用 C++ 设计连乘的n个整数矩阵M1..Mn,各矩阵维数在 1-200 之间,矩阵个数n在5-180 之间,矩阵元素为至多为 2 位非负整数,各矩阵和结果矩阵以文本文件形式存放,文件名为 M1...Mn和M,并输出最佳乘法次序、最少数乘次数最佳连乘花费的时间给出完整的 C++ 代码和注释
//第一版
#include <iostream>
#include <fstream>
#include <vector>
#include <ctime>
#include <cstdlib>
#include <climits>
#include <chrono>
using namespace std;
struct Matrix {
int rows;
int cols;
};
// 生成随机整数矩阵并保存到文件
void RandomMatrix(int n) {
srand(time(nullptr));
for (int i = 1; i <= n; i++) {
int rows = rand() % 200 + 1;
int cols = rand() % 200 + 1;
string filename = "M" + to_string(i) + ".txt";
ofstream matrixFile(filename);
matrixFile << rows << " " << cols << endl;
for (int r = 0; r < rows; r++) {
for (int c = 0; c < cols; c++) {
matrixFile << rand() % 100 << " ";
}
matrixFile << endl;
}
matrixFile.close();
}
}
// 计算最佳乘法次序和最少数乘次数
void MatrixOrder(const vector<Matrix>& matrices, vector<vector<int>>& m, vector<vector<int>>& s) {
int n = matrices.size();
for (int i = 1; i < n; i++) {
m[i][i] = 0;
}
for (int chainLen = 2; chainLen < n; chainLen++) {
for (int i = 1; i < n - chainLen + 1; i++) {
int j = i + chainLen - 1;
m[i][j] = INT_MAX;
for (int k = i; k < j; k++) {
int cost = m[i][k] + m[k + 1][j] + matrices[i - 1].rows * matrices[k].cols * matrices[j].cols;
if (cost < m[i][j]) {
m[i][j] = cost;
s[i][j] = k;
}
}
}
}
}
// 执行矩阵乘法
vector<vector<int>> MatrixMulti(const vector<Matrix>& matrices, const vector<vector<int>>& s) {
int n = matrices.size();
vector<vector<vector<int>> > dp(n, vector<vector<int>>(n, vector<int>(2, 0)));
for (int i = 1; i < n; i++) {
dp[i][i][0] = matrices[i - 1].rows;
dp[i][i][1] = matrices[i - 1].cols;
}
for (int len = 2; len < n; len++) {
for (int i = 1; i <= n - len; i++) {
int j = i + len - 1;
int k = s[i][j];
dp[i][j][0] = dp[i][k][0] * dp[k + 1][j][0];
dp[i][j][1] = dp[k + 1][j][1];
}
}
vector<vector<int>> resultMatrix(n - 1, vector<int>(n - 1));
for (int i = 1; i < n; i++) {
resultMatrix[i - 1] = dp[i][n - 1];
}
return resultMatrix;
}
// 输出最佳乘法次序
void PrintOpt(const vector<vector<int>>& s, int i, int j, ofstream& output) {
if (i == j) {
output << "M" << i;
} else {
output << "(";
PrintOpt(s, i, s[i][j], output);
PrintOpt(s, s[i][j] + 1, j, output);
output << ")";
}
}
int main() {
int n;
cout << "请输入矩阵的个数 (5-180之间): ";
cin >> n;
if (n < 5 || n > 180) {
cout << "矩阵个数不在允许范围内。" << endl;
return 1;
}
// 生成随机整数矩阵并保存到文件
RandomMatrix(n);
vector<Matrix> matrices(n);
for (int i = 0; i < n; i++) {
string filename = "M" + to_string(i + 1) + ".txt";
ifstream matrixFile(filename);
matrixFile >> matrices[i].rows >> matrices[i].cols;
matrixFile.close();
}
vector<vector<int>> m(n, vector<int>(n, 0));
vector<vector<int>> s(n, vector<int>(n, 0));
// 计算最佳乘法次序和最少数乘次数
MatrixOrder(matrices, m, s);
// 计算乘法操作并输出结果
auto start = chrono::high_resolution_clock::now();
vector<vector<int>> resultMatrix = MatrixMulti(matrices, s);
auto end = chrono::high_resolution_clock::now();
auto duration = chrono::duration_cast<chrono::microseconds>(end - start);
// 输出最佳乘法次序和结果到文件M.txt
ofstream output("M.txt");
if (output.is_open()) {
output << "最佳乘法次序: ";
PrintOpt(s, 1, n - 1, output);
output << endl;
output << "最少数乘次数: " << m[1][n - 1] << endl;
output << "最终结果矩阵:\n";
for (int i = 0; i < n - 1; i++) {
for (int j = 0; j < n - 1; j++) {
output << resultMatrix[i][j] << " ";
}
output << endl;
}
output << "最佳连乘花费的时间 (微秒): " << duration.count() << " μs" << endl;
output.close();
cout << "最佳乘法次序、结果和计算时间已保存到M.txt文件中。" << endl;
} else {
cout << "无法打开文件以保存结果。" << endl;
}
return 0;
}
//第二版
#include <iostream>
#include <fstream>
#include <vector>
#include <ctime>
#include <cstdlib>
