Introducción al algoritmo de búsqueda A* en IA
A* (pronunciado 'A-star') es un potente algoritmo de búsqueda de rutas y recorrido de gráficos ampliamente utilizado en inteligencia artificial e informática. Se utiliza principalmente para encontrar el camino más corto entre dos nodos en un gráfico, dado el costo estimado de llegar desde el nodo actual al nodo de destino. La principal ventaja del algoritmo es su capacidad para proporcionar una ruta óptima explorando el gráfico de una manera más informada en comparación con los algoritmos de búsqueda tradicionales como el algoritmo de Dijkstra.
El algoritmo A* combina las ventajas de otros dos algoritmos de búsqueda: el algoritmo de Dijkstra y Greedy Best-First Search. Al igual que el algoritmo de Dijkstra, A* garantiza que el camino encontrado sea lo más corto posible pero lo hace de manera más eficiente al dirigir su búsqueda a través de una heurística similar a Greedy Best-First Search. Una función heurística, denotada como h(n), estima el costo de llegar desde cualquier nodo n hasta el nodo de destino.
La idea principal de A* es evaluar cada nodo en función de dos parámetros:
comparación de cadenas en java
El algoritmo A* selecciona los nodos a explorar en función del valor más bajo de f(n), prefiriendo los nodos con el costo total estimado más bajo para alcanzar la meta. El algoritmo A* funciona:
- Cree una lista abierta de nodos encontrados pero no explorados.
- Cree una lista cerrada para contener nodos ya explorados.
- Agregue un nodo inicial a la lista abierta con un valor inicial de g
- Repita los siguientes pasos hasta que la lista abierta esté vacía o llegue al nodo de destino:
- Encuentre el nodo con el valor f más pequeño (es decir, el nodo con el menor g(n) h(n)) en la lista abierta.
- Mueva el nodo seleccionado de la lista abierta a la lista cerrada.
- Cree todos los descendientes válidos del nodo seleccionado.
- Para cada sucesor, calcule su valor g como la suma del valor g del nodo actual y el costo de pasar del nodo actual al nodo sucesor. Actualice el valor g del rastreador cuando encuentre una ruta mejor.
- Si el seguidor no está en la lista abierta, agréguelo con el valor g calculado y calcule su valor h. Si ya está en la lista abierta, actualice su valor g si la nueva ruta es mejor.
- Repita el ciclo. El algoritmo A* termina cuando se alcanza el nodo objetivo o cuando la lista abierta se vacía, lo que indica que no hay rutas desde el nodo inicial hasta el nodo objetivo. El algoritmo de búsqueda A* se utiliza ampliamente en diversos campos, como la robótica, los videojuegos, el enrutamiento de redes y los problemas de diseño, porque es eficiente y puede encontrar rutas óptimas en gráficos o redes.
Sin embargo, elegir una función heurística adecuada y aceptable es esencial para que el algoritmo funcione correctamente y proporcione una solución óptima.
Historia del algoritmo de búsqueda A* en Inteligencia Artificial
Fue desarrollado por Peter Hart, Nils Nilsson y Bertram Raphael en el Instituto de Investigación de Stanford (ahora SRI International) como una extensión del algoritmo de Dijkstra y otros algoritmos de búsqueda de la época. A* se publicó por primera vez en 1968 y rápidamente ganó reconocimiento por su importancia y eficacia en las comunidades de inteligencia artificial y ciencias de la computación. A continuación se ofrece una breve descripción de los hitos más críticos en la historia del algoritmo de búsqueda A*:
¿Cómo funciona el algoritmo de búsqueda A* en Inteligencia Artificial?
El algoritmo de búsqueda A* (pronunciado 'letra A') es un algoritmo de recorrido de gráficos popular y ampliamente utilizado en inteligencia artificial e informática. Se utiliza para encontrar la ruta más corta desde un nodo inicial hasta un nodo destino en un gráfico ponderado. A* es un algoritmo de búsqueda informado que utiliza heurísticas para guiar la búsqueda de manera eficiente. El algoritmo de búsqueda A* funciona de la siguiente manera:
El algoritmo comienza con una cola de prioridad para almacenar los nodos a explorar. También crea una instancia de dos estructuras de datos g(n): el costo de la ruta más corta hasta el momento desde el nodo inicial al nodo n y h(n), el costo estimado (heurístico) desde el nodo n hasta el nodo de destino. A menudo es una heurística razonable, lo que significa que nunca sobreestima el costo real de lograr un objetivo. Coloque el nodo inicial en la cola de prioridad y establezca su g (n) en 0. Si la cola de prioridad no está vacía, elimine el nodo con la f (n) más baja de la cola de prioridad. f(norte) = gramo(norte) h(norte). Si el nodo eliminado es el nodo de destino, el algoritmo finaliza y se encuentra la ruta. De lo contrario, expanda el nodo y cree sus vecinos. Para cada nodo vecino, calcule su valor g(n) inicial, que es la suma del valor g del nodo actual y el costo de pasar del nodo actual a un nodo vecino. Si el nodo vecino no está en orden de prioridad o el valor g(n) original es menor que su valor g actual, actualice su valor g y establezca su nodo principal en el nodo actual. Calcule el valor f(n) del nodo vecino y agréguelo a la cola de prioridad.
