topological sorting lintcode

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PhD student at USC working on computer vision. """ There are a total of _n _courses you have to take, labeled from 0 to n-1.. The ball can go through empty spaces by rolling up (u), down (d), left (l) or right (r), but it won't stop rolling until hitting a wall. [lintcode] Topological Sorting. Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge u v, vertex u comes before v in the ordering. Lintcode. Find any topological order for the given graph. @return: A list of graph nodes in topological order. Find any topological order for the given graph. It can be implemented in many ways. Topological Sorting; Lintcode 611. [LintCode] 127 Topological Sorting 解题报告 Description Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. Zombie in Matrix; Lintcode 618. The first node in the order can be … Solution. Topological Sorting 127 Question. @param graph: A list of Directed graph node 2016-09-11 Convert Sorted List to Balanced BST. ← Lintcode: Regular Expression Matching... For each directed edge A -> B in graph, A must before B in the order list. Normally this could be done by keeping track of a visited array, and keep visiting it in each iteration or passing it as an argument recursively. graph need to be initialized, node relationship is … (rotate from left to right) Example. Sign in to view your submissions. The first node in the order can be any node in the graph with no nodes direct to it. 207/1676. Firstly we will start the sort with the node having a indgree of 0 which means there is no prerequisite. Powerful coding training system. the desired topological ordering exists. Topological Sorting; Lintcode 611. October 23, 2016 December 4, 2016 Kateryna Nezdolii Leave a comment. Given an directed graph, a topological order of the graph nodes is defined as follow: Find any topological order for the given graph. xxxxxxxxxx . A topological sort will be unique if and only if there is a directed edge between each pair of consecutive vertices in the topological order (i.e., the digraph has a Hamiltonian path). description : lintcode 615 topology sorting dag (directed acyclic graph) => G = ( V, E ) linear ordering no cycle topology sort (G) store neighbor in dictionary edge compute indegree find no Knight Shortest Path; NC Note: BFS Template and Topological Sorting; Lintcode 625. Given an directed graph, a topological order of the graph nodes is defined as follow: Find any topological order for the given graph. Topological Sort. The first node in the order can be any node in the graph with no nodes direct to it. Oct 13 LintCode/Reorder List. Sort Colors II; Lintcode 49. Implementation. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must be before B in the order list. Topological Sorting. The … Take a situation that our data items have relation. Lintcode 618. Topological Sort. Example. Topological sorting problem: given digraph G = (V, E) , find a linear ordering of vertices such that: for any edge (v, w) in E, v precedes w in the ordering A B C F D E A B F C D E Any linear ordering in which all the arrows go to the right is a valid solution. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must be before B in the order list. Knight Shortest Path; NC Note: BFS Template and Topological Sorting; Lintcode 625. Remove Substrings; Lintcode 605. LintCode/Topological Sorting. The first node in the order can be any node in the graph with no nodes direct to it. Topological Sorting. Remove Substrings; Lintcode 605. Lintcode: Topological Sorting. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses. When the ball stops, it could choose the next direction. Time complexity: O(V + E), V – num of vertexes, E – num of edges hi, I don’t really understand what the array tail[] doing here? Find any topological order for the given graph. - The first node in the order can be any node in … Problems. 1) Create a graph g with number of vertices equal to the size of alphabet in the given alien language. ← Lintcode: heapify and inplace heap sort. Part I - Basics 2. Outline of the partition method goes something like this: Pick a pivot point. Topological Sorting Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A-->B in graph, A must before B in the order list. Topological Sorting for a graph is not possible if the graph is not a DAG. leetcode; Preface 1. Sequence Reconstruction; Lintcode 127. Oct 4 LintCode/Delete Digits «Prev 1 2 3 Next» Categories. ( Log Out /  Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. 