Ievads A* meklēšanas algoritmā AI
A* (izrunā 'A-zvaigzne') ir spēcīgs grafu šķērsošanas un ceļa noteikšanas algoritms, ko plaši izmanto mākslīgajā intelektā un datorzinātnēs. To galvenokārt izmanto, lai atrastu īsāko ceļu starp diviem diagrammas mezgliem, ņemot vērā aptuvenās izmaksas, kas saistītas ar nokļūšanu no pašreizējā mezgla uz galamērķa mezglu. Algoritma galvenā priekšrocība ir tā spēja nodrošināt optimālu ceļu, izpētot grafiku vairāk informētā veidā, salīdzinot ar tradicionālajiem meklēšanas algoritmiem, piemēram, Dijkstra algoritmu.
Algoritms A* apvieno divu citu meklēšanas algoritmu priekšrocības: Dijkstra algoritmu un Mantkārīgā labākā pirmā meklēšana. Tāpat kā Dijkstra algoritms, arī A* nodrošina, ka atrastais ceļš ir pēc iespējas īss, taču tas tiek darīts efektīvāk, meklējot meklēšanu, izmantojot heiristiku, kas ir līdzīga Mantkārīgā labākā pirmā meklēšana. Heiristiskā funkcija, kas apzīmēta ar h(n), aplēš izmaksas, kas rodas, nokļūstot no jebkura konkrētā mezgla n uz galamērķa mezglu.
A* galvenā ideja ir novērtēt katru mezglu, pamatojoties uz diviem parametriem:
java atjaunināšana
Algoritms A* izvēlas izpētāmos mezglus, pamatojoties uz zemāko f(n) vērtību, dodot priekšroku mezgliem ar viszemākajām aplēstajām kopējām izmaksām mērķa sasniegšanai. A* algoritms darbojas:
- Izveidojiet atklātu atrasto, bet neizpētīto mezglu sarakstu.
- Izveidojiet slēgtu sarakstu, lai saglabātu jau izpētītos mezglus.
- Pievienojiet sākuma mezglu atvērtajam sarakstam ar sākotnējo vērtību g
- Atkārtojiet šīs darbības, līdz atvērtais saraksts ir tukšs vai sasniedzat mērķa mezglu:
- Atvērtajā sarakstā atrodiet mezglu ar mazāko f vērtību (t.i., mezglu ar mazāko g(n) h(n)).
- Pārvietojiet atlasīto mezglu no atvērtā saraksta uz slēgto sarakstu.
- Izveidojiet visus derīgos atlasītā mezgla pēctečus.
- Katram pēctecim aprēķina g vērtību kā pašreizējā mezgla g vērtības summu un izmaksas, kas saistītas ar pārvietošanos no pašreizējā mezgla uz nākamo mezglu. Atjauniniet izsekotāja g vērtību, kad tiek atrasts labāks ceļš.
- Ja sekotājs nav atvērtajā sarakstā, pievienojiet to ar aprēķināto g vērtību un aprēķiniet tā h vērtību. Ja tas jau ir atvērtajā sarakstā, atjauniniet tā g vērtību, ja jaunais ceļš ir labāks.
- Atkārtojiet ciklu. Algoritms A* beidzas, kad tiek sasniegts mērķa mezgls vai kad atvērtais saraksts iztukšojas, norādot, ka nav ceļu no sākuma mezgla uz mērķa mezglu. A* meklēšanas algoritms tiek plaši izmantots dažādās jomās, piemēram, robotikā, videospēlēs, tīkla maršrutēšanas un projektēšanas problēmās, jo tas ir efektīvs un var atrast optimālus ceļus grafikos vai tīklos.
Tomēr ir svarīgi izvēlēties piemērotu un pieņemamu heiristisko funkciju, lai algoritms darbotos pareizi un nodrošinātu optimālu risinājumu.
Mākslīgā intelekta A* meklēšanas algoritma vēsture
To izstrādāja Pīters Hārts, Nils Nilsons un Bertrams Rafaels Stenfordas pētniecības institūtā (tagad SRI International) kā Dijkstra algoritma un citu tā laika meklēšanas algoritmu paplašinājumu. A* pirmo reizi tika publicēts 1968. gadā un ātri ieguva atzinību par savu nozīmi un efektivitāti mākslīgā intelekta un datorzinātņu kopienās. Šeit ir īss pārskats par vissvarīgākajiem pagrieziena punktiem meklēšanas algoritma A* vēsturē:
Kā A* meklēšanas algoritms darbojas mākslīgajā intelektā?
