矩阵链乘法

动态规划之矩阵链乘法。。。

#include <iostream>

using namespace std;

int columns[] = {30, 35, 15, 5, 10, 20, 25};
const int size = sizeof columns / sizeof *columns;

int m[size][size];
int s[size][size];

void getChainOrder(int *columns, int size)
{
	if (columns == NULL || size <= 0)
		return;

	for (int i = 1; i <= size; i++)
		m[i][i] = 0;

	for (int l = 2; l <= size; l++)
	{
		for (int i = 1; i <= size - l + 1; i++)
		{
			int j = i + l - 1;
			m[i][j] = 65535;
			for (int k = i; k <= j; k++)
			{
				int q = m[i][k] + m[k + 1][j] + columns[i - 1] * columns[k] * columns[j];
				if (q < m[i][j])
				{
					m[i][j] = q;
					s[i][j] = k;
				}
			}
		}
	}
}

void print()
{
	for (int i = 1; i <= size - 1; i++)
	{
		for (int j = 1; j <= size - 1; j++)
			cout << m[i][j] << '\t';
		cout << endl;
	}
}

void printResult(int i = 1, int j = size)
{
	if (i == j)
		cout << "A" << i;
	else
	{
		cout << "(";
		printResult(i, s[i][j]);
		printResult(s[i][j] + 1, j);
		cout << ")";
	}
}

void main()
{
	cout << "size = " << size << endl;
	getChainOrder(columns, size);
	print();
	cout << "m[0][5] = " << m[1][6] << endl;
	printResult();
}