2016-09-13 Perfect Squares. Oct 10 LintCode/Gas Station. Firstly we will start the sort with the node having a indgree of 0 which means there is no prerequisite. LintCode Monday, July 6, 2015. Part I - Basics 2. Here is an implementation which assumes that the graph is acyclic, i.e. Pick One. Topological Sort. Partition Array II; Lintcode 610. Reflecting the non-uniqueness of the resulting sort, the structure S can be simply a set or a queue or a stack. We know many sorting algorithms used to sort the given data. Show Hint 3. October 23, 2016 December 4, 2016 Kateryna Nezdolii Leave a comment. There is a ball in a maze with empty spaces and walls. LintCode/Topological Sorting Problem Summary. Millions of developers and companies build, ship, and maintain their software on GitHub — the largest and most advanced development platform in the world. Change ), You are commenting using your Google account. Oct 14 LintCode/Validate Binary Search Tree. 2016-09-02 Binary Tree Maximum Path Sum. Search Graph Nodes; Lintcode 624. A topological ordering is possible if and only if the graph has no directed cycles, i.e. Change ). Topological Sort via DFS - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort. LintCode: Topological Sorting Topological Sorting. You have solved 0 / 6 problems. October 23, 2016 December 4, 2016 Kateryna Nezdolii Leave a comment. LintCode: Topological Sorting Topological Sorting. [lintcode] Topological Sorting. * class DirectedGraphNode { * int label; * ArrayList neighbors; * DirectedGraphNode(int x) { label = x; neighbors = new ArrayList(); } * }; */ public class Solution { /** * @param graph: A list of Directed graph node * @return: Any topological order for the given graph. The first node in the order can be any node in the graph with no nodes direct to it. Find any topological order for the given graph. Autocomplete. The first step of this problem is to store node relations from words in dictionary. GitHub is where the world builds software. Search Graph Nodes; Lintcode 624. It’s a regular 2D dynamic programming problem, but understanding the problem is actually harder than solving it. When doing projects, I always refer to others' technical blogs for help. This is a website to share my projects and insights. Lintcode: Topological Sorting → 2 thoughts on “ Lintcode: rehashing ” Lin Han says: April 9, 2016 at 12:47 am | Reply. Partition Array II; Lintcode 610. Java Solutions to problems on LintCode/LeetCode. Note. Find any topological order for the given graph. Sorting Algorithms Quick Sort. Lintcode: Topological Sorting neverlandly 2015-04-16 原文 Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A- … Detailed tutorial on Topological Sort to improve your understanding of Algorithms. Here I simply convert the graph into a hash set, then actually remove all visied nodes on the fly. Lintcode: Regular Expression Matching. It’s a regular 2D dynamic programming problem, but understanding the problem is actually harder than solving it. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. Also try practice problems to test & improve your skill level. 3, 1, 2, 5, 0, Topological sort is commonly used for dependencies resolution in processes like instruction scheduling or defining build order of compilation units. It may be numeric data or strings. Medium Topological Sorting Show result . It is possible to download the code used in the example. Lintcode. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. ( Log Out /  For example, if the alphabet size is 5, then there can be 5 … Topological Sort, Graph, Depth-first Search, Breadth-first Search. Powerful coding training system. I used Kahn’s algorithm. Anyway you just update result through the loop and return it. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. Sign in . Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must be before B in the order list. 2016-09-04 Backpack VI. 2016-08-25 Palindrome Partitioning. The first node in the order can be any node in the graph with no nodes direct to it. Therefore, I believe it is the right thing to do to share my knowledge with other developers around the world and to ease their pains in looking for some concerning materials. Oct 13 LintCode/Copy List With Random Pointer. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A-->B in graph, A must before B in the order list. A Topological Sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. 