not appeared before, then. You are given an integer K and source src and destination dst. Given the following grid containing alphabets from A-Z and a string S. Expected Time Complexity: O (R * C) Expected Auxiliary Space: O (1) Constraints: 1 <= R,C <= 103. Back to Explore Page. 1). GFG Weekly Coding Contest; Job-A-Thon: Hiring Challenge; All Contests and Events. , from a cell (i, j) having value k in a matrix M, we can move to ( i+k, j), ( i-k, j), ( i, j+k), or (i, j-k). Given an unweighted graph, a source, and a destination, we need to find the shortest path from source to destination in the graph in the most optimal way. Given a weighted directed graph with N vertices and M edges, a source src and a destination target, the task is to find the shortest monotonic path (monotonically increasing or decreasing) from the source to the destination. Step 5: Add the chosen edge to the MST if it does not. Like Articulation Points, bridges represent vulnerabilities in a connected network and are. Back to Explore Page. For example, lcs of “geek” and “eke” is “ek”. Follow the steps. If the path is not possible between source cell and destination cell, then return -1. For example a solution is 1033, 1733, 3733, 3739, 3779, 8779, 8179. For Example, in the above binary tree the path between the nodes 7 and 4 is 7 -> 3 -> 1 -> 4 . Time Complexity: O(N 2) Efficient Approach: The idea is to use Recursion to solve this problem efficiently. Practice. Print all unique paths from given source to destination in a Matrix moving only down or right. e. Note: edges[i] is defined as u,. Note: You can only move left, right, up and down, and only through cells that contain 1. If a vertices can't be reach from the S then mark the distance as 10^8. Length of shortest safe route is 13. Note: The Graph doesn't contain any negative weight cycle. We have discussed eulerian circuit for an undirected graph. Output: 3. It is practically infeasible as Operating System may. Given a Directed Acyclic Graph of N vertices from 0 to N-1 and a 2D Integer array (or vector) edges [ ] [ ] of length M, where there is a directed edge from edge [i] [0] to edge [i] [1] with. Given an n x n binary matrix grid, return the length of the shortest clear path in the matrix. Now, the shortest distance to reach 2 from 0 through the path 0 -> 1 -> 2 is (4 + 4) = 8. You have to return a list of integers denoting shortest distance between each node and Source vertex S. Nodes are labeled from 0 to n-1, the task is to check if it contains a negative weight cycle or not. Dynamic programming can be used to solve this problem. util. Approach: For every vertex, we check if it is possible to get the shortest cycle involving this vertex. Construct a graph using N vertices whose shortest distance between K pair of vertices is 2. In the path list, for each unvisited vertex, add the copy of the path of its. Exclusively for Freshers! Participate for Free on 21st November & Fast-Track Your Resume to Top Tech Companies. Hence, if dist (a, b) is the cost of shortest path between node a and b, the required minimum cost path will be min { dist (Source, U) + dist (intermediate, U) + dist (destination, U) } for all U. Following figure is taken from this source. distance as 0. The shortest among the two is {0, 2, 3} and weight of path is 3+6 = 9. For Example, in the above binary tree the path between the nodes 7 and 4 is 7 -> 3 -> 1 -> 4 . e. Follow the below steps to solve the problem: Declare a 2-D array count of size M * N. e. A value of cell 2 means Destination. Shortest direction | Practice | GeeksforGeeks. An Efficient Solution doesn’t require the generation of subsequences. The maximum flow problem involves determining the maximum amount of flow that can be sent from a source vertex to a sink vertex in a directed weighted graph, subject to capacity constraints on the edges. Find the shortest possible path to type all characters of given string in given order using only left,right,up and down movements (while staying inside the grid). Meet In The Middle technique can be used to make the solution faster. Approach: The idea is to use topological sorting, Follow the steps mentioned below to solve the problem: Represent the sequences in the ‘ arr [] [] ’ by a directed graph and find its topological sort order. Hard Accuracy: 50. Step 1: Determine an arbitrary vertex as the starting vertex of the MST. Below is the implementation of the approach. Given a square chessboard, the initial position of Knight and position of a target. Your task is to complete the function is_Possible() which takes the grid as input parameter and returns boolean value 1 if there is a path otherwise returns 0. Given a directed graph where every edge has weight as either 1 or 2, find the shortest path from a given source