我一直在尝试使用C++11实现Dijkstra算法,以便处理任意大小的矩阵。具体来说,我想解决Project Euler上83号问题。
我似乎总是遇到这样的情况:与当前节点相邻的每个节点都已经被访问过,如果我正确理解算法的话,这种情况是不应该发生的。
我试图在调试器中查找问题,并多次重新阅读代码,但我不知道哪里出了问题。
以下是我目前的进展:
我似乎总是遇到这样的情况:与当前节点相邻的每个节点都已经被访问过,如果我正确理解算法的话,这种情况是不应该发生的。
我试图在调试器中查找问题,并多次重新阅读代码,但我不知道哪里出了问题。
以下是我目前的进展:
#include <iostream>
#include <fstream>
#include <cstdlib>
#include <vector>
#include <set>
#include <tuple>
#include <cstdint>
#include <cinttypes>
typedef std::tuple<size_t, size_t> Index;
std::ostream& operator<<(std::ostream& os, Index i)
{
os << "(" << std::get<0>(i) << ", " << std::get<1>(i) << ")";
return os;
}
template<typename T>
class Matrix
{
public:
Matrix(size_t i, size_t j):
n(i),
m(j),
xs(i * j)
{}
Matrix(size_t n, size_t m, const std::string& path):
n(n),
m(m),
xs(n * m)
{
std::ifstream mat_in {path};
char c;
for (size_t i = 0; i < n; ++i) {
for (size_t j = 0; j < m - 1; ++j) {
mat_in >> (*this)(i,j);
mat_in >> c;
}
mat_in >> (*this)(i,m - 1);
}
}
T& operator()(size_t i, size_t j)
{
return xs[n * i + j];
}
T& operator()(Index i)
{
return xs[n * std::get<0>(i) + std::get<1>(i)];
}
T operator()(Index i) const
{
return xs[n * std::get<0>(i) + std::get<1>(i)];
}
std::vector<Index> surrounding(Index ind) const
{
size_t i = std::get<0>(ind);
size_t j = std::get<1>(ind);
std::vector<Index> is;
if (i > 0)
is.push_back(Index(i - 1, j));
if (i < n - 1)
is.push_back(Index(i + 1, j));
if (j > 0)
is.push_back(Index(i, j - 1));
if (j < m - 1)
is.push_back(Index(i, j + 1));
return is;
}
size_t rows() const { return n; }
size_t cols() const { return m; }
private:
size_t n;
size_t m;
std::vector<T> xs;
};
/* Finds the minimum sum of the weights of the nodes along a path from 1,1 to n,m using Dijkstra's algorithm modified for matrices */
int64_t shortest_path(const Matrix<int>& m)
{
Index origin(0,0);
Index current { m.rows() - 1, m.cols() - 1 };
Matrix<int64_t> nodes(m.rows(), m.cols());
std::set<Index> in_path;
for (size_t i = 0; i < m.rows(); ++i)
for (size_t j = 0; j < m.cols(); ++j)
nodes(i,j) = INTMAX_MAX;
nodes(current) = m(current);
while (1) {
auto is = m.surrounding(current);
Index next = origin;
for (auto i : is) {
if (in_path.find(i) == in_path.end()) {
nodes(i) = std::min(nodes(i), nodes(current) + m(i));
if (nodes(i) < nodes(next))
next = i;
}
}
in_path.insert(current);
current = next;
if (current == origin)
return nodes(current);
}
}
int64_t at(const Matrix<int64_t>& m, const Index& i) { return m(i); }
int at(const Matrix<int>& m, const Index& i) { return m(i); }
int main()
{
Matrix<int> m(80,80,"mat.txt");
printf("%" PRIi64 "\n", shortest_path(m));
return 0;
}