A* (izrunā 'burts A') meklēšanas algoritms ir populārs un plaši izmantots grafu šķērsošanas algoritms mākslīgajā intelektā un datorzinātnēs. To izmanto, lai svērtā grafikā atrastu īsāko ceļu no sākuma mezgla līdz galamērķa mezglam. A* ir informēts meklēšanas algoritms, kas izmanto heiristiku, lai efektīvi vadītu meklēšanu. Meklēšanas algoritms A* darbojas šādi:
Algoritms sākas ar prioritāro rindu, lai saglabātu izpētāmos mezglus. Tas arī veido divas datu struktūras g(n): līdz šim īsākā ceļa izmaksas no sākuma mezgla līdz mezglam n un h(n), aprēķinātās izmaksas (heiristiskais) no mezgla n līdz galamērķa mezglam. Bieži vien tā ir saprātīga heiristiska, kas nozīmē, ka tā nekad nepārvērtē faktiskās mērķa sasniegšanas izmaksas. Ievietojiet sākotnējo mezglu prioritātes rindā un iestatiet tā g(n) uz 0. Ja prioritātes rinda nav tukša, noņemiet no prioritātes rindas mezglu ar zemāko f(n). f(n) = g(n) h(n). Ja dzēstais mezgls ir galamērķa mezgls, algoritms beidzas un ceļš tiek atrasts. Pretējā gadījumā paplašiniet mezglu un izveidojiet tā kaimiņus. Katram kaimiņu mezglam aprēķiniet tā sākotnējo g(n) vērtību, kas ir pašreizējā mezgla g vērtības summa un izmaksas, kas saistītas ar pārvietošanos no pašreizējā mezgla uz blakus mezglu. Ja kaimiņu mezgls nav prioritārā secībā vai sākotnējā g(n) vērtība ir mazāka par tā pašreizējo g vērtību, atjauniniet tā g vērtību un iestatiet tā vecākmezglu uz pašreizējo mezglu. Aprēķiniet f(n) vērtību no kaimiņu mezgla un pievienojiet to prioritārajai rindai.
Ja cikls beidzas, neatrodot galamērķa mezglu, diagrammai nav ceļa no sākuma līdz beigām. A* efektivitātes atslēga ir heiristiskās funkcijas h(n) izmantošana, kas nodrošina jebkura mezgla mērķa sasniegšanas atlikušo izmaksu aprēķinu. Apvienojot faktiskās izmaksas g (n) ar heiristiskajām izmaksām h (n), algoritms efektīvi pēta daudzsološus ceļus, prioritāri nosakot mezglus, kas, iespējams, ved uz īsāko ceļu. Ir svarīgi atzīmēt, ka A* algoritma efektivitāte ir ļoti atkarīga no heiristiskās funkcijas izvēles. Pieņemama heiristika nodrošina, ka algoritms vienmēr atrod īsāko ceļu, taču informētāka un precīzāka heiristika var novest pie ātrākas konverģences un samazinātas meklēšanas vietas.
A* meklēšanas algoritma priekšrocības mākslīgajā intelektā
A* meklēšanas algoritms piedāvā vairākas priekšrocības mākslīgā intelekta un problēmu risināšanas scenārijos:
A* meklēšanas algoritma trūkumi mākslīgajā intelektā
Lai gan A* (burts A) meklēšanas algoritms ir plaši izmantots un jaudīgs paņēmiens mākslīgā intelekta ceļa noteikšanas un grafika šķērsošanas problēmu risināšanai, tam ir trūkumi un ierobežojumi. Šeit ir daži no galvenajiem meklēšanas algoritma trūkumiem:
A* meklēšanas algoritma pielietojumi mākslīgajā intelektā
Meklēšanas algoritms A* (burts A) ir plaši izmantots un stabils ceļu noteikšanas algoritms mākslīgajā intelektā un datorzinātnēs. Tā efektivitāte un optimālums padara to piemērotu dažādiem lietojumiem. Šeit ir daži tipiski A* meklēšanas algoritma pielietojumi mākslīgajā intelektā:
Šie ir tikai daži piemēri, kā A* meklēšanas algoritms atrod pielietojumu dažādās mākslīgā intelekta jomās. Tā elastība, efektivitāte un optimizācija padara to par vērtīgu rīku daudzu problēmu risināšanai.
