, (0, 0)) to the bottom-right cell (i. 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. Length of shortest safe route is 13. You don't need to read input or print anything. first n characters in input string. The time complexity of this approach is O (N 2 ). Check our Website: case you are thinking to buy courses, please check below: Link to get 20% additional Discount at Coding Ni. The Minimum distance of all nodes from Source, intermediate, and destination can be found by doing Dijkstra’s Shortest Path algorithm from these 3. Approach: The path from any root vertex to any vertex ‘i’ is the path from the root vertex to its parent followed by the parent itself. e. Example1: Input: N = 4, M = 2 edge = [[0,1,2],[0,2,1]] Output: 0 2 1 -1 Explanation: Shortest path from 0 to 1 is 0->1 with edge weight 2. Practice Video Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph. The problem is to find the shortest distances between every pair of vertices in a given edge-weighted directed graph. Shortest Source to Destination Path | Practice | GeeksforGeeks Back to Explore Page Given a 2D binary matrix A (0-based index) of dimensions NxM. While there are non-empty buckets:. 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. Print all shortest paths between given source and destination in. Given a square chessboard, the initial position of Knight and position of a target. Example: Input: n = 9, m= 10 edges= [ [0,1], [0,3], [3,4], [4 , Practice. If the path exists between two nodes then Next [u] [v] = v. There are n stairs, and a person is allowed to jump next stair, skip one stair or skip two stairs. 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. Shortest path from a source cell to a destination cell of a Binary Matrix through cells consisting only of 1s. a) Find the most overlapping string pair in temp []. */. A person wants to go from origin to a particular location, he can move in only 4 directions (i. Below is BFS based solution. 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. For every vertex being processed, we update distances of its adjacent using distance of current vertex. Given a Binary Tree of distinct nodes and a pair of nodes. Shortest path from 0 to 2 is 0->2 with edge weight 1. Step 4: Find the minimum among these edges. 89% Submissions: 109K+ Points: 4. Your Task: You don't need to read or print anything. Follow the steps below to solve the problem: Initialize an array dp [] of size N, where dp [i] stores the minimum number of jumps required to reach the end of the array arr [N – 1] from the index i. For example a solution is 1033, 1733, 3733, 3739, 3779, 8779, 8179. So the space needed is O(V). Set value of count [i] [0] equal to 1 for 0 <= i < M as the answer of subproblem with a single column is equal to 1. 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. Therefore, if shortest paths can be found in G’, then longest paths can also be found in G. Path to reach border cells from a given cell in a 2D Grid without crossing specially marked cells. Therefore, follow the steps below to solve the problem: Perform Depth First Search traversal on the tree starting from the root node. For example, if the target node is 8 and k is 2, then such nodes are 10 and 14. Shortest path length between two given nodes such that adjacent nodes are at bit difference 2. Consider a directed graph whose vertices are numbered from 1 to n. , removing the edge disconnects the graph. A Bellman-Ford algorithm is also guaranteed to find the shortest path in a graph, similar to. Follow the below steps to solve the above problem: 1) Start at the root node and push it onto a stack. Courses. 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. Here, for every vertex in the graph, we have a list of all the other vertices which the particular vertex has an edge to. If there is no clear path, return -1. The path can only be created out of a cell if its value is 1. Follow the steps below to solve the problem: If the current cell is out of the boundary, then return. However, the longest path problem has a linear time solution for directed acyclic 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. Remove nodes from Binary Tree such that sum of all remaining root-to-leaf paths is atleast K. If there is no possible path, return -1. Your task is to complete the function Paths () that takes the root node as an argument and return all the possible path. (weight, vertex). read more. 