#include <climits>
#include <chrono>
#include <filesystem>
using namespace std;
namespace fs = std::filesystem;
struct Matrix {
int rows;
int cols;
};
// 生成随机整数矩阵并保存到文件
void RandomMatrix(int n) {
fs::create_directory("matrices");
srand(time(nullptr));
for (int i = 1; i <= n; i++) {
int rows = rand() % 200 + 1;
int cols = rand() % 200 + 1;
std::string filename = "matrices/M" + std::to_string(i) + ".txt";
std::ofstream matrixFile(filename);
matrixFile << rows << " " << cols << std::endl;
for (int r = 0; r < rows; r++) {
for (int c = 0; c < cols; c++) {
int randomValue = (rand() % 99) + 1; // 生成1到99之间的随机整数
matrixFile << randomValue << " ";
}
matrixFile << std::endl;
}
matrixFile.close();
}
}
// 计算最佳乘法次序和最少数乘次数
void MatrixOrder(const vector<Matrix>& matrices, vector<vector<int>>& m, vector<vector<int>>& s) {
int n = matrices.size();
for (int i = 1; i < n; i++) {
m[i][i] = 0;
}
for (int chainLen = 2; chainLen < n; chainLen++) {
for (int i = 1; i < n - chainLen + 1; i++) {
int j = i + chainLen - 1;
m[i][j] = INT_MAX;
for (int k = i; k < j; k++) {
int cost = m[i][k] + m[k + 1][j] + matrices[i - 1].rows * matrices[k].cols * matrices[j].cols;
if (cost < m[i][j]) {
m[i][j] = cost;
s[i][j] = k;
}
}
}
}
}
// 执行矩阵乘法
vector<vector<int>> MatrixMulti(const vector<Matrix>& matrices, const vector<vector<int>>& s) {
int n = matrices.size();
vector<vector<vector<int>> > dp(n, vector<vector<int>>(n, vector<int>(2, 0)));
for (int i = 1; i < n; i++) {
dp[i][i][0] = matrices[i - 1].rows;
dp[i][i][1] = matrices[i - 1].cols;
}
for (int len = 2; len < n; len++) {
for (int i = 1; i <= n - len; i++) {
int j = i + len - 1;
int k = s[i][j];
dp[i][j][0] = dp[i][k][0] * dp[k + 1][j][0];
dp[i][j][1] = dp[k + 1][j][1];
}
}
vector<vector<int>> resultMatrix(n - 1, vector<int>(n - 1));
for (int i = 1; i < n; i++) {
resultMatrix[i - 1] = dp[i][n - 1];
}
return resultMatrix;
}
// 输出最佳乘法次序
void PrintOpt(const vector<vector<int>>& s, int i, int j, ofstream& output) {
if (i == j) {
output << "M" << i;
} else {
output << "(";
PrintOpt(s, i, s[i][j], output);
PrintOpt(s, s[i][j] + 1, j, output);
output << ")";
}
}
int main() {
int n;
std::cout << "请输入矩阵的个数 (5-180之间): ";
std::cin >> n;
if (n < 5 || n > 180) {
std::cout << "矩阵个数不在允许范围内。" << std::endl;
return 1;
}
// 生成随机整数矩阵并保存到文件夹
RandomMatrix(n);
std::vector<Matrix> matrices(n);
for (int i = 0; i < n; i++) {
std::string filename = "matrices/M" + std::to_string(i + 1) + ".txt";
std::ifstream matrixFile(filename);
matrixFile >> matrices[i].rows >> matrices[i].cols;
matrixFile.close();
}
std::vector<std::vector<int>> m(n, std::vector<int>(n, 0));
std::vector<std::vector<int>> s(n, std::vector<int>(n, 0));
// 计算最佳乘法次序和最少数乘次数
MatrixOrder(matrices, m, s);
// 计算乘法操作并输出结果
auto start = std::chrono::high_resolution_clock::now();
std::vector<std::vector<int>> resultMatrix = MatrixMulti(matrices, s);
auto end = std::chrono::high_resolution_clock::now();
auto duration = std::chrono::duration_cast<std::chrono::microseconds>(end - start);
// 输出最佳乘法次序和结果到文件M.txt
std::ofstream output("matrices/M.txt");
if (output.is_open()) {
output << "最佳乘法次序: ";
PrintOpt(s, 1, n - 1, output);
output << std::endl;
output << "最少数乘次数: " << m[1][n - 1] << std::endl;
output << "最终结果矩阵:\n";
for (int i = 0; i < n - 1; i++) {
for (int j = 0; j < n - 1; j++) {
output << resultMatrix[i][j] << " ";
}
output << std::endl;
}
output << "最佳连乘花费的时间 (微秒): " << duration.count() << " μs" << std::endl;
output.close();
std::cout << "最佳乘法次序、结果和计算时间已保存到matrices文件夹中的M.txt文件中。" << std::endl;
} else {
std::cout << "无法打开文件以保存结果。" << std::endl;
}
return 0;
}