C programma A* meklēšanas algoritmam mākslīgajā intelektā
#include #include #define ROWS 5 #define COLS 5 // Define a structure for a grid cell typedef struct { int row, col; } Cell; // Define a structure for a node in the A* algorithm typedef struct { Cell position; int g, h, f; struct Node* parent; } Node; // Function to calculate the Manhattan distance between two cells int heuristic(Cell current, Cell goal) { return abs(current.row - goal.row) + abs(current.col - goal.col); } // Function to check if a cell is valid (within the grid and not an obstacle) int isValid(int row, int col, int grid[ROWS][COLS]) { return (row >= 0) && (row = 0) && (col <cols) && (grid[row][col]="=" 0); } function to check if a cell is the goal int isgoal(cell cell, goal) { return (cell.row="=" goal.row) (cell.col="=" goal.col); perform a* search algorithm void astarsearch(int grid[rows][cols], start, todo: implement here main() grid[rows][cols]="{" {0, 1, 0, 0}, 0} }; start="{0," 0}; - cols 1}; astarsearch (grid, goal); 0; < pre> <p> <strong>Explanation:</strong> </p> <ol class="points"> <tr><td>Data Structures:</td> A cell structure represents a grid cell with a row and a column. The node structure stores information about a cell during an A* lookup, including its location, cost (g, h, f), and a reference to its parent. </tr><tr><td>Heuristic function (heuristic):</td> This function calculates the Manhattan distance (also known as a 'cab ride') between two cells. It is used as a heuristic to estimate the cost from the current cell to the target cell. The Manhattan distance is the sum of the absolute differences between rows and columns. </tr><tr><td>Validation function (isValid):</td> This function checks if the given cell is valid, i.e., whether it is within the grid boundaries and is not an obstacle (indicated by a grid value of 1). </tr><tr><td>Goal check function (isGoal):</td> This function checks if the given cell is a target cell, i.e., does it match the coordinates of the target cell. </tr><tr><td>Search function* (AStarSearch):</td> This is the main function where the A* search algorithm should be applied. It takes a grid, a source cell, and a target cell as inputs. This activity aims to find the shortest path from the beginning to the end, avoiding the obstacles on the grid. The main function initializes a grid representing the environment, a start, and a target cell. It then calls the AStarSearch function with those inputs. </tr></ol> <p> <strong>Sample Output</strong> </p> <pre> (0, 0) (1, 0) (2, 0) (3, 0) (4, 0) (4, 1) (4, 2) (4, 3) (4, 4) </pre> <h3>C++ program for A* Search Algorithm in Artificial Intelligence</h3> <pre> #include #include #include using namespace std; struct Node { int x, y; // Coordinates of the node int g; // Cost from the start node to this node int h; // Heuristic value (estimated cost from this node to the goal node) Node* parent; // Parent node in the path Node (int x, int y): x(x), y(y), g(0), h(0), parent(nullptr) {} // Calculate the total cost (f = g + h) int f () const { return g + h; } }; // Heuristic function (Euclidean distance) int calculateHeuristic (int x, int y, int goals, int goal) { return static cast (sqrt (pow (goals - x, 2) + pow (goal - y, 2))); } // A* search algorithm vector<pair> AStarSearch (int startX, int startY, int goals, int goal, vector<vector>& grid) { vector<pair> path; int rows = grid. size (); int cols = grid [0].size (); // Create the open and closed lists Priority queue <node*, vector, function> open List([](Node* lhs, Node* rhs) { return lhs->f() > rhs->f(); }); vector<vector> closed List (rows, vector (cols, false)); // Push the start node to the open list openList.push(start Node); // Main A* search loop while (! Open-list. Empty ()) { // Get the node with the lowest f value from the open list Node* current = open-list. Top (); openest. pop (); // Check if the current node is the goal node if (current->x == goals && current->y == goal) { // Reconstruct the path while (current! = nullptr) { path. push_back(make_pair(current->x, current->y)); current = current->parent; } Reverse (path. Begin(), path.end ()); break; } // Mark the current node as visited (in the closed list) Closed-list [current->x] [current->y] = true; // Generate successors (adjacent nodes) int dx [] = {1, 0, -1, 0}; int dy [] = {0, 1, 0, -1}; for (int i = 0; i x + dx [i]; int new Y = current->y + dy [i]; } break; } successor->parent = current; open List.push(successor); } // Cleanup memory for (Node* node: open List) { delete node; } return path; } int main () { int rows, cols; cout <> rows; cout <> cols; vector<vector> grid (rows, vector(cols)); cout << 'Enter the grid (0 for empty, 1 for obstacle):' << endl; for (int i = 0; i < rows; i++) { for (int j = 0; j> grid[i][j]; } } int startX, startY, goalX, goalY; cout <> startX >> start; cout <> goals >> goals; vector<pair> path = AStarSearch (startX, startY, goal, goal, grid); if (! path. Empty ()) { cout << 'Shortest path from (' << startX << ',' << start << ') to (' << goal << ',' << goal << '):' << endl; for (const auto& point: path) { cout << '(' << point. first << ',' << point. second << ') '; } cout << endl; } else { cout << 'No path found!' << endl; } return 0; } </pair></vector></vector></node*,></pair></vector></pair></pre> <p> <strong>Explanation:</strong> </p> <ol class="points"> <tr><td>Struct Node:</td> This defines a nodestructure that represents a grid cell. It contains the x and y coordinates of the node, the cost g from the starting node to that node, the heuristic value h (estimated cost from that node to the destination node), and a pointer to the <li>starting node of the path.</li> </tr><tr><td>Calculate heuristic:</td> This function calculates a heuristic using the Euclidean distance between a node and the target AStarSearch: This function runs the A* search algorithm. It takes the start and destination coordinates, a grid, and returns a vector of pairs representing the coordinates of the shortest path from start to finish. </tr><tr><td>Primary:</td> The program's main function takes input grids, origin, and target coordinates from the user. It then calls AStarSearch to find the shortest path and prints the result. Struct Node: This defines a node structure that represents a grid cell. It contains the x and y coordinates of the node, the cost g from the starting node to that node, the heuristic value h (estimated cost from that node to the destination node), and a pointer to the starting node of the path. </tr><tr><td>Calculate heuristic:</td> This function calculates heuristics using the Euclidean distance between a node and the target AStarSearch: This function runs the A* search algorithm. It takes the start and destination coordinates, a grid, and returns a vector of pairs representing the coordinates of the shortest path from start to finish. </tr></ol> <p> <strong>Sample Output</strong> </p> <pre> Enter the number of rows: 5 Enter the number of columns: 5 Enter the grid (0 for empty, 1 for obstacle): 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 Enter the start coordinates (x y): 0 0 Enter the goal coordinates (x y): 4 4 </pre> <h3>Java program for A* Search Algorithm in Artificial Intelligence</h3> <pre> import java. util.*; class Node { int x, y; // Coordinates of the node int g; // Cost from the start node to the current node int h; // Heuristic value (estimated cost from the current node to goal node) int f; // Total cost f = g + h Node parent; // Parent node in the path public Node (int x, int y) { this. g = x; this. f = y; this. Parent = null; } } public class AStarSearch { // Heuristic function (Manhattan distance) private static int heuristic (Node current, Node goal) { return Math. Abs (current.x - goal.x) + Math. Abs(current.y - goal.y); } // A* search algorithm public static List aStarSearch(int [][] grid, Node start, Node goal) { int rows = grid. Length; int cols = grid [0].length; // Add the start node to the open set opened.add(start); while (! openSet.isEmpty()) { // Get the node with the lowest f value from the open set Node current = openSet.poll(); // If the current node is the goal node, reconstruct the path and return it if (current == goal) { List path = new ArrayList(); while (current != null) { path.add(0, current); current = current.parent; } return path; } // Move the current node from the open set to the closed set closedSet.add(current); // Generate neighbors of the current node int[] dx = {-1, 0, 1, 0}; int[] dy = {0, -1, 0, 1}; for (int i = 0; i = 0 && nx = 0 && ny = neighbor.g) { // Skip this neighbor as it is already in the closed set with a lower or equal g value continue; } if (!openSet.contains(neighbor) || tentativeG <neighbor.g) { update the neighbor's values neighbor.g="tentativeG;" neighbor.h="heuristic(neighbor," goal); neighbor.f="neighbor.g" + neighbor.h; neighbor.parent="current;" if (!openset.contains(neighbor)) add neighbor to open set not already present openset.add(neighbor); } is empty and goal reached, there no path return null; public static void main(string[] args) int[][] grid="{" {0, 0, 0}, 1, 0} }; node start="new" node(0, 0); node(4, 4); list start, (path !