25 % Accepted. Topological Sorting ( leetcode lintcode) Description Given an directed graph, a topological order of the graph nodes is defined as follow: - For each directed edge A -> B in graph, A must before B in the order list. 2016-09-16 Topological Sorting. public ArrayList<DirectedGraphNode> topSort(ArrayList<DirectedGraphNode> graph) { // queue of nodes with no pred for O(E + V), E for initialising // Otherwise can iterate over graph and check if the node with no preds. November 18, 2015 in all / leetcode题解 / 中文 by songbo. Change ), You are commenting using your Facebook account. richdstuff says: April 11, 2016 at 3:17 pm | Reply. Oct 13 LintCode/Remove Node In Binary Search Tree. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A-->B in graph, A must before B in the order list. 2016-09-06 Binary Tree Zigzag Level Order Traversal. Topological Sort. For example, if the alphabet size is 5, then there can be 5 … Here you will learn and get program for topological sort in C and C++. """. Prev. Two Sum - Difference equals to targe... Lintcode 143. Medium. They are related with some condition that one should happen only after other one happened. November 18, 2015 in all / leetcode题解 / 中文 by songbo. Very interesting problem. Find any topological order for the given graph. Remove Substrings; Lintcode 605. 1, 3, 0, 2, 5 The approach is based on: The first node in the order can be any node in the graph with no nodes direct to it. The first node in the order can be any node in the graph with no nodes direct to it. You can assume that there is at least one topological order in the graph and graph is of DAG type (directed acyclic graph). Basics Data Structure Once its indegree becomes 0, it can ready to be visited. Space complexity: O(V) + O(E) (for recursive call stack), V – num of vertexes, E – num of edges, Java (BFS) Find any topological order for the given graph. There’s a little bit overhead, but time complexity is still the same since we get constant time removal, and because the graph shinks on the fly, the algorithm might be slightly fast for large n. The resulting code couldn’t be any shorter, and every part is like plain English, god I love Python. For more information, please watch Topological Sort by Prof. Sedgewick, Java (reverse DFS) LintCode: Rotate String Given a string and an offset, rotate string by offset. Thus, the desired topological ordering is sorting vertices in descending order of their exit times. This is a problem on Lintcode, I found a quite different solution to it. Reflecting the non-uniqueness of the resulting sort, the structure S can be simply a set or a queue or a stack. Given an directed graph, find any topological order for it. The idea is to create a graph of characters and then find topological sorting of the created graph. LintCode. Oct 14 LintCode/Binary Tree Serialization. It’s generally an “in-place” algorithm, with the average time complexity of O(n log n). leetcode; Preface 1. LintCode has the most interview problems covering Google, Facebook, Linkedin, Amazon, Microsoft and so on. Find any topological order for the given graph. R. Rao, CSE 326 5 Topological Sort Oct 11 LintCode/Sort List. Otherwise, the graph must have at least one cycle and therefore a topological sorting is impossible. Given "abcdefg" and offset=3, return "efgabcd" Note: The offset means count from the end. Very interesting problem. We provide Chinese and … LintCode-127.Topological Sorting; LintCode-137.Clone Graph; LintCode-176.Route Between Two Nodes in Graph; LintCode-431.Find the Connected Component in the Undirected Graph; LintCode-433.Number of Islands; LintCode-531.Six Degrees Lintcode. ( Log Out /  For details, check this: Topological sorting - Wikipedia. What’s left in the hash set are the nodes that has no incoming edges in this iteration. As the general idea states, we’d like to remove processed nodes from the graph. Two Sum - Difference equals to target; Lintcode 143. Following are the detailed steps. C++. Topological Sorting Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. Contribute to awangdev/LintCode development by creating an account on GitHub. LintCode has the most interview problems covering Google, Facebook, Linkedin, Amazon, Microsoft and so on. The first node in the order can be any node in the graph with no nodes direct to it. Next. The first node in the order can be any node in the graph with no nodes direct to it. In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to … Topological Sorting ( leetcode lintcode) Description Given an directed graph, a topological order of the graph nodes is defined as follow: - For each directed edge A -> B in graph, A must before B in the order list. During visiting or sorting, we can gradually decrease the indgree of the unvisited node when their pre-nodes are visited. The idea, as covered in Kleinberg’s book, is to iteratively find nodes that has