Given a boolean matrix of size RxC where each cell contains either 0 or 1, modify it such that if a matrix cell matrix [i] [j] is 1 then all the cells in its ith row and jth column will become 1. Given a weighted, directed and connected graph of V vertices and E edges, Find the shortest distance of all the vertex's from the source vertex S. Number of shortest paths to reach every cell from bottom-left cell in the grid; Print all paths from a source point to all the 4 corners of a Matrix; Count of all unique paths from given source to destination in a Matrix; Find. If a node X lies on multiple root-to-leaf paths and if any of the paths has path length >= k, then X is not deleted from Binary Tree. Example 1: Input: grid = [[1,3,1],[1,5,1],[4,2,1]] Output: 7 Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum. Therefore the cost of the path = 3 + 5 + 4 = 12. Method 1. But for a Directed Acyclic Graph, the idea of topological sorting can be used to optimize the process by a lot. Expected Time Complexity: O (n*m) Expected Space Compelxity: O (n) Constraints: 1 <= n <= 100. Shortest path in a directed graph by Dijkstra’s algorithm. In this problem statement, we have assumed the source vertex to be ‘0’. Jobs. Explanation: The number of shortest path from node 1 to node 4 is 2, having cost 5. We then work backwards from the target vertex t to the source vertex s. ; Initialise a priority-queue pq with S and its weight as 1 and a visited array v[]. You have to return a list of integers denoting shortest distance between each node and Source vertex S. Sort all the edges in non-decreasing order of their weight. You are given an integer K and source src and destination dst. Courses. If there are 0 odd vertices, start anywhere. We define ‘ g ’ and ‘ h ’ as simply as possible below. Sum of all odd nodes in the path connecting two given nodes. Your task is to complete the function findShortestPath () which takes matrix as input parameter and return an integer denoting the shortest path. (The values are returned as vector in cpp, as. The task is to find the minimum number. 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. There are n stairs, and a person is allowed to jump next stair, skip one stair or skip two stairs. We have discussed Dijkstra’s Shortest Path algorithm in the below posts. Courses. Dijkstra's shortest path algorithm in Java using PriorityQueue. Step by step Shortest Path from source node to destination node in a Binary Tree. 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 edges, s and d ,count the number of. Change the value of matrix [0] [2] and matrix [1] [2] to 0 and the path is 0,0 -> 0,1 -> 0,2 -> 1,2 -> 2,2. 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. You don't need to read input or print anything. , there is a directed edge from node i to node graph[i][j]). GCD from root to leaf path in an N-ary tree. Now when we are at leaf node and it is equal to arr [index] and there is no further element in given sequence of root to leaf path, this means that path exist in given tree. step 1 : If graph is Eulerian, return sum of all edge weights. It chooses one element from each next row. Approach: To solve the problem, the idea is to use Breadth-First-Search traversal. From each cell you can either move only to right or down. It's a common practice to augment dynamic programming algorithms to store parent pointers. , whose minimum distance from the source is calculated and finalized. e. 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. 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. Platform to practice programming problems. Check our Website: case you are thinking to buy courses, please check below: Link to get 20% additional Discount at Coding Ni. Find the length of the shortest transformation sequence from startWord to targetWord. Following is complete algorithm for finding shortest distances. cost. Try all 8 possible positions where a Knight can reach from its position. Output: 3. The graph is given adjacency matrix representation where. Time Complexity: O(N 2) Auxiliary Space: O(N) Efficient Approach:The problem can be solved. Example 2: Input: K = 3 3 / 2 1 / 5 3 Output: 5 3. Courses. Time Complexity: O (N), the time complexity of this algorithm is O (N), where N is the number of nodes in the tree. To learn more about Minimum Spanning Tree, refer to this article. Given a Binary Tree of size N, you need to find all the possible paths from root node to all the leaf node's of the binary tree. Example 1: Input: K = 0 1 / 3 2 Output: 1. The idea is to find paths from root nodes to the two nodes and store them in two separate vectors or arrays say path1 and path2. Your task is to complete the function findShortestPath () which takes matrix as input parameter and return an integer denoting the shortest path. It is practically infeasible as Operating System may. Expected Auxiliary Space is O (MN) for a M x N matrix. You are a hiker preparing for an upcoming hike. Copy contents. Print all unique paths from given source to destination in a Matrix moving only down or right. Please to report an issue. ; Loop till queue is empty. Time Complexity: O(m x n) Auxiliary Space: O( m *n)+O(m+n) , (m*n) extra array space and (m+n) recursive stack space. util. Bottom up – Start from the nodes on the bottom row; the min pathsum for these nodes are the values of the nodes themselves. Strings are considered a data type in general and are typically represented as arrays of bytes (or words) that store a sequence of characters. Thus, d(S, X) = min U ∈ S(d(S, U) + w(U, X)). Given a weighted directed graph with n nodes and m edges. Improve this answer. For each current word, find the possible next words present in str [] by changing each character from. The description of cells is as follows: A value of cell 1 means Source. Example 1: Input: n = 5, m= 6 edges = [ [1,2,2], [2,5,5], [2,3,4], [1,4,1], [4,3,3], [3,5,1]] Output: 1 4 3 5 Explanation: The source vertex is 1. Output: 7 3 1 4. Transitive closure of above graphs is 1 1 1 1 1 1. . A move can be made to a cell grid [i] [j] only if grid [i] [j] = 0 and only left, right, up and down movements are permitted. The Floyd-Warshall algorithm, named after its creators Robert Floyd and Stephen Warshall, is a fundamental algorithm in computer science and graph theory. You are given an array graph where graph [i] is a list of. Sum of weights of path between nodes 2 and 3 = 3. Practice this problem. ​Example 2:Min cost path using Dijkstra’s algorithm: To solve the problem follow the below idea: We can also use the Dijkstra’s shortest path algorithm to find the path with minimum cost. Try all 8 possible positions where a Knight can reach from its position. Back to Explore Page. add the substring to the list. The algorithm maintains a set of visited vertices. geeksforgeeks. While there are non-empty buckets:. Given an n x n binary matrix grid, return the length of the shortest clear path in the matrix. You don't need to read input or print anything. The problem reduces to finding the shortest path in a graph. Initialize a counter [] [] vector, this array will keep track of the number of remaining obstacles that can be eliminated for each visited cell. The idea is to use Dijkstra’s algorithm to find the shortest path from source vertex a to all other vertices in the graph using the straight edges and store the result in array da[], and then from the destination vertex b to all other vertices and store the result in db[]. This algorithm can be used on both weighted and unweighted graphs. Given a weighted, directed and connected graph of V vertices and E edges, Find the shortest distance of all the vertex's from the source vertex S. We are allowed to move exactly k steps from any cell in the matrix where k is the cell’s value, i. Input: N = 5, M = 8. The path can only be created out of a cell if its value is 1. countSub (n) = 2*Count (n-1) - Repetition. Print path from root to a given node in a binary tree; Enumeration of Binary Trees; Subtree with given sum in a Binary Tree; Sink Odd nodes in Binary Tree; Minimum moves to convert Tree to Star Tree; Print Binary Tree in 2-Dimensions; Find depth of the deepest odd level leaf node; Find distance from root to given node in a binary treeCourses. Note: Y. Initialising the Next array. 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. Find the shortest path from src(0) vertex to all the vertices and if it is impossible to reach any vertex, then return -1 for that vertex. Therefore, BFS is an appropriate algorithm to solve this problem. e. Hence, the shortest distance. Back to Explore Page. Shortest path between two nodes in array like representation of binary tree. e. Modify the above solution to find weight of longest path from a given source. 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. No cycle is formed, include it. Explanation: Path is 1 2. Expected Time complexity is O (MN) for a M x N matrix. The graph is denoted by G (V, E). Follow the steps mentioned below to implement the idea: Create a recursive function. Courses. e. Second path of length 2 is the shortest. Widest Path Problem | Practical application of Dijkstra's Algorithm. 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. Auxiliary Space: O (V+E) If you like GeeksforGeeks and would like to contribute, you can also write an article using write. . Using the fact that the second shortest path can not contain all the edges same as that in the shortest path. Note: The Graph doesn't contain any negative weight cycle. After the shortest distances have been calculated, you can print the shortest path to a node x by starting from x and following parent pointers p [x], p [p [x]], etc, until you hit the source. Examples: Input: N1 = 7, N2 = 4. Given a 2D binary matrix A(0-based index) of dimensions NxM. In the below map of Ninjaland let say you want to go from S=1 to T=8, the shortest path is (1, 3, 8). Also go through detailed tutorials. You need to find the shortest distance between a given source cell to a destination cell. e East, West, North, South) but his friend gave him a long route, help a person to find minimum Moves so that he can reach to the destination. The path can only be created out of a cell if its value is 1. e. ATTEMPTED BY: 2015 SUCCESS RATE: 86% LEVEL: Medium. An edge in an undirected connected graph is a bridge if removing it disconnects the graph. add the substring to the list. Return the length of the shortest path that visits every node. GFG Weekly Coding Contest; Job-A-Thon: Hiring