="null)" system.out.println('path found:'); for (node : path) system.out.println('(' node.x ', ' node.y ')'); else system.out.println('no found.'); < pre> <p> <strong>Explanation:</strong> </p> <ol class="points"> <tr><td>Node Class:</td> We start by defining a nodeclass representing each grid cell. Each node contains coordinates (x, y), an initial node cost (g), a heuristic value (h), a total cost (f = g h), and a reference to the parent node of the path. </tr><tr><td>Heuristicfunction:</td> The heuristic function calculates the Manhattan distance between a node and a destination The Manhattan distance is a heuristic used to estimate the cost from the current node to the destination node. </tr><tr><td>Search algorithm* function:</td> A Star Search is the primary implementation of the search algorithm A*. It takes a 2D grid, a start node, and a destination node as inputs and returns a list of nodes representing the path from the start to the destination node. </tr><tr><td>Priority Queue and Closed Set:</td> The algorithm uses a priority queue (open Set) to track thenodes to be explored. The queue is ordered by total cost f, so the node with the lowest f value is examined The algorithm also uses a set (closed set) to track the explored nodes. </tr><tr><td>The main loop of the algorithm:</td> The main loop of the A* algorithm repeats until there are no more nodes to explore in the open Set. In each iteration, the node f with the lowest total cost is removed from the opener, and its neighbors are created. </tr><tr><td>Creating neighbors:</td> The algorithm creates four neighbors (up, down, left, right) for each node and verifies that each neighbor is valid (within the network boundaries and not as an obstacle). If the neighbor is valid, it calculates the initial value g from the source node to that neighbor and the heuristic value h from that neighbor to the destination The total cost is then calculated as the sum of f, g, and h. </tr><tr><td>Node evaluation:</td> The algorithm checks whether the neighbor is already in the closed set and, if so, whether the initial cost g is greater than or equal to the existing cost of the neighbor If true, the neighbor is omitted. Otherwise, the neighbor values are updated and added to the open Set if it is not already there. </tr><tr><td>Pathreconstruction:</td> When the destination node is reached, the algorithm reconstructs the path from the start node to the destination node following the main links from the destination node back to the start node. The path is returned as a list of nodes </tr></ol> <p> <strong>Sample Output</strong> </p> <pre> Path found: (0, 0) (0, 1) (1, 1) (2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (4, 4) </pre> <h2>A* Search Algorithm Complexity in Artificial Intelligence</h2> <p>The A* (pronounced 'A-star') search algorithm is a popular and widely used graph traversal and path search algorithm in artificial intelligence. Finding the shortest path between two nodes in a graph or grid-based environment is usually common. The algorithm combines Dijkstra's and greedy best-first search elements to explore the search space while ensuring optimality efficiently. Several factors determine the complexity of the A* search algorithm. Graph size (nodes and edges): A graph's number of nodes and edges greatly affects the algorithm's complexity. More nodes and edges mean more possible options to explore, which can increase the execution time of the algorithm.</p> <p>Heuristic function: A* uses a heuristic function (often denoted h(n)) to estimate the cost from the current node to the destination node. The precision of this heuristic greatly affects the efficiency of the A* search. A good heuristic can help guide the search to a goal more quickly, while a bad heuristic can lead to unnecessary searching.