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 6

using 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+1

				if ( 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;

}