vertex ‘s’ to a given destination vertex ‘t’. Approach: The main idea here is to use a matrix (2D array) that will keep track of the next node to point if the shortest path changes for any pair of nodes. You have to return a list of integers denoting shortest distance between each node and Source vertex S. Output: Length -> 3 , Path -> ( 1, 3 ) and ( 3, 1 ) In the first example, the minimum length of the shortest path is equal to the maximum sum of the points, which is 1+3 or 2+2. The Greedy Choice is to pick the edge that connects the two sets and is on the smallest weight path from the source to the set that contains not yet included vertices. Cycle 6 -> 1 -> 2 -> 6. Dijkstra’s algorithm is a popular algorithms for solving many single-source shortest path problems having non-negative edge weight in the graphs i. Method 1. The robot can only move either down or right at any point in time. Given a graph of N Nodes and E edges in form of {U, V, W} such that there exists an edge between U and V with weight W. */. But its worst-case time complexity is still O(V^2). Initially, this set is empty. Step 3: Pick edge 6-5. Using DFS calculate the subtree size connected to the edges. One possible Topological order for the graph is 5, 4, 2, 1, 3, 0. unweighted graph of 8 vertices. Return the length of the shortest path that visits every node. Practice. Approach: The idea is to use breadth first search to calculate the shortest path from source to destination. The path from root node to node 4 is 0 -> 1 -> 3 -> 4. , str [n-1] of str has. An Efficient Solution doesn’t require the generation of subsequences. The idea is to consider the given snake and ladder board as a directed graph with a number of vertices equal to the number of cells in the board. We have discussed Dijkstra’s Shortest Path algorithm in the below posts. Distance from the Source (Bellman-Ford Algorithm) | Practice | GeeksforGeeks. Explanation: The first and last node of the input sequence is 1 and 4 respectively. The red cells are blocked, white cell denotes the path and the green cells are not blocked cells. a) Find the most overlapping string pair in temp []. 8. 2 Given node s nd shortest path from s to all other nodes. Length of shortest safe route is 13. Below is the implementation of the approach. Output: 3. Given adjacency list adj as input parameters . Find out the minimum steps a Knight will take to reach the target position. This problem can be solved using the concept of ageing. Example 1: Input: 1 / 2 3 Output: 1 2 #1 3 # ExplanatFollow the steps below to solve the problem: Initialize a variable, say res, to store all possible shortest paths. a) Extract minimum distance vertex from Set. For every vertex first, push current vertex into the queue and then it’s neighbours and if the vertex which is already visited comes again then the cycle is present. e. So, the minimum spanning tree formed will be having (9 – 1) = 8 edges. Contests. If the path exists between two nodes then Next [u] [v] = v. 1 I have a working implementation of Djikstra's algorithm which calculates the length of the shortest path between any two nodes. Shortest path in a directed graph by Dijkstra’s algorithm. The time complexity of this approach is O (N 2 ). Your task is to complete the function shortestPath () which takes n vertex and m edges and vector of edges having weight as inputs and returns the shortest path between vertex 1 to n. Shortest path from source to destination such that edge weights along path are alternatively increasing and decreasing. Expected Time Complexity: O( log(n) ) Expected Auxiliary Space: O(1) Constraints:Given two strings, find the length of longest subsequence present in both of them. Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path. If there is no possible path, return -1. Another method: It can be solved in polynomial time with the help of Breadth First Search. Note: If the Graph contains. For example, the following graph has eulerian cycle as {1, 0, 3, 4, 0, 2, 1}Input: For given graph G. Check if it is possible to make all elements into 1 except obstacles. The first line of each test case has. (weight, vertex). Sum of all odd nodes in the path connecting two given nodes. To find cycle in a directed graph we can use the Depth First Traversal (DFS) technique. The idea is to browse through all paths of length k from u to v using the approach discussed in the previous post and return weight of the shortest path. It chooses one element from each next row. . The robot tries to move to the bottom-right corner (i. Given a path in the form of a rectangular matrix having few. Example 1: Input: n = 3, edges. The problem is to find the shortest distances between every pair of vertices in a given edge-weighted directed graph. , we can move to (i+1, j) or (i, j+1) or. Copy contents. Contests. Menu. ArrayList; import java. Find the minimum. This problem is mainly an extension of Find distance between two given keys of a Binary Tree. Given a Binary Tree of distinct nodes and a pair of nodes. The task is to find the minimum number of edges in a path from vertex 1 to vertex n. Note: edges [i] is defined as u, v and weight. Dijkstra’s shortest path for adjacency matrix representation. The task is to do Breadth First Traversal of this graph starting from 0. Distance between two nodes of binary tree with node values from. Approach: This problem is similar to finding the shortest path in an unweighted graph. The main idea is to recursively get the longest path from the left. You are given an integer K and source src and destination dst. Single source shortest path between two cities. Step 2: Define a function “findLongestFromACell” that takes in a cell’s row and column index, the matrix, and a lookup table. Your task is to complete the function minimumCostPath () which takes grid as input parameter and returns the minimum cost to react at bottom right cell from top left cell. Set value of count [0] [j] equal to 1 for 0 <= j < N as the answer of subproblem with a single row is equal to 1. Assume that the claim is true in some given stage, and prove that it will hold for the next step. 4. Dijkstra’s algorithm is applied on the re. You. Now, there arises two different cases: Explanation: The shortest path is: 3 → 1 → 5 → 2 → 6. The Minimum distance of all nodes from Source, intermediate, and destination can be found by doing Dijkstra’s Shortest Path algorithm from these 3. Step 2: Pick edge 8-2. Given a binary matrix mat[][] of dimensions of N * M and pairs of integers src and dest representing source and destination cells respectively, the task is to find the shortest sequence of moves from the given source cell to the destination cell via cells consisting only of 1s. 64 %. Explanation: Largest minimum distance = 5. Number of shortest paths in an Undirected Weighted Graph; Johnson's algorithm for All-pairs shortest paths; Check if given path between two nodes of a graph represents a shortest paths; Shortest distance between two nodes in Graph by reducing weight of an edge by half; Print negative weight cycle in a Directed GraphThe basic idea behind the iterative DFS approach to finding the maximum path sum in a binary tree is to traverse the tree using a stack, maintaining the state of each node as we visit it. Hence, the shortest distance of node 0 is 0 and the shortest distance. So “ek” becomes “geeke” which is shortest common supersequence. If there are 2 odd vertices, start at one of them. Also, replace the guards with 0 and walls with -1 in output matrix. More formally a Graph is composed of a set of vertices ( V ) and a set of edges ( E ). Explanation: Path is 4 2 1 3. Complexity Analysis: Time Complexity: O(V+E) where V is number of vertices in the graph and E is number of edges in the graph. In the maze matrix, 0 means the block is a dead end and 1 means the block can be used in the path from source to destination. Note: If the Graph contains a n Explanation: { 1, 2, 3 } is the only shortest common supersequence of {1, 2}, {1, 3} and {2, 3}. Path to reach border cells from a given cell in a 2D Grid without crossing specially marked cells. It is a Greedy Algorithm. Input: Num1 = 1033 Num2 = 8179 Output: 6 Explanation: 1033 -> 1733 -> 3733 -> 3739 -> 3779 -> 8779 -> 8179. Johnson's algorithm for All-pairs shortest paths; Shortest Path in Directed Acyclic Graph; Multistage Graph (Shortest Path) Shortest path in an unweighted graph; Karp's minimum mean (or average) weight cycle algorithm; 0-1 BFS (Shortest Path in a Binary Weight Graph) Find minimum weight cycle in an undirected graph Explanation: There exists no path from start to end. While performing BFS if an edge having weight. Output: 7 3 1 4. It uses the Bellman-Ford algorithm to re-weight the original graph, removing all negative weights. Every item of set is a pair. Example 2: Input: Output: 1 Explanation: The output 1 denotes that the order is valid. Auxiliary Space: O(ALPHABET_SIZE^L+n*L) Approach 2: Using Dynamic Programming. Below are the steps for finding MST using Kruskal’s algorithm. Approach: The main idea here is to use a matrix (2D array) that will keep track of the next node to point if the shortest path changes for any pair of nodes. 