动态规划——最长公共子序列（LCS）

/** * @brief longest common subsequence(LCS)  * @author An * @data  2013.8.26                                                                  **/#include <iostream>#include <string>using namespace std;enum Direction { Zero, LeftUp, Up, Left };static int m;    // length of the first sequencestatic int n;     // length of the second sequencestatic int **c;  // the length for every subsequencestatic Direction **b;  // record the pathvoid LCS_Length( string x, string y );void Print_LCS( string x, int i, int j );void PrintTable();int main(){string x = "ABCBDAB";string y = "BDCABA";LCS_Length( x, y );Print_LCS( x, m, n );cout << endl;PrintTable();}void LCS_Length( string x, string y ){// initialize two tablesm = x.length();n = y.length();c = new int*[m + 1];b = new Direction*[m + 1];for ( int i = 0; i <= m; ++i ){c[i] = new int[n + 1];b[i] = new Direction[n + 1];}// zero row and columnfor ( int i = 0; i <= m; ++i ){c[i][0] = 0;b[i][0] = Zero;}for ( int j = 1; j <= n; ++j ){c[0][j] = 0;b[0][j] = Zero;}// calculate the two tables from bottom to topfor ( int i = 1; i <= m; ++i ){for ( int j = 1; j <= n; ++j ){if ( x[i - 1] == y[j - 1] ){c[i][j] = c[i - 1][j - 1] + 1;b[i][j] = LeftUp;}else if ( c[i - 1][j] >= c[i][j - 1] ){c[i][j] = c[i - 1][j];b[i][j] = Up;}else{c[i][j] = c[i][j - 1];b[i][j] = Left;}} // end for} //end for} // end LCS_Length()void Print_LCS( string x, int i, int j ){if ( i == 0 || j == 0 ){return;}if ( b[i][j] == LeftUp ){Print_LCS( x, i - 1, j - 1 );cout << x[i - 1];}else if ( b[i][j] == Up ){Print_LCS( x, i - 1, j );}else{Print_LCS( x, i, j - 1 );}}void PrintTable(){for ( int i = 0; i <= m; ++i ){for ( int j = 0; j <= n; ++j ){cout << c[i][j] << " ";}cout << endl;}cout << endl;for ( int i = 0; i <= m; ++i ){for ( int j = 0; j <= n; ++j ){cout << b[i][j] << " ";}cout << endl;}}