Challenge; All Contests and Events. Solve company interview questions and improve your coding intellectUnique Paths II - You are given an m x n integer array grid. Problem: Given the adjacency list and number of vertices and edges of a graph, the task is to represent the adjacency list for a directed graph. You don't need to read input or print anything. There is one shortest path vertex 0 to vertex 0 (from each vertex there is a single shortest path to itself), one shortest path between vertex 0 to vertex 2. a) Extract minimum distance vertex from Set. Exclusively for Freshers! Participate for Free on 21st November & Fast-Track Your Resume to Top Tech Companies. You are also given an integer k. Approach: The given problem can be solved by maintaining two arrays, the shortest distance array taking source node as A which. Shortest cycle in an undirected unweighted graph. Practice. This can be achieved by modifying the Breadth-First-Traversal of the tree. The task is to find and print the path between the two given nodes in the binary tree. e. Follow the steps below to solve the problem: Create a set sptSet (shortest path tree set) that keeps track of vertices included in the shortest path tree, i. Find the shortest path from sr. Another method: It can be solved in polynomial time with the help of Breadth First Search. 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 a distance of edge [i] [2] for all i. Naive Approach: The idea is to generate all possible paths from the root node to all leaf nodes, keep track of the path with maximum length, finally print the longest path. A Computer Science portal for geeks. read more. Practice. But if I need to find the actual path,. 1 2 3. The following code prints the shortest distance from the source_node to all the other nodes in the graph. Let dp [X] [J] be the shortest path from. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3 * i. Following is the Backtracking algorithm for Knight’s tour problem. Exercise 5. Add the value of the current node to the path sum. You are given an integer K and source src and destination dst. Note: The Graph doesn't contain any negative weight cycle. A value of cell 3 means Blank cell. If you like GeeksforGeeks and would like to. The task is to print the cyclic path whose sum of weight is negative. Remove each edge of the shortest path one at a time and keep finding the shortest path, then one of them has to be the required second shortest path. Example 1: Input: V = 5, E = 5 adj. Practice. Find the distance of the shortest path from Num1. e. Approach: The simplest way to solve this problem is to use the LCA (Lowest Common Ancestor) of a binary tree. Find the shortest path from src(0) vertex to all the vertices and if it is impossible to reach any vertex, then return -1 for that vertex. 2) In weighted graph, minimum total weight of edges to duplicate so that given graph converts to a graph with Eulerian Cycle. Note: It is assumed that negative cost cycles do not exist in input matrix. Two cells are. 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. Below are steps. 3) While the stack is not empty, do the following: a) Pop the top node from the stack and add it to the path stack. Example 1: Input: n = 3, edges. 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. e. Print all shortest paths between given source and destination in an undirected graph. Algorithm: Step 1: Initialize a matrix and set its size to n x n. Start with the source node s and set its shortest path estimate to 0. Menu. : memo [k] [i] = min ( memo [k+1] [i], memo [k+1] [i+1]) + A [k] [i];You don't need to read input or print anything. BFS is generally used to find the Shortest Paths in the graph and the minimum distance of all nodes from Source, intermediate nodes, and Destination can be calculated by the. It defines a path with landmines which are marked as 0. Example 2: Input: K = 3 3 / 2 1 / 5 3 Output: 5 3. 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. Space Complexity: O(V). Below is the step by step process of finding longest paths –. Bellman-Ford Algorithm. Notation: If s is clear from context we may use dist(u)as short hand for dist(s;u). Length of shortest safe route is 13. "contribute", "practice"} word1 = "geeks" word2 = "practice" Output: 2 Explanation: Minimum distance between the words "geeks" and "practice" is 2. When it finds the first leaf node, it calls the printPath function to print the path from the leaf node to the root. Let the src be 2 and dst be 3. Start from the given start word. Return -1 if it is not possible to visit every edge once. 8. Step 3: Drop kth character from the substring obtained. 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. Strings are defined as an array of characters. of pq is a pair (weight, vertex). Given a weighted, directed and connected graph of V vertices and E edges, Find the shortest distance of all the vertex's from the source vertex S. nanoTime (); //population size int populationSize = 30; //Number of. Following figure is taken from this source. Print nodes having maximum and minimum degrees; Check if a cell can be visited more than once in a String; How to setup Competitive Programming in Visual Studio Code for C++; Multistage Graph (Shortest Path) Minimum number of edges that need to be added to form a triangle; Count of node sequences of length K consisting of at least one. For example, consider below graph. Given a Binary Tree of distinct nodes and a pair of nodes. Explanation: The shortest path is: 2 → 1. Given an undirected graph with V vertices and E edges, check whether it contains any cycle or not. /. 