2K 161 You have an undirected, connected graph of n nodes labeled from 0 to n - 1. Let us consider another. Print all the paths from root to leaf, with a specified sum in Binary tree. + 3 more. Step 4: Pick edge 0-1. e. This gives the shortest path. A clear path in a binary matrix is a path from the top-left cell (i. Auxiliary Space: O (V+E) If you like GeeksforGeeks and would like to contribute, you can also write an article using write. No cycle is formed, include it. Strings are considered a data type in general and are typically represented as arrays of bytes (or words) that store a sequence of characters. e. Minimum steps to reach the target by a Knight using BFS:. cost. Following is Fleury’s Algorithm for printing the Eulerian trail or cycle. Maximize sum of path from the Root to a Leaf node in N-ary Tree. Find Longest Common Subsequence (lcs) of two given strings. The Ford-Fulkerson algorithm is a widely used algorithm to solve the maximum flow problem in a flow network. This can be achieved by modifying the Breadth-First-Traversal of the tree. Algorithm 1) Create a set sptSet (shortest path tree set) that keeps track of vertices included in shortest path tree, i. Two cells are. Shortest Path Revisited. Given two strings X and Y, print the shortest string that has both X and Y as subsequences. package ga; import java. Example 1: Input: V = 5, E = 5 adj. Given a Binary Tree with all unique values and two nodes value, n1 and n2. Find minimum number of edges between (1, 5). Complete the function Kdistance () that accepts root node and k as parameter and return the value of the nodes that are at a distance k from the root. Explanation: Vertex 3 from vertex 1 via vertices 2 or 4. Practice. Dijkstra’s Algorithm: It works on Non-Negative Weighted graphs. The task is to find the lowest common ancestor of the given two nodes. . You are. You are given an Undirected Graph having unit weight, Find the shortest path from src to all the vertex and if it is unreachable to reach any vertex, then return -1 for that vertex. Discuss. So, if you have, implemented your function correctly, then output would be 1 for all test cases. So the space needed is O(V). Given a directed graph and a source vertex in the graph, the task is to find the shortest distance and path from source to target vertex in the given graph where edges are weighted (non-negative) and directed from parent vertex to source vertices. A Graph is a non-linear data structure consisting of vertices and edges. Also,Initialize the steps as 0. The idea is similar to linear time solution for shortest path in a directed acyclic graph. Given a directed graph where every edge has weight as either 1 or 2, find the shortest path from a given source vertex ‘s’ to a given destination vertex ‘t’. Initialize an unordered_map, say adj to store the edges. Like Prim’s MST, we generate a SPT (shortest path tree) with a given source as a root. Your task is to complete the function minimumStep() which takes an integer n as inputs and returns the minimum number of edges in a path from vertex 1 to vertex N. Hence, the shortest distance of node 0 is 0 and the shortest distance. Given a Directed Graph having V nodes numbered from 0 to V-1, and E directed edges. Output : 3. Time Complexity: 4^ (R*C), Here R and C are the numbers of rows and columns respectively. where e is the number of edges in the graph. Practice. Push the word in the queue. Given a 2-D binary matrix of size n*m, where 0 represents an empty space while 1 represents a wall you cannot walk through. In the previous problem only going right and the bottom was allowed but in this problem, we are allowed to go bottom, up, right and left i. Method 1 (Simple) One straight forward solution is to do a BFS traversal for every node present in the set and then find all the reachable nodes. Count of cells in a matrix which give a Fibonacci number when the. Examples: Input: src = 0, the graph is shown below. Therefore, the problem can be solved using BFS. Step-2: Pick all the vertices with in-degree as 0 and add them into a queue (Enqueue operation) Step-3: Remove a vertex from the. Return -1 if it is not possible to visit every edge once. We can. Bellman-Ford Algorithm. Pseudo code to print the path backwards: v = end_node while v != start_node print (v) v = adjacent node for which a sum: distance + edge_weight (v,adjacent) is minimum print (v) // print start node. Output: 0 4. Input: N = 5, M = 8. Can you solve this real interview question? Shortest Path Visiting All Nodes - You have an undirected, connected graph of n nodes labeled from 0 to n - 1. When it finds the first leaf node, it calls the printPath function to print the path from the leaf node to the root. Disclaimer: Please watch Part-1 and Part-2 Part-1: Shortest distance between given nodes in a bidirectional weighted graph by removing any K edges. BFS will be okay. Note:The initial and the target position coordinates of Knight have been given accord. C / C++ Program for Dijkstra's shortest path algorithm | Greedy Algo-7. org. Contests. Approach: The idea is to use queue and visit every adjacent node of the starting nodes that traverses the graph in