</p> <ol class="points"> <tr><td>Data Structures:</td> A* maintains two maindata structures: an open list (priority queue) and a closed list (or visited pool). The efficiency of these data structures, along with the chosen implementation (e.g., priority queue binary heaps), affects the algorithm's performance. </tr><tr><td>Branch factor:</td> The average number of followers for each node affects the number of nodes expanded during the search. A higher branching factor can lead to more exploration, which increases </tr><tr><td>Optimality and completeness:</td> A* guarantees both optimality (finding the shortest path) and completeness (finding a solution that exists). However, this guarantee comes with a trade-off in terms of computational complexity, as the algorithm must explore different paths for optimal performance. Regarding time complexity, the chosen heuristic function affects A* in the worst case. With an accepted heuristic (which never overestimates the true cost of reaching the goal), A* expands the fewest nodes among the optimization algorithms. The worst-case time complexity of A * is exponential in the worst-case O(b ^ d), where 'b' is the effective branching factor (average number of followers per node) and 'd' is the optimal </tr></ol> <p>In practice, however, A* often performs significantly better due to the influence of a heuristic function that helps guide the algorithm to promising paths. In the case of a well-designed heuristic, the effective branching factor is much smaller, which leads to a faster approach to the optimal solution.</p> <hr></neighbor.g)></pre></cols)> C++ programma A* meklēšanas algoritmam mākslīgajā intelektā
#include #include #include using namespace std; struct Node { int x, y; // Coordinates of the node int g; // Cost from the start node to this node int h; // Heuristic value (estimated cost from this node to the goal node) Node* parent; // Parent node in the path Node (int x, int y): x(x), y(y), g(0), h(0), parent(nullptr) {} // Calculate the total cost (f = g + h) int f () const { return g + h; } }; // Heuristic function (Euclidean distance) int calculateHeuristic (int x, int y, int goals, int goal) { return static cast (sqrt (pow (goals - x, 2) + pow (goal - y, 2))); } // A* search algorithm vector<pair> AStarSearch (int startX, int startY, int goals, int goal, vector<vector>& grid) { vector<pair> path; int rows = grid. size (); int cols = grid [0].size (); // Create the open and closed lists Priority queue <node*, vector, function> open List([](Node* lhs, Node* rhs) { return lhs->f() > rhs->f(); }); vector<vector> closed List (rows, vector (cols, false)); // Push the start node to the open list openList.push(start Node); // Main A* search loop while (! Open-list. Empty ()) { // Get the node with the lowest f value from the open list Node* current = open-list. Top (); openest. pop (); // Check if the current node is the goal node if (current->x == goals && current->y == goal) { // Reconstruct the path while (current! = nullptr) { path. push_back(make_pair(current->x, current->y)); current = current->parent; } Reverse (path. Begin(), path.end ()); break; } // Mark the current node as visited (in the closed list) Closed-list [current->x] [current->y] = true; // Generate successors (adjacent nodes) int dx [] = {1, 0, -1, 0}; int dy [] = {0, 1, 0, -1}; for (int i = 0; i x + dx [i]; int new Y = current->y + dy [i]; } break; } successor->parent = current; open List.push(successor); } // Cleanup memory for (Node* node: open List) { delete node; } return path; } int main () { int rows, cols; cout <> rows; cout <> cols; vector<vector> grid (rows, vector(cols)); cout << 'Enter the grid (0 for empty, 1 for obstacle):' << endl; for (int i = 0; i < rows; i++) { for (int j = 0; j> grid[i][j]; } } int startX, startY, goalX, goalY; cout <> startX >> start; cout <> goals >> goals; vector<pair> path = AStarSearch (startX, startY, goal, goal, grid); if (! path. Empty ()) { cout << 'Shortest path from (' << startX << ',' << start << ') to (' << goal << ',' << goal << '):' << endl; for (const auto& point: path) { cout << '(' << point. first << ',' << point. second << ') '; } cout << endl; } else { cout << 'No path found!' << endl; } return 0; } </pair></vector></vector></node*,></pair></vector></pair> Paskaidrojums:
Kylie Jenner vecums
- ceļa sākuma mezgls.