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}. So whenever the target word is found for the first time that will be the length of the shortest chain of words. 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. An Adjacency List is used for representing graphs. Example 1: Input: 1 2 3 4 5 6. Shortest Path-Printing using Dijkstra's Algorithm for Graph (Here it is implemented for undirected Graph. So there are n stairs. Step 3: Find edges connecting any tree vertex with the fringe vertices. Shortest Path by Removing K walls. Explanation: After reducing the weight of the edge connecting 1 and 2 by half modifies its new weight to 4. Shortest distance between two nodes in BST. The problem is to find the shortest distances between every pair of vertices in a given edge-weighted directed graph. Dijkstra's shortest path algorithm in Java using PriorityQueue. if there a multiple short paths with same cost then choose the one with the minimum number of edges. Follow the steps below to solve the given problem. Given two strings X and Y, print the shortest string that has both X and Y as subsequences. Algorithm to find shortest closed path or optimal Chinese postman route in a weighted graph that may not be Eulerian. Time Complexity: O (R * C), where R is number of rows and C are the number of columns in the given matrix. 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. Shortest path from a source cell to a destination cell of a Binary Matrix through cells consisting only of 1s. org or mail your article to [email protected] Path: An undirected graph has Eulerian Path if following two conditions are true. If there is no such path present then print “-1” . Follow the steps below to solve the problem: If the current cell is out of the boundary, then return. e. The sum of weight in the above path is -3 + 2 – 1 = -2. Output: Sort the nodes in a topological way. Step 5: Add the chosen edge to the MST if it does not. Otherwise, for each of four adjacent cells of the current cell, enqueue each of the valid cells with +1 distance and. 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’. Follow the steps below to solve the problem: Start from the root node of the Binary tree with the initial path sum of 0. We add an edge back before we process the next edge. 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. A solution that always finds shortest superstring takes exponential time. A simple solution is to start from u, go to all adjacent vertices, and recur for adjacent vertices with k as k-1, source. Shortest path in a graph from a source S to destination D with exactly K edges for multiple Queries. Since a policeman is present at the 1 st house, the only path that can be chosen is the 2nd path. Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph. Nodes are labeled from 0 to n-1, the task is to check if it contains a negative weight cycle or not. Meet In The Middle technique can be used to make the solution faster. The task is to find the cheapest cost path from given source to destination from K stops. Suppose,you need to find the shortest path. Examples: Input: X = "AGGTAB", Y = "GXTXAYB" Output: "AGXGTXAYB" OR "AGGXTXAYB" OR Any string that represents shortest supersequence of X and Y Input:. A value of cell 2 means Destination. Your task is to complete the function Paths () that takes the root node as an argument and return all the possible path. The rat can move only in two directions: forward and down. For example, the following graph has eulerian cycle as {1, 0, 3, 4, 0, 2, 1}Input: For given graph G. in all 4 directions. Given a directed graph. We can move exactly n steps from a cell in 4 directions i. The main idea is to recursively get the longest path from the left. It may cause starvation if shorter processes keep coming. We choose one of the 8 moves in this step). If current character, i. We can start from m [n-1] [m-1] as the base case with the length of longest increasing subsequence be 1, moving upwards and leftwards updating the value of cells. The task is to find the shortest path with minimum edges i. Time Complexity: O (R * C), where R is number of rows and C are the number of columns in the given matrix. 