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```python
def a_star(start, end, map_grid):
open_list = PriorityQueue()
open_list.put((0, start))
came_from = {}
cost_so_far = {start: 0}

while not open_list.empty():
current = open_list.get()[1]
if current == end:
break
for next_node in get_neighbors(current, map_grid):
new_cost = cost_so_far[current] + 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(end, next_node)
open_list.put((priority, next_node))
came_from[next_node] = current
return reconstruct_path(came_from, start, end)
```
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