Dijkstra's algorithm: set or priority_queue?

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Блог пользователя Diplomate

Dijkstra's algorithm: set or priority_queue?

Автор Diplomate, история, 8 лет назад, По-английски

What is the best for Dijkstra's algorithm: set with erasing of the vertices adjacent to the current one and the subsequent insertion of them with the new values or a priority_queue with a lot of irrelevant vertices? Or maybe some other approach using std?

std, stl, dijkstra, set priority queue

Diplomate
8 лет назад
25

Комментарии (18)

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duckladydinh

8 лет назад, # |

I remember in an article on Topcoder about STL (you can google it easily, part 2), they are said to not differ much in terms of performance, only by 0.1% in practice.

Dijkstra with set, in my opinion, is clearer to code.

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UnknownNooby

8 лет назад, # ^ |

← Rev. 2 →

+13

How did you measure that?

Try solving this with std::set.

I didn't manage to succeed even though I'm pretty sure my code is optimal enough, std::set is slower than std::priority_queue by more that 30 times on this specific task.

Submissions' summary

I have also submitted 20C - Dijkstra? more than 30 times with using many different data structures, so I guess that priority_queue is WAY faster than std::set, at least like 2-3 times, but sometimes this advantage can be up to 20-30 times on some specific graphs.

The only drawback I've seen so far is that the memory consumed by this Dijkstra is not O(N) but is O(M).

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kpw29

8 лет назад, # ^ |

The task from main (sums) could be solved without Dijkstra, in a linear way. You're always adding edges as a kind of a cycle. For this specific problem, set might be slower but I've heard that it's better in general.

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UnknownNooby

8 лет назад, # ^ |

← Rev. 6 →

+10

This might be because when priority_queue allocates O(M) memory it will work in $\text{[math]}$ . It might be slower for graphs where M is several orders greater than N.

Why do I think it shouldn't affect really much

Usually in tasks you see something like 1 ≤ N, M ≤ 10⁵ so, I believe, in general it is better to use priority_queue.

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misof

8 лет назад, # ^ |

← Rev. 3 →

You are mixing apples and oranges.

First of all, if you use Dijkstra to solve Sums from MAIN, you should use an O(n^2) implementation, because it is a dense graph. The set/priority_queue implementations are both O(n^2 log n) for dense graphs. The log n overhead is unnecessary.

Benchmarking set vs. priority queue on dense graphs is pointless, as you shouldn't use either data structure in that setting.

Second, you are probably doing something wrong/suboptimal in your Sums implementation. I just submitted an O(n^2 log n) solution using Dijkstra with a set for Sums and got 100 points.

Finally, regarding the big picture: For sparse graphs I've seen a lot of benchmarks. The exact results of this comparison depended on way too many factors, such as the platform, compiler version, and optimization flags used. Still, the result was always (that I remember) that the runtime of one implementation was within twice the runtime of the other. In terms of programming contests (and also in terms of real life) a factor of two is negligible. I would never use the words "much faster" in this context.

Feel free to choose the implementation you like better, in the tasks when using either is appropriate.

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amarAnand

7 лет назад, # ^ |

off the topic but i wanted to know how to solve the above problem in linear way. I don't know how to approach the problem. Even a little hint would be very helpful.

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duckladydinh

7 лет назад, # ^ |

This is the infamous article where I learn STL, I do not do any measurement but I think there is no reason I should not believe in this great post

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breno

4 года назад, # ^ |

← Rev. 3 →

-31

UPD: Just now I've realized that it doesn't make any sense since the Dijkstra algorithm should use the set/priority_queue to get the minimum element and the unordered_set does not give us that.

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dalex

8 лет назад, # |

+10

From my experience, priority_queue is much faster, maybe 2x faster than set.

http://codeforces.net/contest/20/status/C?order=BY_CONSUMED_TIME_ASC

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kpw29

8 лет назад, # ^ |

A friend of mine has made such "comparisons" as well. You know what? The results were different :D

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Diplomate

8 лет назад, # ^ |

This is all really weird.)

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likecs

8 лет назад, # |

← Rev. 2 →

I tested Dijkstra's speed on this problem on spoj. ( spoj.com/problems/TSHPATH )

As per the results: Set: 1.51 seconds while Priority Queue: 0.98 seconds.

In my opinion too, priority queue is much faster than set.

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siehpe

8 лет назад, # |

← Rev. 2 →

Correct me if im wrong but priority queue is basically a heap so we get the min element in O(1) whereas set is a balanced bst so extract min is a O(logn) operation

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misof

8 лет назад, # ^ |

Yes, you are wrong. In a heap you can find the minimum in O(1), but you then need O(log(heap_size)) anyway if you want to remove (pop) it from the heap. Which, in Dijkstra's algorithm, you do need.

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Ehsan_sShuvo

7 лет назад, # |

-10

Sometimes set is faster than priority_queue because priority_queue includes extra set of vertices which makes my code lengthy.This submission

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Living_Tribunal

4 года назад, # ^ |

← Rev. 2 →

-56

I don't know much coz i'm a beginner, i always used priority_queue for dijkshtra purpose but today used set for the below problem related to dijkshtra.

i found set took 4 seconds whereas Priority_queue implementation took 6 seconds.

what i concluded is Use set for sparse data when most of the valus are repeating or null(0) otherwise use priority_queue(note: std:p_queue is max heap , so pass negative distance for appropriate shortest cost and again negate it when retriving distances fom it)

Question link is here Synchronomous shopping Hackerrank

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