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. Complete the function shortest path () which takes a 2d vector or array edges representing the edges of undirected graph with unit weight, an integer N as number nodes, an integer M as number of edges and an integer src as the input parameters and returns an integer array or vector, denoting the vector of distance from src to all nodes. Back to Explore Page. The task is to find the cheapest cost path from given source to destination from K stops. Let us consider another. Here adj[i] contains vectors of size 2,Euler first introduced graph theory to solve this problem. Shortest Path-Printing using Dijkstra's Algorithm for Graph (Here it is implemented for undirected Graph. Sum of weights of path between nodes 2 and 3 = 3. 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. GfG Weekly + You = Perfect Sunday Evenings! Register for free now. Example 1: Input: N = 9 Output: 2 Explanation: 9 -> 3 -> 1, so number of steps are 2. 8. 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. The task is to find the shortest path with minimum edges i. Given a square maze containing positive numbers, find all paths from a corner cell (any of the extreme four corners) to the middle cell. Explanation: Path is 1 2. Below is the step by step process of finding longest paths –. Hard Accuracy: 50. , there is a directed edge from node i to node graph[i][j] ). The task is to find and print the path between the two given nodes in the binary tree. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. distance) is used as first item of pair. Note: All weights are non-negative. Your task is to complete the function longestPath() which takes matrix ,source and destination as input parameters and returns an integer denoting the longest path. Example 1: Input: V = 2 adj [] = { { {1, 9}}, { {0, 9}}} S = 0 Output: 0 9 Explanation: The source vertex is 0. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. 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. If a vertices can't be reach from the S then mark the distance as 10^8. 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. Watch the new video in more detail about dijsktra:. Solve one problem based on Data Structures and Algorithms every day and win exciting prizes. Lesser overheads than Bellman-Ford. Given a 3-D array arr [l] [m] [n], the task is to find the minimum path sum from the first cell of the array to the last cell of the array. Platform to practice programming problems. You. From each cell you can either move only to right or down. Shortest Path by Removing K walls. 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. Dijkstra’s Algorithm: It works on Non-Negative Weighted graphs. Strings are considered a data type in general and are typically represented as arrays of bytes (or words) that store a sequence of characters. C++ Program for Shortest distance between two cells in a matrix or grid. Paytm. ATTEMPTED BY: 2015 SUCCESS RATE: 86% LEVEL: Medium. VMWare. A value of cell 3 means Blank cell. Explanation: The first and last node of the input sequence is 1 and 4 respectively. Print all root to leaf paths with there relative positions. Output: 3. The task is to find the minimum number. Below are steps. We use a double-ended queue to store the node. Output: 3. 2) Create an empty set. Find minimum number of edges between (1, 5). Disclaimer: Please watch Part-1 and Part-2 Part-1:. Overview. If a vertices can't be reach from the S then mark the distance as 10^8. 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. For target node 8 and k is 2, the node 22 comes in this category. 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. Menu. Medium Accuracy: 32. Here we not only find the shortest distance but also the path. Try all 8 possible positions where a Knight can reach from its position. If there is no possible path, return -1. Your task is to complete the function findShortestPath () which takes matrix as input parameter and return an integer denoting the shortest path. The robot can only move either down or right at any point in time. Therefore, the problem can be solved using BFS. Shortest Path between two nodes of graph. The problem is to find the shortest distances between every pair of vertices in a given edge-weighted directed graph. In this article, an O (E*K) approach is discussed for solving this problem. Output. Push the word in the queue. in order to generate different substring. Find the length of the shortest transformation sequence from startWord to targetWord. Another method: It can be solved in polynomial time with the help of Breadth First Search. Example 2: Input: 10 / 20 30 40 60 / 2 Output: 3 Explanation: Minimum depth. 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. The task is to find the minimum sum of a falling path through A. Print all root to leaf paths of an N-ary tree. Dijkstra’s shortest path for adjacency matrix representation. Check if it is possible to make all elements into 1 except obstacles. Input: N = 3, M = 2, edges = { {1, 2, 4}, {1, 3, 5}} Output: 1. Approach: The given problem can be solved by maintaining two arrays, the shortest distance array taking source node as A which. Practice. An Efficient Solution doesn’t require the generation of subsequences. This problem is mainly an extension of Find distance between two given keys of a Binary Tree. Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph. If there is no possible path, return -1. If current character, i. 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. Below is the implementation of the approach. Pick the smallest edge. Output: Shortest path length is:5. Contests. Improve this answer. Back to Explore Page. Given an n x n binary matrix grid, return the length of the shortest clear path in the matrix. The task is to find the sum of weights of the edges of the Minimum Spanning Tree. Following figure is taken from this source. Find out the minimum steps a Knight will take to reach the target position. 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. You are also given an integer k. Approach: The solution is to perform BFS or DFS to find whether there is a path or not. Note: edges [i] is defined as u, v and weight. Hard Accuracy: 50. The idea is similar to linear time solution for shortest path in a directed acyclic graph. Step 1: Determine an arbitrary vertex as the starting vertex of the MST. Sum of weights of path between nodes 1 and 2 = 2. It chooses one element from each next row. e. 2) Assign a distance value to all vertices in the input graph. Given two strings X and Y, print the shortest string that has both X and Y as subsequences. Print all shortest paths between given source and destination in an undirected graph. We would like to show you a description here but the site won’t allow us. One possible Topological order for the graph is 3, 2, 1, 0. If the reachable position is not already visited and is inside the board, push. Your Task: You don't need to read input or print anything. Courses. For example, lcs of “geek” and “eke” is “ek”. Share. Find All possible paths from top left to bottom right. The idea is to use dynamic-programming to solve this problem. Practice Given an undirected and unweighted graph and two nodes as source and destination, the task is to print all the paths of the shortest length between the given source and destination. Otherwise, for each of four adjacent cells of the current cell, enqueue each of the valid cells with +1 distance and. There are 3 different paths from 2 to 3. Approach: For every vertex, we check if it is possible to get the shortest cycle involving this vertex. 0-1 BFS (Shortest Path in a Binary Weight Graph) Shortest path between two nodes in array like representation of binary tree. Approach: The idea is to traverse all vertices of the graph using BFS and use priority queue to store the vertices for which the shortest distance. Shortest path from 1 to n | Practice | GeeksforGeeks. Dijkstra. Eventually, the shortest path, if one exists, is found and the spring has been relaxed to its resting length. Time Complexity: O (V+E) where V is the number of vertices and E is the number of edges. A node is at k distance from a leaf if it is present k levels above the leaf and also, is a direct ancestor of this. Expected Time Complexity: O (R * C) Expected Auxiliary Space: O (1) Constraints: 1 <= R,C <= 103. Given a directed acyclic graph (DAG) with n nodes labeled from 0 to n-1. Approach: The idea is to use breadth first search to calculate the shortest path from source to destination. Complete the function printPath() which takes N and 2D array m[ ][ ] as input parameters and returns the list of paths in lexicographically increasing order. e. It may cause starvation if shorter processes keep coming. Assume any vertex (let’s say ‘0’) as source and assign dist = 0. Expected Time Complexity: O (n*m) Expected Space Compelxity: O (n) Constraints: 1 <= n <= 100. Examples: Input: N = 4, M = 5. Consider the following directed graph. The description of cells is as follows: A value of cell 1 means Source. distance as 0. e. It's based on the observation that edge for which dist + edge_weight is minimum is on the path (when looking backwards). Print all paths from a given source to a destination using BFS. 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. if there a multiple short paths with same cost then choose the one with the minimum number of edges. Shortest cycle in an undirected unweighted graph. Step 5: Add the chosen edge to the MST if it does not. Explanation: Vertex 3 from vertex 1 via vertices 2 or 4. 