动态规划之矩阵连乘

/* Matrix.h */

#pragma once
#ifndef MATRIX_H
#define MATRIX_H

class Matrix
{
public:
    Matrix();         //构造函数
    ~Matrix();        //析构函数
    bool Run();       //运行接口函数
private:
    int W;         //记录矩阵的个数
    int **m;       //存放最优值，即最小运算量
    int **s;       //断开位置
    int *p;        //存放

    bool Input();  //处理输入
    bool MatrixChain();//计算最优值算法
    void Traceback(int i, int j, int **s);   //输出矩阵加括号的方式
};

#endif

/* Matrix.c */

#define N 50
#include <iostream>
#include <stdlib.h>
#include "Matrix.h"

//构造函数，作变量初始化工作，为指针分配内存空间
Matrix::Matrix()
{
    W = 0;
    m = new int*[N];
    s = new int*[N];
    for (int i = 0; i<N; i++)
    {
        m[i] = new int[N];
        s[i] = new int[N];
    }
    p = new int[N];
}

//析构函数，释放内存
Matrix::~Matrix()
{
    for (int i = 0; i<N; i++)
    {
        delete[]m[i];
        delete[]s[i];
    }
    delete[]m;
    delete[]s;
    delete[]p;
}

//处理键盘输入
bool Matrix::Input()
{
    using namespace std;
    int w;
    cout << "矩阵个数：";
    cin >> w;
    W = w;
    cout << "输入矩阵A1维数" << "：";
    cin >> p[0] >> p[1];
    for (int i = 2; i <= W; i++)
    {
        int m = p[i - 1];
        cout << "输入矩阵A" << i << "维数：";
        cin >> p[i - 1] >> p[i];
        if (p[i - 1] != m)
        {
            cout << endl << "维数不对，矩阵不可乘！" << endl;
            exit(1);
        }
        //cout<<endl;
    }
    if (p != NULL)
        return true;
    else
        return false;
}

//计算最优值算法
bool Matrix::MatrixChain()
{
    if (NULL == p)
        return false;
    for (int i = 1; i <= W; i++)
        m[i][i] = 0;
    for (int r = 2; r <= W; r++)
        for (int i = 1; i <= W - r + 1; i++)
        {
            int j = i + r - 1;
            m[i][j] = m[i + 1][j] + p[i - 1] * p[i] * p[j];
            s[i][j] = i;
            for (int k = i + 1; k<j; k++)
            {
                int t = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j];
                if (t<m[i][j])
                {
                    m[i][j] = t;
                    s[i][j] = k;
                }
            }
        }
    return true;
}

//输出矩阵结合方式，加括号
void Matrix::Traceback(int i, int j, int **s)
{
    using namespace std;
    if (i == j)
    {
        cout << "A" << i;
    }
    else if (i + 1 == j)
    {
        cout << "(A" << i << "A" << j << ")";
    }
    else
    {
        cout << "(";
        Traceback(i, s[i][j], s);
        Traceback(s[i][j] + 1, j, s);
        cout << ")";
    }
}

bool Matrix::Run()
{
    using namespace std;
    if (Matrix::Input())
    {
        if (Matrix::MatrixChain())
        {
            Matrix::Traceback(1, W, s);
            cout << endl;
            return true;
        }
        else
            return false;
    }
    else
        return false;
}

/* Main.c */

#include "Matrix.h"

int main()
{
    Matrix matrix;
    matrix.Run();
    return 0;
}

作者：耑新新，发布于  博客园

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