Si el ciclo termina sin encontrar el nodo destino, el gráfico no tiene recorrido de principio a fin. La clave de la eficiencia de A* es el uso de una función heurística h(n) que proporciona una estimación del coste restante para alcanzar el objetivo de cualquier nodo. Al combinar el costo real g (n) con el costo heurístico h (n), el algoritmo explora efectivamente caminos prometedores, priorizando los nodos que probablemente conduzcan al camino más corto. Es importante señalar que la eficiencia del algoritmo A* depende en gran medida de la elección de la función heurística. Las heurísticas aceptables garantizan que el algoritmo siempre encuentre el camino más corto, pero unas heurísticas más informadas y precisas pueden conducir a una convergencia más rápida y un espacio de búsqueda reducido.
Ventajas del algoritmo de búsqueda A* en Inteligencia Artificial
El algoritmo de búsqueda A* ofrece varias ventajas en escenarios de inteligencia artificial y resolución de problemas:
Desventajas del algoritmo de búsqueda A* en inteligencia artificial
Aunque el algoritmo de búsqueda A* (letra A) es una técnica poderosa y ampliamente utilizada para resolver problemas de recorrido de gráficos y búsqueda de rutas de IA, tiene desventajas y limitaciones. Estas son algunas de las principales desventajas del algoritmo de búsqueda:
Aplicaciones del Algoritmo de Búsqueda A* en Inteligencia Artificial
El algoritmo de búsqueda A* (letra A) es un algoritmo de búsqueda de rutas robusto y ampliamente utilizado en inteligencia artificial e informática. Su eficiencia y optimización lo hacen adecuado para diversas aplicaciones. A continuación se muestran algunas aplicaciones típicas del algoritmo de búsqueda A* en inteligencia artificial:
Estos son sólo algunos ejemplos de cómo el algoritmo de búsqueda A* encuentra aplicaciones en diversas áreas de la inteligencia artificial. Su flexibilidad, eficiencia y optimización lo convierten en una herramienta valiosa para muchos problemas.
unión izquierda vs unión derecha
Programa C para el Algoritmo de Búsqueda A* en Inteligencia Artificial
#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)> Programa C++ para el algoritmo de búsqueda A* en Inteligencia Artificial
#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> Explicación:
- Nodo inicial del camino.
Salida de muestra
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
Programa Java para el Algoritmo de Búsqueda A* en Inteligencia Artificial
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* Complejidad del algoritmo de búsqueda en inteligencia artificial
El algoritmo de búsqueda A* (pronunciado 'A-star') es un algoritmo de búsqueda de rutas y recorrido de gráficos popular y ampliamente utilizado en inteligencia artificial. Generalmente es común encontrar el camino más corto entre dos nodos en un entorno gráfico o basado en cuadrícula. El algoritmo combina los elementos de búsqueda de Dijkstra y los codiciosos mejores primero para explorar el espacio de búsqueda y al mismo tiempo garantizar la optimización de manera eficiente. Varios factores determinan la complejidad del algoritmo de búsqueda A*. Tamaño del gráfico (nodos y aristas): la cantidad de nodos y aristas de un gráfico afecta en gran medida la complejidad del algoritmo. Más nodos y aristas significan más opciones posibles para explorar, lo que puede aumentar el tiempo de ejecución del algoritmo.
Función heurística: A* utiliza una función heurística (a menudo denominada h(n)) para estimar el costo desde el nodo actual hasta el nodo de destino. La precisión de esta heurística afecta en gran medida la eficiencia de la búsqueda A*. Una buena heurística puede ayudar a guiar la búsqueda hacia un objetivo más rápidamente, mientras que una mala heurística puede conducir a búsquedas innecesarias.
En la práctica, sin embargo, A* suele funcionar significativamente mejor debido a la influencia de una función heurística que ayuda a guiar el algoritmo hacia caminos prometedores. En el caso de una heurística bien diseñada, el factor de ramificación efectivo es mucho menor, lo que conduce a un acercamiento más rápido a la solución óptima.