void MatrixChainSolver::editResult(const vector<vector<Record>>& records, int b, int e, string& str) const
{
if (b == e)
str += string("M") + boost::lexical_cast<string>(b);
else
{
str += "(";
editResult(records, b, records[b][e].middle, str);
editResult(records, records[b][e].middle + 1, e, str);
str += ")";
}
}
long MatrixChainSolver::solve(string& format) const
{
auto size = matrices_.size();
vector<vector<Record>> records;
for (int i = 0; i < size; ++i)
{
vector<Record> temp;
auto r = Record(i);
for (int i = 0; i < size; ++i)
temp.push_back(r);
records.push_back(temp);
}
/*
* 加入第i个矩阵Ai后，最小的cost为下面情况之一
Min(A1A2...Ai-1) * Min(Ai)
Min(A1A2...Ai-2) * Min(Ai-1Ai)
...
Min(A1A2) * Min(A3A4...Ai)
Min(A1) * Min(A2A3...Ai)
* 而Min(AjAj+1...Ai)则又可以由Min(Aj...Ak) * Min(Ak...Ai)得到
*/
for (int i = 1; i < size; ++i) // 添加第i个矩阵
{
for (int j = i - 1; j >= 0; --j) // 计算records[j][i]的最小值
{
auto minCost = records[j][i - 1].cost + records[i][i].cost
+ matrices_[j]->nRow_ * matrices_[i-1]->nColumn_ * matrices_[i]->nColumn_;
auto minMiddle = i - 1;
for (int k = i - 2; k >= j; --k)
{
auto temp = records[j][k].cost + records[k + 1][i].cost
+ matrices_[j]->nRow_ * matrices_[k]->nColumn_ * matrices_[i]->nColumn_;
if (minCost > temp)
{
minCost = temp;
minMiddle = k;
}
}
records[j][i].cost = minCost;
records[j][i].middle = minMiddle;
}
}
/*
* 编辑计算顺序
*/
editResult(records, 0, size - 1, format);
return records[0][size - 1].cost;
}
MainWindow::MainWindow(QWidget *parent) :
QMainWindow(parent),
ui(new Ui::MainWindow)
{
ui->setupUi(this);
ui->operation->addItem("+");
ui->operation->addItem("-");
ui->operation->addItem("*");
ui->operation->addItem("/");
connect(ui->argument1, SIGNAL(valueChanged(int)), this, SLOT(editResult()));
connect(ui->operation, SIGNAL(currentTextChanged(QString)), this, SLOT(editResult()));
connect(ui->argument2, SIGNAL(valueChanged(int)), this, SLOT(editResult()));
}
