 {
     public:
         vector <string> makeProgram(vector <string> opt){
             vector<string> tmp; tmp.clear();
             int n = opt.size(), m = opt[].size();
             for (int i = n-; i >= ; -- i){
                 for (int j = m-; j >= ; -- j){
                     char a = opt[i][j], b = opt[i][j+];
                     char &c = opt[i+][j], &d = opt[i+][j+];

                     if (a == 'B' && b == 'B')
                         swap (c, d);
                     if (a == 'B' && b == 'W'){
                         if (c == 'W' || d == 'W') return tmp;
                         else d = c = '?';
                     }
                     if (a == 'W' && b == 'B'){
                         if (c == 'B' || d == 'B') return tmp;
                         else c = d = '?';
                     }
                 }
                 replace (opt[i+].begin(), opt[i+].end(), '?', 'B');
             }
             return opt;
         }

 // 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() { string Arr0[] = {"WWWWWWW",
  "WWWWWWB",
  "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)); }
     void test_case_1() { string Arr0[] = {"BBBBB",
  "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)); }
     void test_case_2() { string Arr0[] = {"BBBB",
  "BBBB",
  "BBWB",
  "WWBB",
  "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)); }
     void test_case_3() { string Arr0[] = {"WWBBBBW",
  "BWBBWBB",
  "BWBBWBW",
  "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)); }

 // END CUT HERE

 };

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