Izvades paraugs
Enter the number of rows: 5 Enter the number of columns: 5 Enter the grid (0 for empty, 1 for obstacle): 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 Enter the start coordinates (x y): 0 0 Enter the goal coordinates (x y): 4 4
Java programma A* meklēšanas algoritmam mākslīgajā intelektā
import java. util.*; class Node { int x, y; // Coordinates of the node int g; // Cost from the start node to the current node int h; // Heuristic value (estimated cost from the current node to goal node) int f; // Total cost f = g + h Node parent; // Parent node in the path public Node (int x, int y) { this. g = x; this. f = y; this. Parent = null; } } public class AStarSearch { // Heuristic function (Manhattan distance) private static int heuristic (Node current, Node goal) { return Math. Abs (current.x - goal.x) + Math. Abs(current.y - goal.y); } // A* search algorithm public static List aStarSearch(int [][] grid, Node start, Node goal) { int rows = grid. Length; int cols = grid [0].length; // Add the start node to the open set opened.add(start); while (! openSet.isEmpty()) { // Get the node with the lowest f value from the open set Node current = openSet.poll(); // If the current node is the goal node, reconstruct the path and return it if (current == goal) { List path = new ArrayList(); while (current != null) { path.add(0, current); current = current.parent; } return path; } // Move the current node from the open set to the closed set closedSet.add(current); // Generate neighbors of the current node int[] dx = {-1, 0, 1, 0}; int[] dy = {0, -1, 0, 1}; for (int i = 0; i = 0 && nx = 0 && ny = neighbor.g) { // Skip this neighbor as it is already in the closed set with a lower or equal g value continue; } if (!openSet.contains(neighbor) || tentativeG <neighbor.g) { update the neighbor\'s values neighbor.g="tentativeG;" neighbor.h="heuristic(neighbor," goal); neighbor.f="neighbor.g" + neighbor.h; neighbor.parent="current;" if (!openset.contains(neighbor)) add neighbor to open set not already present openset.add(neighbor); } is empty and goal reached, there no path return null; public static void main(string[] args) int[][] grid="{" {0, 0, 0}, 1, 0} }; node start="new" node(0, 0); node(4, 4); list start, (path !="null)" system.out.println(\'path found:\'); for (node : path) system.out.println(\'(\' node.x \', \' node.y \')\'); else system.out.println(\'no found.\'); < pre> <p> <strong>Explanation:</strong> </p> <ol class="points"> <tr><td>Node Class:</td> We start by defining a nodeclass representing each grid cell. Each node contains coordinates (x, y), an initial node cost (g), a heuristic value (h), a total cost (f = g h), and a reference to the parent node of the path. </tr><tr><td>Heuristicfunction:</td> The heuristic function calculates the Manhattan distance between a node and a destination The Manhattan distance is a heuristic used to estimate the cost from the current node to the destination node. </tr><tr><td>Search algorithm* function:</td> A Star Search is the primary implementation of the search algorithm A*. It takes a 2D grid, a start node, and a destination node as inputs and returns a list of nodes representing the path from the start to the destination node. </tr><tr><td>Priority Queue and Closed Set:</td> The algorithm uses a priority queue (open Set) to track thenodes to be explored. The queue is ordered by total cost f, so the node with the lowest f value is examined The algorithm also uses a set (closed set) to track the explored nodes. </tr><tr><td>The main loop of the algorithm:</td> The main loop of the A* algorithm repeats until there are no more nodes to explore in the open Set. In each iteration, the node f with the lowest total cost is removed from the opener, and its neighbors are created. </tr><tr><td>Creating neighbors:</td> The algorithm creates four neighbors (up, down, left, right) for each node and verifies that each neighbor is valid (within the network boundaries and not as an obstacle). If the neighbor is valid, it calculates the initial value g from the source node to that neighbor and the heuristic value h from that neighbor to the destination The total cost is then calculated as the sum of f, g, and h. </tr><tr><td>Node evaluation:</td> The algorithm checks whether the neighbor is already in the closed set and, if so, whether the initial cost g is greater than or equal to the existing cost of the neighbor If true, the neighbor is omitted. Otherwise, the neighbor values are updated