算法导论-矩阵链乘法

代码：

#include <iostream>
using namespace std;

const int N = 6;
const int MaxNum = 0x3f3f3f3f;

int p[N + 1] = {30,35,15,5,10,20,25};
int m[N + 1][N + 1] = {0};
int s[N + 1][N + 1] = {0};

int MatrixChainOrder()
{
	//初始化-处理区间中元素为1的区间
	for (int i = 1;i <= N;i++)
	{
		m[i][i] = 0;
	}
	//递推
	for (int len = 2;len <= N;len++)//区间长度
	{
		for (int i = 1;i <= N - len + 1;i++)//每种区间的起点
		{
			int j = i + len - 1; //每种区间的终点
			
			m[i][j] = MaxNum;
			for (int k = i;k < j;k++)
			{
				int cost = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j];
				if (m[i][j] > cost)
				{
					m[i][j] = cost;
					s[i][j] = k;
				}
			}
		}
	}
	return m[1][N];
}

//x和y表示区间的起点和终点
void PrintOptimalParens(int x,int y)
{
	if (x == y) //区间起点 = 终点时，表示区间中只有一个元素
	{
		cout<<"A"<<x;
		return;
	}
	else
	{
		cout<<"(";
		PrintOptimalParens(x,s[x][y]);
		PrintOptimalParens(s[x][y] + 1,y);
		cout<<")";
	}

}

int main()
{
	cout<<MatrixChainOrder()<<endl;
	PrintOptimalParens(1,N);
	system("pause");
	return 1;
}