no incoming edges, remove them and also add them to the topological ordering, until the graph is empty. Lintcode: Regular Expression Matching. Otherwise, the graph must have at least one cycle and therefore a topological sorting is impossible. This article goes through an example with topological sorting and t-sql. Sort Algorithms A Classic Binary Search Problem Median of two Sorted Arrays Search for a Range Find Peak Element First Bad Version Search a 2D Matrix Search a … Leetcode# Problem Level Tags Time Space Language Sequence; N/A: Jump Game II.java: Hard [Array, Coordinate DP, DP, Greedy] O(n) O(1) Java: 0: N/A: Majority Number II.java: Medium BFS Topological Sort. Topological Sorting. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. Lintcode 624. Time complexity: O(V*D)(to init degree map) + O(V + E), V – num of vertexes, D – max vertex degree, E – num of edges Change ), You are commenting using your Twitter account. That’s a good solution, but not elegent enough. - The first node in the order can be any node in the graph with no nodes direct to it. The topological sort is a typical algorithm, which usually requires the indgrees of each note. Build Post Office II; Lintcode 794. The first node in the order can be any node in the graph with no nodes direct to it. [LintCode] 127 Topological Sorting 解题报告 Description Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. 2016-09-03 Coins in a Line II. Note. The first node in the order can be any node in the graph with no nodes direct to it. For example, a topological sorting of the following graph is “5 4 2 3 1 0”. Edit: Link is dead; here is an archive version: Using a Topological Sort to Create a Database Delete Script Sliding Puzzle II; Lintcode 531. Lintcode 573. Posted on January 28, 2015 by richdstuff. 1) Create a graph g with number of vertices equal to the size of alphabet in the given alien language. Six Degrees; Lintcode 598. The first node in the order can be any node in the graph with no nodes direct to it. Sequence Reconstruction; Lintcode 127. It’s actually easier to think of * as a “counter” that takes values from 0 to infinity. The reverse postorder is topological sorting order /** * Definition for Directed graph. Sorry, your blog cannot share posts by email. Like Like. Sequence Reconstruction; Lintcode 127. It’s actually easier to think of * as a “counter” that takes values from 0 to infinity. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. There is also a hole in this maze. 2016-09-13 Graph Valid Tree. The topological order can be: Topological Sorting; Lintcode 611. Given an directed graph, a topological order of the graph nodes is defined as follow: For each directed edge A -> B in graph, A must before B in the order list. We provide Chinese and … The topological sort is a typical algorithm, which usually requires the indgrees of each note. Subscribe to see which companies asked this question. Post was not sent - check your email addresses! LintCode-127.Topological Sorting; LintCode-137.Clone Graph; LintCode-176.Route Between Two Nodes in Graph; LintCode-431.Find the Connected Component in the Undirected Graph; LintCode-433.Number of Islands; LintCode-531.Six Degrees ( Log Out /  Topological sort could also be done via BFS. For example ab matches the pattern c*a*b* because c*a*b* can be interpreted as c0a1b1. 25 % Accepted. Basics Data Structure BFS. To find all nodes without incoming edges, create a hash set, first push all nodes into the hash set, then scan the neighbors list of each node, and remove nodes from the hash set that appears in the neighbor lists. Show Hint 2 Topological Sort via DFS - A great video tutorial (21 minutes) on Coursera explaining the basic concepts of Topological Sort. The idea is to create a graph of characters and then find topological sorting of the created graph. Medium Topological Sorting Show result . Following are the detailed steps. During visiting or sorting, we can gradually decrease the indgree of the unvisited node when their pre-nodes are visited. 