and added to the open Set if it is not already there. </tr><tr><td>Pathreconstruction:</td> When the destination node is reached, the algorithm reconstructs the path from the start node to the destination node following the main links from the destination node back to the start node. The path is returned as a list of nodes </tr></ol> <p> <strong>Sample Output</strong> </p> <pre> Path found: (0, 0) (0, 1) (1, 1) (2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (4, 4) </pre> <h2>A* Search Algorithm Complexity in Artificial Intelligence</h2> <p>The A* (pronounced 'A-star') search algorithm is a popular and widely used graph traversal and path search algorithm in artificial intelligence. Finding the shortest path between two nodes in a graph or grid-based environment is usually common. The algorithm combines Dijkstra's and greedy best-first search elements to explore the search space while ensuring optimality efficiently. Several factors determine the complexity of the A* search algorithm. Graph size (nodes and edges): A graph's number of nodes and edges greatly affects the algorithm's complexity. More nodes and edges mean more possible options to explore, which can increase the execution time of the algorithm.</p> <p>Heuristic function: A* uses a heuristic function (often denoted h(n)) to estimate the cost from the current node to the destination node. The precision of this heuristic greatly affects the efficiency of the A* search. A good heuristic can help guide the search to a goal more quickly, while a bad heuristic can lead to unnecessary searching.</p> <ol class="points"> <tr><td>Data Structures:</td> A* maintains two maindata structures: an open list (priority queue) and a closed list (or visited pool). The efficiency of these data structures, along with the chosen implementation (e.g., priority queue binary heaps), affects the algorithm's performance. </tr><tr><td>Branch factor:</td> The average number of followers for each node affects the number of nodes expanded during the search. A higher branching factor can lead to more exploration, which increases </tr><tr><td>Optimality and completeness:</td> A* guarantees both optimality (finding the shortest path) and completeness (finding a solution that exists). However, this guarantee comes with a trade-off in terms of computational complexity, as the algorithm must explore different paths for optimal performance. Regarding time complexity, the chosen heuristic function affects A* in the worst case. With an accepted heuristic (which never overestimates the true cost of reaching the goal), A* expands the fewest nodes among the optimization algorithms. The worst-case time complexity of A * is exponential in the worst-case O(b ^ d), where 'b' is the effective branching factor (average number of followers per node) and 'd' is the optimal </tr></ol> <p>In practice, however, A* often performs significantly better due to the influence of a heuristic function that helps guide the algorithm to promising paths. In the case of a well-designed heuristic, the effective branching factor is much smaller, which leads to a faster approach to the optimal solution.</p> <hr></neighbor.g)> A* Meklēšanas algoritma sarežģītība mākslīgajā intelektā
Meklēšanas algoritms A* (izrunā 'A-zvaigzne') ir populārs un plaši izmantots grafu šķērsošanas un ceļa meklēšanas algoritms mākslīgajā intelektā. Parasti parasti tiek atrasts īsākais ceļš starp diviem mezgliem grafiskā vai režģa vidē. Algoritms apvieno Dijkstra un mantkārīgos labākos vispirms meklēšanas elementus, lai izpētītu meklēšanas telpu, vienlaikus efektīvi nodrošinot optimālumu. Vairāki faktori nosaka A* meklēšanas algoritma sarežģītību. Grafika lielums (mezgli un malas): grafa mezglu un malu skaits lielā mērā ietekmē algoritma sarežģītību. Vairāk mezglu un malu nozīmē vairāk iespēju izpētīt, kas var palielināt algoritma izpildes laiku.
Heiristiskā funkcija: A* izmanto heiristisko funkciju (bieži apzīmē h(n)), lai novērtētu izmaksas no pašreizējā mezgla līdz galamērķa mezglam. Šīs heiristikas precizitāte lielā mērā ietekmē A* meklēšanas efektivitāti. Laba heiristika var palīdzēt ātrāk virzīt meklēšanu uz mērķi, savukārt slikta heiritika var izraisīt nevajadzīgu meklēšanu.
Tomēr praksē A* bieži darbojas ievērojami labāk heiristiskās funkcijas ietekmes dēļ, kas palīdz virzīt algoritmu uz daudzsološiem ceļiem. Labi izstrādātas heiristikas gadījumā efektīvais sazarošanas faktors ir daudz mazāks, kas noved pie ātrākas pieejas optimālajam risinājumam.