If a heuristic is consistent, then it is admissable.

This statement is true. A heuristic is said to be admissible if it never overestimates the cost of reaching the goal. A heuristic is said to be consistent if the estimated cost of reaching a goal from a given node is no greater than the sum of the cost of reaching the next node and the estimated cost of reaching the goal from that next node. It can be shown that every consistent heuristic is admissible.

相关问题

If a heuristic is admissable, then it is consistent

This statement is true. In fact, if a heuristic is admissible, then it is guaranteed to be consistent.

A heuristic is admissible if it never overestimates the actual cost of reaching the goal state from the current state. Consistency, on the other hand, requires that the estimated cost of reaching a neighboring state plus the cost of getting from that neighboring state to the goal state is never lower than the estimated cost of getting to the goal state directly from the current state.

Because an admissible heuristic never overestimates the actual cost, it also satisfies the requirements for consistency. Therefore, any admissible heuristic is also consistent.

class Node(Generic[T]): def __init__(self, state: T, parent: Optional[Node], cost: float = 0, heuristic: float = 0) -> None: self.state: T = state self.parent: Optional[Node] = parent self.cost: float = cost self.heuristic = heuristic def __lt__(self, other): return (self.cost + self.heuristic) < (other.cost + other.heuristic)什么意思

这是一个实现 A* 搜索算法的节点类。A* 搜索算法是一种启发式搜索算法，用于解决最短路径问题，其中启发函数（heuristic function）用于评估每个节点的估价函数值，以估计该节点到目标节点的距离。该节点类中，state 表示节点的状态，parent 表示父节点，cost 表示从起始节点到该节点的路径长度，heuristic 表示该节点到目标节点的估价函数值。__lt__ 方法用于比较两个节点的优先级，优先级按照节点的 f 值（f = g + h，其中 g 是从起始节点到该节点的实际路径长度，h 是该节点到目标节点的估价函数值）排序，f 值越小，优先级越高。