4) Huffman. Example 1: Input: 1 / 3 2 / 4 Output: 2 Explanation: Minimum depth is between nodes 1 and 2 since minimum depth is defined as the number of nodes along the shortest path from the root node down to the nearest leaf node. Given two four digit prime numbers, suppose 1033 and 8179, we need to find the shortest path from 1033 to 8179 by altering only single digit at a time such that every number that we get after changing a digit is prime. So “ek” becomes “geeke” which is shortest common supersequence. (The values are returned as vector in cpp, as. e. e. Shortest Path in a weighted Graph where weight of an edge is 1 or 2. e. Copy contents. We can make above string palindrome as "CBABC". Read. of pq is a pair (weight, vertex). Every item of set is a pair. Longest path is from 5 to 7 of length 5. For a disconnected undirected graph, the definition is similar, a bridge is an edge removal that increases the number of disconnected components. Nodes should be printed from left to right. It was conceived by Dutch computer scientist Edsger W. Output: Sort the nodes in a topological way. You are given an array graph where graph [i] is a list of. 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. The graph is denoted by G (V, E). 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. We then work backwards from the target vertex t to the source vertex s. Also, you should only take nodes directly or indirectly connected from Node. Initialize dist [] = {INF, INF,. Algorithm : create a queue which will store path(s) of type vector initialise the queue with first path starting from src Now run a loop till queue is not empty get the frontmost path from queue check if the lastnode of this path is destination if true then print the path run a loop for all the vertices connected to the. 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. Therefore, print 8. A value of cell 2 means Destination. Another method: It can be solved in polynomial time with the help of Breadth First Search. 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. Shortest Path by Removing K walls. Also go through detailed tutorials. Time Complexity: O(n*n*L) where n is the length of the input string and L is the maximum length of word in the dictionary. Your Task: You don't need to read input or print anything. Given a weighted directed graph with n nodes and m edges. Given a binary tree, you need to find the number of all root to leaf paths along with their path lengths. Since distance of + 5 and – 5 from 0 is same, hence we find answer for absolute value of destination. If there are 0 odd vertices, start anywhere. Algorithm. Copy contents. 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. , str [n-1] of str has. a) Extract minimum distance vertex from Set. 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. Expected Time Complexity: O (sqrt (N!)) Expected Auxiliary Space: O (N*N. Below is an Approximate Greedy algorithm. Note that only one vertex with odd degree is not possible in an undirected graph (sum of all degrees is always even in an. These paths should no. Note: The Graph doesn't contain any negative weight cycle. The valid moves are: Go Top: (x, y) ——> (x – 1, y) Go. 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. Your Task: You don't need to read input or print anything. In this problem, we are given a matrix mat [] []. Note: Y. You don't need to read input or print anything. Nodes are labeled from 0 to n-1, the task is to check if it contains a negative weight cycle or not. Space Complexity: The space complexity of Dijkstra’s algorithm is O (V), where V is the number of vertices in the graph. 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. For example consider the below graph. If there is no such path present then print “-1” . Return the length of the shortest path that visits every node. Method 1. 1) Create an auxiliary array of strings, temp []. Algorithm: Steps involved in finding the topological ordering of a DAG: Step-1: Compute in-degree (number of incoming edges) for each of the vertex present in the DAG and initialize the count of visited nodes as 0. And after that, minimum pathsum at the ith node of kth row would be the minimum of the pathsum of its two children + the node’s value, i. 