IDA*是否与使用启发式函数的IDS相同？

import heapq

def heuristic(state):
    # 计算启发式值（例如曼哈顿距离）
    distance = 0
    for i in range(3):
        for j in range(3):
            if state[i][j] != 0:
                goal_i, goal_j = divmod(state[i][j] - 1, 3)
                distance += abs(i - goal_i) + abs(j - goal_j)
    return distance

def ida_star(initial_state):
    threshold = heuristic(initial_state)
    while True:
        visited = set()
        t, f = dfs(initial_state, 0, threshold, visited)
        if t == -1:
            return False
        if t == 0:
            return True
        threshold = f

def dfs(state, cost, threshold, visited):
    f = cost + heuristic(state)
    if f > threshold:
        return f, f
    if is_goal(state):
        return 0, 0
    visited.add(tuple(map(tuple, state)))
    min_cost = float('inf')
    for next_state in get_next_states(state):
        if tuple(map(tuple, next_state)) not in visited:
            t, f = dfs(next_state, cost + 1, threshold, visited)
            if t == 0:
                return 0, 0
            if t != -1:
                min_cost = min(min_cost, t)
    visited.remove(tuple(map(tuple, state)))
    return -1, min_cost

def is_goal(state):
    # 检查是否达到目标状态
    return state == [[1, 2, 3], [4, 5, 6], [7, 8, 0]]

def get_next_states(state):
    # 生成所有可能的下一步状态
    next_states = []
    i, j = find_zero(state)
    moves = [(0, 1), (1, 0), (0, -1), (-1, 0)]
    for move in moves:
        new_i, new_j = i + move[0], j + move[1]
        if 0 <= new_i < 3 and 0 <= new_j < 3:
            new_state = [row[:] for row in state]
            new_state[i][j], new_state[new_i][new_j] = new_state[new_i][new_j], new_state[i][j]
            next_states.append(new_state)
    return next_states

def find_zero(state):
    # 找到空白格的位置
    for i in range(3):
        for j in range(3):
            if state[i][j] == 0:
                return i, j

# 示例初始状态
initial_state = [[1, 2, 3], [4, 0, 5], [6, 7, 8]]
print(ida_star(initial_state))