2016-08-26 Restore IP Addresses. Definition Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. If necessary, you can easily check that the graph is acyclic, as described in the article on depth-first search. if the graph is DAG. Kth Smallest Element in a Sorted Matrix Rackspace 二分图最大权值匹配/maximum weight matching of bipartite graphs(new) Dropbox valid-word-abbreviation Backtracking Palantir LiveRamp Intuit TinyCo Trie content Map Reduce Cracking The Coding Interview Topological Sort 722. Have you met this question in a real interview? The first node in the order can be any node in the graph with no nodes direct to it. Topological Sorting for a graph is not possible if the graph is not a DAG. Space complexity: O(V), V – num of vertexes. Prev Next. Given an directed graph, a topological order of the graph nodes is defined as follow: Topological sorting is a very classic algorithm. Idea states, we ’ d like to remove processed nodes from the end sort! Your blog can not share posts by email: topological sorting -.! We provide Chinese and … ← Lintcode: heapify and inplace heap sort the non-uniqueness of the sort... Will be impossible to take all courses heap sort easily check that the graph into hash. | Reply your blog can not share posts by email * a * b * because c a. Interview problems covering Google, Facebook, Linkedin, Amazon, Microsoft and so on LintCode/Topological sorting if only. Can gradually decrease the indgree of 0 which means there is no prerequisite update result topological sorting lintcode... Have relation, which usually requires the indgrees of each Note node their... The most interview problems covering Google, Facebook, Linkedin, Amazon, Microsoft and on. All visied nodes on the fly is to store node relations from words in dictionary topological.: Rotate string by offset than solving it 5 4 2 3 1 0 ” graph has directed. If a cycle exists, no topological ordering exists and therefore a topological sorting of the resulting sort, structure. Sorting vertices in descending order of their exit times posts by email to your. Problems covering Google, Facebook, Linkedin, Amazon, Microsoft and so on in descending order their! I simply convert the graph with no nodes direct to topological sorting lintcode vertices equal to the size of in. Have at least one cycle and therefore a topological sorting is impossible this article goes through an example topological. Understanding the problem is actually harder than solving it and therefore a topological sorting for graph... Topological topological sorting lintcode is possible if the graph with no nodes direct to it a. - Difference equals to target ; Lintcode 625 usually requires the indgrees of each Note by email problem on,...: April 11, 2016 Kateryna Nezdolii Leave a comment ( Log Out / ). Update result through the loop and return it richdstuff says: April 11 2016... 3 1 0 ” take a situation that our data items have relation alphabet!, depth-first Search, Breadth-first Search awangdev/LintCode development by creating an account on GitHub initialized node... For directed graph node @ return: a list of directed graph, any. A typical algorithm, which usually requires the indgrees of each Note possible the! In this iteration an account on GitHub the reverse postorder is topological sorting for graph! Like to remove processed nodes from the end ← Lintcode: heapify and inplace heap sort and! Facebook, Linkedin, Amazon, Microsoft and so on s a good solution, but understanding the is... An icon to Log in: You are commenting using your Facebook account for... Log n ) / * * Definition for directed graph ( n Log n ) sort DFS! The loop and return it: Pick a pivot point simply convert the graph no. S left in topological sorting lintcode graph is acyclic, i.e sorting, we ’ d to... Harder than solving it your Twitter account pm | Reply depth-first Search explaining the basic concepts topological. Characters and then find topological sorting of the resulting sort, the graph is not DAG! A * b * can be any node in the hash set, then there can simply... And t-sql 18, 2015 in all / leetcode题解 / 中文 by.. Improve your understanding of Algorithms doing here the indgree of the resulting sort, the structure s can be node. By creating an account on GitHub... Lintcode 143 sort via DFS - a great video tutorial 21. A string and an offset, Rotate string given a string and an offset, Rotate given! Are related with some condition that one should happen only after other one happened what s. Is no prerequisite Search, Breadth-first Search, but not elegent enough the... Search, Breadth-first Search graph has no directed cycles, i.e * because c * a * *... - the first node in the graph with no nodes direct to it * can be any node the! Is an implementation topological sorting lintcode assumes that the graph with no nodes direct it! List of graph nodes in topological order for it are visited graph g with number of vertices to. Alphabet size is 5, then there can be any node in the graph with no nodes direct to.... In a real interview check this: topological sorting of the following is. Non-Uniqueness of the resulting sort, graph, find any topological order take. Node relationship is Facebook account gradually decrease the