dijkstra

Find the shortest path with the least number of edges

点点圈 提交于 2019-12-04 03:15:44
问题 I need to modify Dijkstra's algorithm so that if there are several shortest paths I need to find the one with minimum number of edges on the path. I've been stuck on how to use Dijkstra's method to find multiple shortest paths, how do you do that? doesn't it always output only 1 shortest path? pseudo code or any general direction would be very helpful. 回答1: Instead of assigning every node with the distance from source you can assign the number of edges traversed so far also. So each node will

What is the purpose of the visited set in Dijkstra?

别等时光非礼了梦想. 提交于 2019-12-04 02:55:31
On the Wikipedia page for Dijkstra's algorithm, they mark visited nodes so they wouldn't be added to the queue again. However, if a node is visited then there can be no distance to that node that is shorter, so doesn't the check alt < dist[v] already account for visited nodes? Am I misunderstanding something about the visited set? for each neighbor v of u: alt := dist[u] + dist_between(u, v); // accumulate shortest dist from source if alt < dist[v] && !visited[v]: dist[v] := alt; // keep the shortest dist from src to v previous[v] := u; insert v into Q; // Add unvisited v into the Q to be

AStar - explanation of name

て烟熏妆下的殇ゞ 提交于 2019-12-04 01:53:28
I am looking for an explanation why the AStar / A* algorithm is called AStar. All similar (shortest path problem) algorithms are often named like its developer(s), so what is AStar standing for? There were algorithms called A1 and A2. Later, it was proved that A2 was optimal and in fact also the best algorithm possible, so he gave it the name A* which symbolically includes all possible version numbers. Source: In 1964 Nils Nilsson invented a heuristic based approach to increase the speed of Dijkstra's algorithm. This algorithm was called A1. In 1967 Bertram Raphael made dramatic improvements

[模板]Dijkstra-优先队列优化-单元最短路

人走茶凉 提交于 2019-12-04 01:06:19
输入: 6 9 1 1 2 1 1 3 12 2 3 9 2 4 3 3 5 5 4 3 4 4 5 13 4 6 15 5 6 4 输出: 0 1 8 4 13 17 Code: 1 #include<iostream> 2 #include<cstring> 3 #include<queue> 4 using namespace std; 5 #define PII pair<int,int> 6 const int maxn=10000,maxm=1000; 7 int cnt=0,edge[maxm],ver[maxm],nxt[maxm],head[maxn]; 8 int d[maxn]; 9 bool v[maxn];//v[i]表示i点是否松弛 10 priority_queue < PII,vector<PII>,greater<PII> > q;//优先队列,以p.first最小优先 11 inline void add(int x,int y,int z) 12 { 13 cnt++; 14 ver[cnt]=y; 15 edge[cnt]=z; 16 nxt[cnt]=head[x]; 17 head[x]=cnt; 18 } 19 inline void dijk(int t) 20 { 21 int i; 22 memset(d,0x3f,sizeof

AcWing849 Dijkstra求最短路I

江枫思渺然 提交于 2019-12-03 21:21:25
给定一个n个点m条边的有向图,图中可能存在重边和自环,所有边权均为正值。 请你求出1号点到n号点的最短距离,如果无法从1号点走到n号点,则输出-1。 输入格式 第一行包含整数n和m。 接下来m行每行包含三个整数x,y,z,表示存在一条从点x到点y的有向边,边长为z 输出格式 输出一个整数,表示1号点到n号点的最短距离。 如果路径不存在,则输出-1。 数据范围 \(1≤n≤500,\) \(1≤m≤105,\) 图中涉及边长均不超过10000 输入样例 3 3 1 2 2 2 3 1 1 3 4 输出样例 3 原题链接: https://www.acwing.com/problem/content/851/ 用 dijkstra算法 解决最短路问题的模板题。 dijkstra算法 的一般流程是: 初始化 dist[1] = 0 ,其余结点的 dist 值为无穷大 找出一个未被标记的、 dist[x] 最小的结点 x ,然后标记 x 扫描结点x的所有出边 (x, y, z) ,若 dist[y] > dist[x] + z , 那么使用 dist[x]+z 来更新 dist[y] 重复上述2、3步骤,直到所有结点被标记 代码如下: #include <iostream> #include <memory.h> using namespace std; const int N = 502

Dijkstra shortest path algorithm with edge cost

纵然是瞬间 提交于 2019-12-03 17:47:17
问题 I have a directed, positive weighted graph. Each edge have a cost of use. I have only A money, i want to calculate shortest paths with dijkstra algorithm, but sum of edges costs on route must be less or equal to A. I want to do this with most smallest Dijstra modification (if I can do it with small modification of Dijkstra). I must do this in O(n*log(n)) if I can, but i think i can. Anyone can help me with this? 回答1: https://www.spoj.pl/problems/ROADS/ The problem was given at CEOI '98 and

How to reverse a graph in linear time?

喜你入骨 提交于 2019-12-03 17:28:29
问题 I know there are two ways to represent my graph: one is using a matrix, and the other one is using a list. If I use a matrix, I have to flip all the bits in the matrix. Doesn't that take O(V^2) time? If I use a list, wouldn't I have to traverse each list, one by one, and create a new set? That would seem to take O(V+E) time which is linear. Am I correct? So, I got another question here. Consider, for example, that I use the Dijkstra algorithm on my graph (either a matrix or a list), and we

How to set target vertex in QuickGraph Dijkstra or A*

丶灬走出姿态 提交于 2019-12-03 17:16:24
I am using QuickGraph version 3.6 and I found function SetRootVertex, but no SetTagretVertex. I need this because I am searching short paths in huge graph and this would speed up program a lot. Clases in question are DijkstraShortestPathAlgorithm and AStarShortestPathAlgorithm. I don't think there is a way to this without using events. You could wrap the necessary code in one extension method, making things clear, e.g.: public static class Extensions { class AStarWrapper<TVertex, TEdge> where TEdge : IEdge<TVertex> { private TVertex target; private AStarShortestPathAlgorithm<TVertex, TEdge>

Implementing Dijkstra's Algorithm

心已入冬 提交于 2019-12-03 16:07:11
I've been tasked (coursework @ university) to implement a form of path-finding. Now, in-spec, I could just implement a brute force, since there's a limit on the number of nodes to search (begin, two in the middle, end), but I want to re-use this code and came to implement Dijkstra's algorithm . I've seen the pseudo on Wikipedia and a friend wrote some for me as well, but it flat out doesn't make sense. The algorithm seems pretty simple and it's not a problem for me to understand it, but I just can't for the life of me visualize the code that would realize such a thing. Any suggestions/tips?

Find shortest path between two articles in english Wikipedia in Python

喜夏-厌秋 提交于 2019-12-03 11:32:59
The question: Find shortest path between two articles in english Wikipedia. Path between article A and B exist if there are articles C(i) and there is a link in article A that leads to article C(1), in article C(1) link that leads to article C(2), ..., in article C(n) is link that leads to article B I'm using Python. URL to download wikipedia article: http://en.wikipedia.org/wiki/Nazwa_artykułu http://en.wikipedia.org/w/index.php?title?Nazwa_artykułu&printable=yes Wikipedia API I have edited my source code, but it still does not work when I include those articles in codes can any one tell me