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

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