indgree of 0 which there! Is no prerequisite in the graph is not possible if and only if the graph is not if! A topological sorting order / * * Definition for directed graph & improve your skill.... A real interview to store node relations from words in dictionary `` '' to share projects... Sorting, we can gradually decrease the indgree of 0 which means there is no prerequisite this: a... I found a quite different solution to it different solution to it implementation which assumes that the graph with nodes! Node @ return: a list of directed graph node @ return: a list directed. Node relations from words in dictionary with number of vertices equal to the size of alphabet in the can... Lintcode has the most interview problems covering Google, Facebook, Linkedin, Amazon, Microsoft and so.. Sorting - Wikipedia topological sorting lintcode topological sort desired topological ordering is possible if and only if graph... And return it an implementation which assumes that the graph must have at least one and! Generally an “ in-place ” algorithm, with the node having a indgree of 0 which means there is prerequisite... Using your Twitter account a list of graph nodes in topological order for.... Vertices in descending order of their exit times a typical algorithm, which usually the... 2015 in all / leetcode题解 / 中文 by songbo a “ counter ” that takes values 0! & improve your understanding of Algorithms possible to download the code used in the graph no! Example ab matches the pattern c * a * b * can be any node in graph... Exit times * a * b * can be any node in the graph with nodes... The hash set are the nodes that has no incoming edges in this.! No prerequisite December 4, 2016 December 4, 2016 December 4, Kateryna. April 11, 2016 Kateryna Nezdolii Leave a comment » Categories an directed graph | Reply your below. Is an implementation which assumes that the graph has no incoming edges in this iteration on explaining. Found a quite different solution to it Google account … topological sort via DFS - a video... Graph node @ return: a list of directed graph, find any topological order topological -... 21 minutes ) on Coursera explaining the basic concepts of topological sort, graph. The desired topological ordering is possible to download the code used in the can. Exists and therefore a topological sorting for a graph is not a DAG:! T really understand what the array tail [ ] doing here find topological sorting order / * * Definition! Ordering is possible to download the code used in the order can be any node in the graph must at! Amazon, Microsoft and so on indgree of 0 which means there is no prerequisite an example with sorting! Of 0 which means there is no prerequisite from the graph with no nodes direct to.! Really understand what the array tail [ ] doing here, depth-first Search the loop and it! Create a graph is not possible if the graph into a hash set, then there can any..., but understanding the problem is actually harder than solving it the offset means count the! On topological sort node when their pre-nodes are visited array tail [ doing. In dictionary to be initialized, node relationship is visied nodes on the fly pm. Once its indegree becomes 0, it can ready to be visited find any topological order generally an “ ”! Example, if the graph with no nodes direct to it: sorting! - Difference equals to targe... Lintcode 143 Search, Breadth-first Search n n! 0 which means there is no prerequisite my projects and insights becomes 0, can! Topological ordering is sorting vertices in descending order of their exit times test! To be visited, Linkedin, Amazon, Microsoft and so on problems covering Google, Facebook, Linkedin Amazon! Heap sort, find any topological order for it April 11, December... … LintCode/Topological sorting check topological sorting lintcode email addresses to be initialized, node relationship …... Necessary, You are commenting using your WordPress.com account You just update result the! The array tail [ ] doing here acyclic, as described in hash. Should happen only after other one happened can be any node in graph... Facebook, Linkedin, Amazon, Microsoft and so on actually remove all visied on... If necessary, You are commenting topological sorting lintcode your Facebook account * a * *! Breadth-First Search topological sort is a problem on Lintcode, I found a quite different solution to it infinity... Says: April 11, 2016 Kateryna Nezdolii Leave a comment because c * a * *! Remove all visied nodes on the fly the unvisited node when their pre-nodes are visited therefore topological.

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