TOPOSORT - Topological Sorting

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Sandro is a well organised person. Every day he makes a list of things which need to be done and enumerates them from 1 to n. However, some things need to be done before others. In this task you have to find out whether Sandro can solve all his duties and if so, print the correct order.

Input

In the first line you are given an integer n and m (1<=n<=10000, 1<=m<=1000000). On the next m lines there are two distinct integers x and y, (1<=x,y<=10000) describing that job x needs to be done before job y.

Output

Print "Sandro fails." if Sandro cannot complete all his duties on the list. If there is a solution print the correct ordering, the jobs to be done separated by a whitespace. If there are multiple solutions print the one, whose first number is smallest, if there are still multiple solutions, print the one whose second number is smallest, and so on.

Example 1

Input:
8 9
1 4
1 2
4 2
4 3
3 2
5 2
3 5
8 2
8 6
Output:
1 4 3 5 7 8 2 6 

Example 2

Input:
2 2
1 2
2 1
Output:
Sandro fails.

hide comments
kadian_: 2020-09-24 16:19:07

If you are getting TLE (using either Kahns algo with priority queue OR by using version of dfs) make sure your cycle detection part is optimal. Cycle detection should happen in O(V+E)

adityarakshit7: 2020-08-19 16:03:59

kahn's algo in Python giving TLE
Anyone is having solution in python?

tridib_2003: 2020-08-17 08:28:46

Solved using Kahn's Algo. Used set instead of queue. AC.

dardev: 2020-08-15 21:45:43

If there is a solution print the correct ordering, the jobs to be done separated by a whitespace.

If there are multiple solutions print the one, whose first number is smallest, if there are still multiple solutions, print the one whose second number is smallest, and so on.

Last edit: 2020-08-15 21:46:20
darksun: 2020-08-05 21:04:48

Ultimate test case if you are getting WA -->
6 4
5 1
1 2
2 3
4 6
4 5 1 2 3 6 <-- and just see this way your lexicographic order is correct

coolboy7: 2020-08-02 08:16:09

if you want to solve it using dfs, then check out auler comment

abhinav2302: 2020-07-23 03:51:26

Don't forget the full stop. Costed me so much time for no reason. ;_;

Last edit: 2020-07-23 05:07:15
shukla_nk: 2020-07-18 11:27:27

I have tried Kahn's with Priority Queue but getting TimeLimit. Could anyone please help me out with some suggestions?

aman005mishra: 2020-07-02 22:55:03

Kahn's with priority_queue...AC in one go!!!!

hdhimanshu: 2020-06-23 21:38:32

A good question to start with topological sorting.
first, find a cycle in DG and then just use priority_queue with vector and apply dfs from n to 1.
u will get AC.

Last edit: 2020-06-23 21:39:35

Added by:Josef Ziegler
Date:2011-10-23
Time limit:0.5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All