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. Top-down approach for printing Longest Common Subsequence: Follow the steps below for the implementation: Check if one of the two strings is of size zero, then we return an empty string because the LCS, in this case, is empty (base case). , 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). The task is to find the sum of weights of the edges of the Minimum Spanning Tree. Step 4: if the subsequence is not in the list then recur. countSub (n) = 2*Count (n-1) - Repetition. Courses. A Simple Solution is to use Dijkstra’s shortest path algorithm, we can get a shortest path in O (E + VLogV) time. Input: 1 / 2 3 Output: 1 2 #1 3 # Explanation: All possible paths: 1->2 1->3. Find the minimum number of steps required to reach from (0,0) to (X, Y). You have to return a list of integers denoting shortest distance between each node and Source vertex S. 2K 161 You have an undirected, connected graph of n nodes labeled from 0 to n - 1. Count all possible paths from source to destination in given 3D array. The important thing to note is we can reach any destination as it is always possible to make a move of length 1. e. When we find “. used to compare two pairs. Expected Time Compelxity: O (n2*log (n)) Expected Auxiliary Space: O (n2) Constraints: 1 ≤ n ≤ 500. Here we not only find the shortest distance but also the path. Same as condition (a) for Eulerian Cycle. 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 graphPractice. e. The graph is given as follows: graph[i] is a list of all nodes you can visit from node i (i. Solve DSA problems on GfG Practice. e. Use a table to store solutions of subproblems to avoiding recalculate the same subproblems multiple times. The idea is to use the Bellman–Ford algorithm to compute the shortest paths from a single source vertex to all the other vertices in a given weighted digraph. Bellman-Ford algorithm for Shortest Path Algorithm: 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. Explanation: Path is 4 2 1 3. 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 our path, we simply pop the topmost element as we have to jump back to parent’s directory. e. We have discussed Dijkstra’s Shortest Path algorithm in the below posts. Return -1 if it is not possible to visit every edge once. 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. Method 1. In this Video, we are going to learn about Shortest Path in DAG. Shortest Path Revisited. The main idea is to recursively get the longest path from the left. Practice. It's a common practice to augment dynamic programming algorithms to store parent pointers. If a graph contains a. Step by step Shortest Path from source node to destination node in a Binary Tree. Shortest path in a directed graph by Dijkstra’s algorithm. Back to Explore Page. add the substring to the list. , a node points to one of its ancestors] present in the graph. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution. 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. Expected Time Complexity: O (N). Path is:: 2 1 0 3 4 6. This gives the shortest path. Given a Binary Tree and a number k, remove all nodes that lie only on root to leaf path (s) of length smaller than k. Output : 3. Follow the steps below to solve the problem: Create dp [N] [N] and ANS [N] [N] tables with all values set to INT_MAX and INT_MIN. Use Breadth First Search to find the solution optimally. A Graph is a non-linear data structure consisting of vertices and edges. Step 2: Iterate from the end of string. For every index we have four options, so our overall time complexity will become 4^ (R*C). Expected time complexity is O (V+E). Hence, the shortest distance. Bellman-Ford Algorithm. We can make above string palindrome as AAAACECAAAA. Note: If the Graph contains. A falling path will start at any element in the first row and ends in last row. Eulerian Circuit is an Eulerian Path which starts and ends on the same vertex. Example 2: Input: x = 8, y = 10 Output: 4 Explanation: 8-> 4-> 2-> 5-> 10 The length of the shortest path between 8 and 10 is 4. 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. Auxiliary Space: O (V) 5. 2) Other nodes, may be an ancestor of target, or a node in some other subtree. 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. 2) Create an empty priority_queue pq. Discuss. Approach: The idea is to use Dijkstra’s shortest path algorithm with a slight variation. You are situated in the top-left cell, (0, 0), a . A clear path in a binary matrix is a path from the top-left cell (i. It is practically infeasible as Operating System may. An Adjacency List is used for representing graphs. Find the length of the shortest transformation sequence from startWord to targetWord. 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[]. Dynamic programming can be used to solve this problem. Hence, sum = 1 + 3 + 6 + 2 + 5 + 3 = 20. Note: edges[i] is defined as u,. Consider a directed graph whose vertices are numbered from 1 to n. Meet In The Middle technique can be used to make the solution faster. Given two strings X and Y, print the shortest string that has both X and Y as subsequences. Example 1: Input: K = 0 1 / 3 2 Output: 1. Practice. Output. unweighted graph of 8 vertices. Exclusively for Freshers! Participate for Free on 21st November & Fast-Track Your Resume to Top Tech Companies. Back to Explore Page. There is a robot initially located at the top-left corner (i. package ga; import java.