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#include <iostream>
#include <fstream>
#include <eigen3/Eigen/Dense>
#include <io.h>
#include <fcntl.h>
#include <chrono>
using std::cout, std::wcout, std::endl;
using std::chrono::high_resolution_clock,
std::chrono::duration_cast, std::chrono::microseconds;
using Eigen::Matrix, Eigen::MatrixXi, Eigen::Dynamic;
using MatrixXXi = Matrix<MatrixXi, Dynamic, Dynamic>;
using MatrixXch = Matrix<wchar_t, Dynamic, Dynamic>;
const int BIT1 = 1 << 0, BIT2 = 1 << 1;
std::wostream &operator<<(std::wostream &o, const MatrixXch &m) {
for (int i = 0; i < m.rows(); ++i) {
for (int j = 0; j < m.cols(); ++j) {
o << m(i, j);
}
o << endl;
}
return o;
}
int main() {
// 从文件中读取价值数据，并存入价值矩阵V中
std::ifstream in_file{"input.txt"};
int n;
in_file >> n;
const int nm = n - 1;
MatrixXi V = MatrixXi::Zero(n, n);
{
int i, j, v;
in_file >> i >> j >> v;
while (i != 0 && j != 0 && v != 0) {
V(i - 1, j - 1) = v;
in_file >> i >> j >> v;
}
}
in_file.close();
// 初始化缓存价值矩阵EV，以及方向记录矩阵D
MatrixXXi EV{n, n}, D{n, n};
for (int x1 = 0; x1 < n; ++x1) {
for (int y1 = 0; y1 < n; ++y1) {
EV(x1, y1) = MatrixXi::Zero(n, n);
D(x1, y1) = MatrixXi::Zero(n, n);
if (x1 == 0) {
D(x1, y1).setConstant(BIT1);
}
for (int y2 = 0; y2 < n; ++y2) {
D(x1, y1)(0, y2) |= BIT2;
}
}
}
// 更新函数
int mv = 0;
auto update = [&V, &EV, &D, &mv](int x1, int y1, int x2, int y2, int v, int d) {
v += V(x1, y1);
if (x1 != x2 || y1 != y2) {
v += V(x2, y2);
}
if (v > EV(x1, y1)(x2, y2)) {
EV(x1, y1)(x2, y2) = v;
D(x1, y1)(x2, y2) = d;
}
if (v > mv) {
mv = v;
}
};
// 遍历整个矩阵
auto time_start = high_resolution_clock::now();
EV(0, 0)(0, 0) = V(0, 0);
for (int s = 0; s < nm + nm; ++s) {
int op = 0, ed = s;
if (s > nm) {
op = s - nm, ed = nm;
}
for (int x1 = op; x1 <= ed; ++x1) {
for (int x2 = op; x2 <= ed; ++x2) {
int y1 = s - x1;
int y2 = s - x2;
int v = EV(x1, y1)(x2, y2);
if (x1 != nm) {
if (x2 != nm) update(x1 + 1, y1, x2 + 1, y2, v, 0);
if (y2 != nm) update(x1 + 1, y1, x2, y2 + 1, v, BIT2);
}
if (y1 != nm) {
if (x2 != nm) update(x1, y1 + 1, x2 + 1, y2, v, BIT1);
if (y2 != nm) update(x1, y1 + 1, x2, y2 + 1, v, BIT1 | BIT2);
}
}
}
}
auto time_stop = high_resolution_clock::now();
// 计算花费时间
auto duration = duration_cast<microseconds>(time_stop - time_start);
cout << "Time cost: " << duration.count() << "ms" << endl;
// 将结果写入文件中
std::ofstream out_file{"output.txt"};
out_file << EV(nm, nm)(nm, nm);
out_file.close();
// 还原路线图
wchar_t wh = L'◽', bl = L'◾';
MatrixXch M1{n, n}, M2{n, n};
M1.setConstant(wh), M2.setConstant(wh);
int x1 = nm, y1 = nm, x2 = nm, y2 = nm;
while (x1 != 0 || y1 != 0) {
M1(x1, y1) = bl, M2(x2, y2) = bl;
int d = D(x1, y1)(x2, y2);
if (d & BIT1) {
--y1;
} else {
--x1;
}
if (d & BIT2) {
--y2;
} else {
--x2;
}
}
M1(x1, y1) = bl, M2(x2, y2) = bl;
// 配置使C++可以输出Unicode
constexpr char cp_utf16le[] = ".1200"; // UTF-16 little-endian locale.
setlocale(LC_ALL, cp_utf16le);
_setmode(_fileno(stdout), _O_WTEXT);
// 输出路线图
wcout << "Path 1:" << endl << M1 <<
"Path 2:" << endl << M2;
}
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