BFS 打印最短路径

BFS print shortest path

本文关键字：最短路径 打印 BFS      更新时间：2023-10-16

我正在尝试实现BFS算法以在统一加权图上找到最短路径。下面的代码是从这里直接实现BFS：https://www.redblobgames.com/pathfinding/a-star/introduction.html

void print_path(vector<vector<int>> & gr, int xf, int yf, int xt, int yt)
{
/* Cell neighbours */
const vector<pair<int,int>> nbr {{-1, 0}, {1, 0}, {0, 1}, {0, -1}};
/* route breadcrumbs */
map<pair<int,int>,pair<int,int>> route;
queue<pair<int,int>> q;
/* Represent each node as a pair<int,int> */
pair<int,int> start = {xf, yf};
pair<int,int> end = {xt, yt};
/* NULL node */
route[start] = {-1, -1};
q.push(start);
while (!q.empty()) {
auto current = q.front();
q.pop();
if (current == end) break;
/* Iterate through all possible neighbours */
for (const auto & n : nbr) {
/* pair<int,int> operator+ overloaded */
auto next = current + n;
/* Can move to the next node and it is not yet in the route */
if (can_move_to(next, gr) && route.find(next) == route.end()) {
q.push(next);
route[next] = current;
}
}
}
/* Trace back the shortest path */
while (route[end] != pair<int,int>(-1, -1)) {
cout << end.first << ';' << end.second << endl;
end = route[end];
}
/* Print the starting node */
cout << end.first << ';' << end.second << endl;
}

也许我错过了一些东西，但代码没有产生最短的路径(我不明白为什么要这样做(。此功能沿直角边打印路径，而不是围绕斜边"摆动"。

好吧，在纸和铅笔的帮助下，解决方案非常明显(但我无法证明这一点(。如果我改变每个"层"的邻居迭代顺序，那么对角线路径将改变它的方向，从而产生有效的(最短的？(路径。话虽如此，内部 nbr 循环应该看起来像这样：

if ((current.first + current.second) & 1) {
/* Odd layers */
for (auto it = nbr.begin(); it != nbr.end(); it++) {
auto next = current + *it;
if (can_move_to(next, gr) && route.find(next) == route.end()) {
q.push(next);
route[next] = current;
}
}
}
else {
/* Even layers */
for (auto it = nbr.rbegin(); it != nbr.rend(); it++) {
auto next = current + *it;
if (can_move_to(next, gr) && route.find(next) == route.end()) {
q.push(next);
route[next] = current;
}
}
}
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