Breadth-First Search manner to find the shortest path between two nodes of the graph. Here we not only find the shortest distance but also the path. There are two types of nodes to be considered. Eulerian Circuit is an Eulerian Path which starts and ends on the same vertex. Back to Explore Page. Iterate over all M edges and for each edge U and V set dp [U] [V] to 1 and ANS [U] [V] to A [U] + A [V]. Initially, the cost of the shortest path is an overestimate, likened to a stretched-out spring. Your task is to complete the function. For each node, store the count of nodes in its subtree ( includes the node). Finally, return the largest of all minimum distances. If source is already any of the corner then. Find shortest safe route in a path with landmines; Print all paths from a source point to all the 4 corners of a Matrix; Printing all solutions in N-Queen Problem; Longest path in a Matrix from a specific source cell to destination cell; Count of Possible paths of given Matrix having Bitwise XOR equal to K; Print all unique paths from given. We can move in 4 directions from a given cell (i, j), i. Input: N = 2 m[][] = {{1, 0}, {1, 0}} Output:-1 Explanation: No path exists and destination cell is blocked. Queries to find distance between two nodes of a Binary tree. He considered each of the lands as a node of a graph and each bridge in between as an edge in between. Step 4: if the subsequence is not in the list then recur. distance as 0. Output: Yes. Output − List of the shortest distance of all vertices from the starting node. Practice. Disclaimer: Please watch Part-1 and Part-2 Part-1:. Input: root = [2, 1], startValue = 2, destValue = 1. Practice. If zero or two vertices have odd degree and all other vertices have even degree. Traverse all words that adjacent (differ by one character) to it and push the word in a queue (for BFS)A rat starts from source and has to reach the destination. You dont need to read input or print anything. Below is algorithm based on set data structure. Print root to leaf paths without using recursion. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Paytm. Detailed solution for Shortest Path in Undirected Graph with unit distance: G-28 - Given an Undirected Graph having unit weight, find the shortest path from the source to all other nodes in this graph. Time Complexity: The time complexity of Dijkstra’s algorithm is O (V^2). U = 1, V = 3. Given a Graph of V vertices and E edges and another edge(c - d), the task is to find if the given edge is a Bridge. This problem is mainly an extension of Find distance between two given keys of a Binary Tree. Going from one node to its left child node is indicated by the letter ‘L’. def BFS_SP (graph, start,. Shortest path length between two given nodes such that adjacent nodes are at bit difference 2. Example 1: Input: N=3, Floyd Warshall. /. Last Updated: 13 October 2022. Output: Yes. In this post, the same is discussed for a directed graph. A falling path will start at any element in the first row and ends in last row. Determine the shortest path tree. Let both start and finish be roots. in all 4 directions. Expected Time Complexity: O (R * C) Expected Auxiliary Space: O (1) Constraints: 1 <= R,C <= 103. Shortest Path by Removing K walls. Back to Explore Page. Output: Sort the nodes in a topological way. Example1: Input: N = 4, M = 2 edge =. 2) Other nodes, may be an ancestor of target, or a node in some other subtree. Expected Time complexity is O (MN) for a M x N matrix. Given an adjacency matrix graph representing paths between the nodes in the given graph. (The values are returned as vector in cpp, as. Create a Set to store all the visited words in current path and once the current path is completed, erase all the visited words. Example 2: Input: 10 / 20 30 40 60 / 2 Output: 3 Explanation: Minimum depth. Input: i = 4, j = 3. Output: “L”. Here adj [i] contains vectors of size 2,Frequencies of Limited Range Array Elements. You are given an Undirected Graph having unit weight, Find the shortest path from src to all the vertex and if it is unreachable to reach any vertex, then return -1 for that vertex. An Adjacency List is used for representing graphs. Consider the following directed graph. The important thing to note is we can reach any destination as it is always possible to make a move of length 1. Johnson's algorithm for All-pairs shortest paths; Shortest Path in Directed Acyclic Graph; Multistage Graph (Shortest Path) Shortest path in an unweighted graph; Karp's minimum mean (or average) weight cycle algorithm; 0-1 BFS (Shortest Path in a Binary Weight Graph) Find minimum weight cycle in an undirected graphExplanation: There exists no path from start to end. Expected Time Complexity: O (n*m) Expected Space Compelxity: O (n) Constraints: 1 <= n <= 100. Approach: Use recursion to move first right then down from each cell in the path of the matrix mat[][], starting from source, and store each value in a vector. In the above algorithm, we start by setting the shortest path distance to the target vertex t as 0 and all other vertices as infinity. Given a 2-D binary matrix of size n*m, where 0 represents an empty space while 1 represents a wall you cannot walk through. Note: It is assumed that negative cost cycles do not exist in input matrix. Explanation: The shortest path is: 2 → 1. A Bellman-Ford algorithm is also guaranteed to find the shortest path in a graph, similar to. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. What A* Search Algorithm does is that at each step it picks the node according to a value-‘ f ’ which is a parameter equal to the sum of two other parameters – ‘ g ’ and ‘ h ’. Example 1: Input: matrix = { {0,25}, {-1,0}} Output: { {0,25}, {-1,0}} Explanation: The shortest distance between every pair is already given (if it exists). Note: There are only a single source and a single. Algorithm to Find Negative Cycle in a Directed Weighted Graph Using Bellman-Ford: Initialize distance array dist [] for each vertex ‘v‘ as dist [v] = INFINITY. Given a directed graph, find out if a vertex j is reachable from another vertex i for all vertex pairs (i, j) in the given graph. 4% Submissions: 18K+ Points: 8. 1 ≤ cost of cells ≤ 1000. Make sure the graph has either 0 or 2 odd vertices. Complete function shortestPath() which takes two integers Num1 and Num2 as input parameters and returns the distance of the shortest path from Num1 to Num2. To learn more about Minimum Spanning Tree, refer to this article. Approach: The solution is to perform BFS or DFS to find whether there is a path or not. Follow the steps below to solve the problem: Initialize a 3D array that ensures that we don’t visit the same cell again and again. Given a directed acyclic graph (DAG) of n nodes labeled from 0 to n - 1, find all possible paths from node 0 to node n - 1 and return them in any order. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3 * i. Output: 2. The diagram below shows two trees each with diameter nine, the leaves that form the ends of the longest path are shaded (note that there is more than one path in each tree of length nine, but no path longer than nine nodes). The distance between the two nodes i and j will be equal to dist (i, LCA (i, j)) + dist (j, LCA (i. One solution is to solve in O (VE) time using Bellman–Ford. So “ek” becomes “geeke” which is shortest common supersequence. , there is a directed edge from node i to node graph[i][j] ). Follow the below steps to solve the problem: Create a 2-D dp array to store answer for each cell; Declare a priority queue to perform dijkstra’s algorithm; Return. The only difference between SPFA and your algorithm is that SPFA checks if the vertex is already in queue before pushing it. e. Find shortest possible path to type all characters of given string using the remote. Approach 1: By looking at examples we can see that the above simplification process just behaves like a stack. In this article, an O (E*K) approach is discussed for solving this problem. Example 1: Input: 1 2 3 4 5 6. Compute the minimum number of steps required for each index to reach the end of the array by iterating over indices N – 2 to 1. Below is the implementation of the above approach: C++. 2) Create a separate stack to store the path from the root to the current node. If it is unreachable then return -1. Practice. 3 elements arranged at positions 1, 7 and 12, resulting in a minimum distance of 5 (between 7 and 12) A Naive Solution is to consider all subsets of size 3 and find the minimum distance for every subset. Given an unweighted directed graph, can be cyclic or acyclic. 4) Huffman. Input : str = "AACECAAAA"; Output : 2. The task is to find the minimum sum of a falling path through A. Bellman-Ford is a single source shortest path algorithm that determines the shortest path between a given source vertex and every other vertex in a graph. Complete the function printPath() which takes N and 2D array m[ ][ ] as input parameters and returns the list of paths in lexicographically increasing order. Complete the function printKDistantfromLeaf () that takes root node and k as inputs and returns the number of nodes that are at distance k from a leaf node. Johnson's algorithm for All-pairs shortest paths; Shortest Path in Directed Acyclic Graph; Multistage Graph (Shortest Path) Shortest path in an unweighted graph; Karp's minimum mean (or average) weight cycle algorithm; 0-1 BFS (Shortest Path in a Binary Weight Graph) Find minimum weight cycle in an undirected graph Practice. Widest Path Problem | Practical application of Dijkstra's Algorithm.