Aunque ambos equipos mostraron su poderío ofensivo, fue la defensa zonal implementada por Real Madrid lo que marcó la diferencia, limitando las opciones ofensivas del FC Barcelona.
Dentro del análisis detallado podemos observar cómo cada jugador cumplió su rol defensivo con precisión, haciendo casi imposible encontrar espacios libres para anotar desde posiciones ventajosas.
A pesar del dominio inicial del FC Barcelona con un impresionante 30-20 al final del primer cuarto, Real Madrid ajustó sus tácticas durante el descanso corto logrando equilibrar el marcador hacia mediados del segundo cuarto (45-42).
Luego continuaron intensificando su presión defensiva combinada con rápidas transiciones ofensivas aprovechando errores menores cometidos por su rival, finalizando con un contundente 90-85 favorable al Real Madrid.
assistantTo solve the problem of finding the shortest path in a grid with obstacles using the A* algorithm, we'll follow these steps:
1. **Understand the Grid**: The grid is represented as a 2D list where `0` indicates an open cell and `1` indicates an obstacle.
2. **Define the A* Algorithm**: A* is a pathfinding algorithm that uses heuristics to efficiently find the shortest path from a start point to an end point.
3. **Heuristic Function**: Use the Manhattan distance as the heuristic function since we can only move up, down, left, or right.
4. **Implement the A* Algorithm**:
- Use a priority queue to explore nodes with the lowest cost first.
- Track the cost to reach each node and the path taken to get there.
- Use a set to keep track of visited nodes to avoid processing them multiple times.
5. **Edge Cases**: Handle cases where the start or end is an obstacle or if no path exists.
Here's a Python implementation:
python
import heapq
def heuristic(a, b):
# Manhattan distance
return abs(a[0] - b[0]) + abs(a[1] - b[1])
def astar(grid, start, goal):
rows, cols = len(grid), len(grid[0])
# Directions for moving in the grid (up, down, left, right)
directions = [(-1, 0), (1, 0), (0, -1), (0, 1)]
# Priority queue for A* (cost so far + heuristic)
open_set = []
heapq.heappush(open_set, (0 + heuristic(start, goal), 0, start))
# Cost to reach each node
cost_so_far = {start: 0}
# Path tracking
came_from = {start: None}
while open_set:
_, current_cost, current = heapq.heappop(open_set)
if current == goal:
# Reconstruct path
path = []
while current:
path.append(current)
current = came_from[current]
return path[::-1]
for direction in directions:
next_node = (current[0] + direction[0], current[1] + direction[1])
if 0 <= next_node[0] < rows and 0 <= next_node[1] < cols:
if grid[next_node[0]][next_node[1]] == 1:
continue
new_cost = current_cost + 1
if next_node not in cost_so_far or new_cost < cost_so_far[next_node]:
cost_so_far[next_node] = new_cost
priority = new_cost + heuristic(next_node, goal)
heapq.heappush(open_set, (priority, new_cost, next_node))
came_from[next_node] = current
return None # No path found
# Example usage
grid = [
[0, 1, 0, 0, 0],
[0, 1, 0, 1, 0],
[0, 0, 0, 1, 0],
[0, 1, 1, 1, 0],
[0, 0, 0, 0, 0]
]
start = (0, 0)
goal = (4, 4)
path = astar(grid, start, goal)
print("Path:", path)
### Explanation:
- **Heuristic Function**: Calculates the Manhattan distance between two points.
- **Priority Queue**: Uses `heapq` to manage nodes by their total estimated cost (actual cost + heuristic).
- **Cost Tracking**: Keeps track of the lowest cost to reach each node.
- **Path Reconstruction**: Backtracks from the goal to the start using `came_from` to reconstruct the path.
This implementation will find the shortest path from `start` to `goal` if one exists. If no path is found due to obstacles blocking all routes or invalid start/goal positions within obstacles, it returns `None`.
