动态规划——矩阵链相乘

/** * @brief MatrixChainMultiplication  Algorithm 15.2 * @author An * @data  2013.8.25                                                                  **/#include <iostream>#include <limits>#define  N 6using namespace std;static int **m = new int*[N];static int **s = new int*[N];// static int *p = new int[N];void MatrixChainOrder( int *p ){for ( int i = 0; i != N; ++i ){m[i] = new int[N];s[i] = new int[N];}for ( int i = 0; i != N; ++i ){for ( int j = 0; j != N; ++j ){m[i][j] = 0;s[i][j] = 0;}}for ( int i = 0; i != N; ++i ){m[i][i] = 0;}for ( int l = 2; l <= N; ++l ){for ( int i = 0; i != N - l + 1; ++i ){int j = i + l - 1;m[i][j] = INT_MAX;for ( int k = i; k != j; ++k ){int q = m[i][k] + m[k + 1][j] + p[i] * p[k + 1] * p[j + 1]; // p+1if ( q < m[i][j] ){m[i][j] = q;s[i][j] = k;}}}}}void PrintOptimalParens( int **ss, int i, int j ){if ( i == j ){cout << "A" << i + 1;}else{cout << "(";PrintOptimalParens( ss, i, s[i][j] );PrintOptimalParens( ss, s[i][j] + 1, j );cout << ")";}}void PrintMatrix( int **Ma, int length ){for ( int i = 0; i != length; ++i ){for ( int j = 0; j != length; ++j ){cout << Ma[i][j] << " ";}cout << endl;}cout << endl;}int main(){int *p = new int[N + 1];int a[] = { 30, 35, 15, 5, 10, 20, 25 };for ( int i = 0; i != N + 1; ++i ){p[i] = a[i];}MatrixChainOrder( p );PrintOptimalParens( s, 0, N - 1);cout << endl;PrintMatrix( m, N );PrintMatrix( s, N );return 0;}