mirror of
https://github.com/mfocko/blog.git
synced 2024-09-20 10:26:55 +02:00
136 lines
3.8 KiB
C++
136 lines
3.8 KiB
C++
#ifndef _BF_HPP
|
||
#define _BF_HPP
|
||
|
||
#include <cassert>
|
||
#include <iostream>
|
||
#include <utility>
|
||
#include <vector>
|
||
|
||
#include "graph.hpp"
|
||
|
||
static auto _check_vertex(const graph& g,
|
||
std::vector<std::vector<int>>& distances, int v,
|
||
bool check_only = false) -> bool {
|
||
bool improvement_found = false;
|
||
|
||
// unpack the vertex coordinates
|
||
int y = v / g.width();
|
||
int x = v % g.width();
|
||
|
||
// skip the cells we cannot reach
|
||
if (distances[y][x] == graph::unreachable()) {
|
||
return false;
|
||
}
|
||
|
||
// go through the neighbours
|
||
auto u = std::make_pair(x, y);
|
||
for (const auto& [dx, dy] : DIRECTIONS) {
|
||
auto v = std::make_pair(x + dx, y + dy);
|
||
auto cost = g.cost(u, v);
|
||
|
||
// if we can move to the cell and it's better, relax¹ it
|
||
if (cost != graph::unreachable() &&
|
||
distances[y][x] + cost < distances[y + dy][x + dx]) {
|
||
if (check_only) {
|
||
return true;
|
||
}
|
||
|
||
distances[y + dy][x + dx] = distances[y][x] + cost;
|
||
improvement_found = true;
|
||
}
|
||
}
|
||
|
||
return improvement_found;
|
||
}
|
||
|
||
auto bf(const graph& g, const vertex_t& source, const vertex_t& destination)
|
||
-> int {
|
||
// ‹source› must be within the bounds
|
||
assert(g.has(source));
|
||
|
||
// ‹destination› must be within the bounds
|
||
assert(g.has(destination));
|
||
|
||
// we need to initialize the distances
|
||
std::vector<std::vector<int>> distances(
|
||
g.height(), std::vector(g.width(), graph::unreachable()));
|
||
|
||
// ‹source› destination denotes the beginning where the cost is 0
|
||
auto [sx, sy] = source;
|
||
distances[sy][sx] = 0;
|
||
|
||
// now we need to improve the paths as long as possible
|
||
bool improvement_found;
|
||
do {
|
||
// reset the flag at the beginning
|
||
improvement_found = false;
|
||
|
||
// go through all of the vertices
|
||
for (int v = g.height() * g.width() - 1; v >= 0; --v) {
|
||
improvement_found = _check_vertex(g, distances, v) || improvement_found;
|
||
}
|
||
} while (improvement_found);
|
||
|
||
return distances[destination.second][destination.first];
|
||
}
|
||
|
||
auto bf_finite(const graph& g, const vertex_t& source,
|
||
const vertex_t& destination) -> int {
|
||
// ‹source› must be within the bounds
|
||
assert(g.has(source));
|
||
|
||
// ‹destination› must be within the bounds
|
||
assert(g.has(destination));
|
||
|
||
// we need to initialize the distances
|
||
std::vector<std::vector<int>> distances(
|
||
g.height(), std::vector(g.width(), graph::unreachable()));
|
||
|
||
// ‹source› destination denotes the beginning where the cost is 0
|
||
auto [sx, sy] = source;
|
||
distances[sy][sx] = 0;
|
||
|
||
// now we only iterate as many times as cells that we have
|
||
for (int i = g.height() * g.width(); i > 0; --i) {
|
||
// go through all of the vertices
|
||
for (int v = g.height() * g.width() - 1; v >= 0; --v) {
|
||
_check_vertex(g, distances, v);
|
||
}
|
||
}
|
||
|
||
return distances[destination.second][destination.first];
|
||
}
|
||
|
||
auto bellman_ford(const graph& g, const vertex_t& source)
|
||
-> std::vector<std::vector<int>> {
|
||
// ‹source› must be within the bounds
|
||
assert(g.has(source));
|
||
|
||
// we need to initialize the distances
|
||
std::vector<std::vector<int>> distances(
|
||
g.height(), std::vector(g.width(), graph::unreachable()));
|
||
|
||
// ‹source› destination denotes the beginning where the cost is 0
|
||
auto [sx, sy] = source;
|
||
distances[sy][sx] = 0;
|
||
|
||
// now we only iterate as many times as cells that we have
|
||
for (int i = g.height() * g.width(); i > 0; --i) {
|
||
// go through all of the vertices
|
||
for (int v = g.height() * g.width() - 1; v >= 0; --v) {
|
||
_check_vertex(g, distances, v);
|
||
}
|
||
}
|
||
|
||
// now we check for the negative loops
|
||
for (int v = g.height() * g.width() - 1; v >= 0; --v) {
|
||
if (_check_vertex(g, distances, v, true)) {
|
||
std::cerr << "[Bellman-Ford] Found a negative loop\n";
|
||
break;
|
||
}
|
||
}
|
||
|
||
return distances;
|
||
}
|
||
|
||
#endif /* _BF_HPP */
|