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. Practice. Step 4: if the subsequence is not in the list then recur. The graph is given as follows: graph[i] is a list of all nodes you can visit from node i (i. It is based on the idea that there is a cycle in a graph only if there is a back edge [i. , whose minimum distance from source is calculated and finalized. Step by step Shortest Path from source node to destination node in a Binary Tree. The task is to find the minimum sum of a falling path through A. in all 4 directions. The allowed moves are moving a cell left (L), right (R), up (U), and. The remote contains left, right, top and bottom keys. Print path between any two nodes in a Binary Tree; Preorder Traversal of Binary Tree; Count pairs of leaf nodes in a Binary Tree which are at most K distance apart; Print all root-to-leaf paths with maximum count of even nodes; Count nodes having highest value in the path from root to itself in a Binary Tree; Height and Depth of a node in a. Space Complexity: The space complexity of Dijkstra’s algorithm is O (V), where V is the number of vertices in the graph. Expected Time Complexity: O (R * C) Expected Auxiliary Space: O (1) Constraints: 1 <= R,C <= 103. Input: source vertex = 0 and destination vertex is = 7. Unique paths covering every non-obstacle block exactly once in a grid. We may assume that either both n1 and n2 are present in the tree or none of them are pres. Given a weighted, undirected and connected graph of V vertices and an adjacency list adj where adj [i] is a list of lists containing two integers where the first integer of each list. Initialize dist [] = {INF, INF,. Introduction to Kruskal’s Algorithm: Here we will discuss Kruskal’s. Dijkstra's Shortest Path Algorithm using priority_queue of STL. Your Task: You don't have to take input. 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 node points to one of its ancestors] present in the graph. The idea is to find paths from root nodes to the two nodes and store them in two separate vectors or arrays say path1 and path2. Characteristics of SJF Scheduling: Shortest Job first has the advantage of having a minimum average waiting time among all scheduling algorithms. , we use Topological Sorting . If a vertices can't be reach from the S then mark the distance as 10^8. , they are. Print a given matrix in spiral form using the simulation approach: To solve the problem follow the below idea: Draw the path that the spiral makes. Your task is to complete the function chinesePostmanProblem () which takes the edge list e [] [], number of nodes as input parameters and returns the length of the shortest path that visits each edge at least once. Example: Input: n = 9, m= 10 edges= [ [0,1], [0,3], [3,4. In this article we’re focusing on the differences between shortest path algorithms that are: Depth-First Search (DFS) Breadth-First Search (BFS) Multi-Source. Every item of set is a pair. The shortest path between 1 and 4 is 1 -> 3 -> 4 hence, the output is NO for the 1st example. Repeat Step 2 and 3 for all the subsequent nodes of the binary tree. Below is the implementation of the above approach: Python3. Therefore, BFS is an appropriate algorithm to solve this problem. Initialize a queue data structure that contains a list that will be composed of the. Therefore, print 8. e. Given the following grid containing alphabets from A-Z and a string S. Being at node 2, we need to take two steps ahead in order to reach. The robot tries to move to the bottom-right corner (i. Output -1 if no monotonic path is possible. Cycle 6 -> 1 -> 2 -> 6. Note that only one vertex with odd degree is not possible in an undirected graph (sum of all degrees is always even in an. In this post, O (ELogV) algorithm for. Replace all of the O’s in the matrix with their shortest distance from a guard, without being able to go through any walls. Expected Time Complexity: O (sqrt (N!)) Expected Auxiliary Space: O (N*N. 2) Create a separate stack to store the path from the root to the current node. Step 2: Pick edge 8-2. Using this it's clear to see that you can generate the shortest path with one linear scan of a topological ordering (pseudocode): Graph g Source s top_sorted_list = top_sort (g) cost = {} // A mapping between a node, the cost of its shortest path, and //its parent in the shortest path for each vertex v in top_sorted_list: cost [vertex]. Medium Accuracy: 32. 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. So the space needed is O(V). The task is to find and print the path between the two given nodes in the binary tree. A Graph is a non-linear data structure consisting of vertices and edges. Also go through detailed tutorials to improve your understanding to the topic. Cycle 6 -> 1 -> 2 -> 6. Approach: The solution is to perform BFS or DFS to find whether there is a path or not. You are given an Undirected Graph having unit weight, Find the shortest path from src to all the vertex and if. 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. Find the BFS traversal of the graph starting from the 0th vertex, from left to right according to the input graph. 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. Back to Explore Page. 1 ≤ cost of cells ≤ 1000. The edge (a, b) must be excluded if there is. Expected Time Complexity: O (N) Expected Auxillary Space: O (1) Constraints: 1 ≤ |S| ≤ 106. 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. Your task is to complete the function findShortestPath () which takes matrix as input parameter and return an integer denoting the shortest path. Therefore, if shortest paths can be found in G’, then longest paths can also be found in G. We start BFS from both the roots, start and finish at the same time but using only one queue. If a vertex is unreachable from the source node, then return -1 for that vertex. If it is unreachable then return -1. Keep the following conditions in mMinimum steps to reach the target by a Knight using BFS:. Same as condition (a) for Eulerian Cycle.