



'''simple docstring'''





import heapq
import sys

import numpy as np

_lowerCAmelCase										=     tuple[int, int]






class 	lowerCAmelCase_:
  '''simple docstring'''




  def __init__(   self				)   ->		List[str]:
      lowerCAmelCase__			:  Optional[int]											= []
      lowerCAmelCase__			:  List[str]											= set()




  def 							UpperCAmelCase_     (   self				)   ->		Any:
      if not self.empty():
          return self.elements[0][0]
      else:
          return float("""inf"""				)




  def 							UpperCAmelCase_     (   self				)   ->		List[str]:
      return len(self.elements				) == 0




  def 							UpperCAmelCase_     (   self  ,__UpperCAmelCase  ,__UpperCAmelCase				)   ->		Optional[int]:
      if item not in self.set:
          heapq.heappush(self.elements  ,(priority, item)				)
          self.set.add(__UpperCAmelCase				)
      else:
          # update
          # print("update", item)
          lowerCAmelCase__			:  Tuple											= []
          ((lowerCAmelCase__)				,       (lowerCAmelCase__))			:  int											= heapq.heappop(self.elements				)
          while x != item:
              temp.append((pri, x)				)
              ((lowerCAmelCase__)				,       (lowerCAmelCase__))			:  Tuple											= heapq.heappop(self.elements				)
          temp.append((priority, item)				)
          for pro, xxx in temp:
              heapq.heappush(self.elements  ,(pro, xxx)				)




  def 							UpperCAmelCase_     (   self  ,__UpperCAmelCase				)   ->		Optional[Any]:
      if item in self.set:
          self.set.remove(__UpperCAmelCase				)
          lowerCAmelCase__			:  Optional[Any]											= []
          ((lowerCAmelCase__)				,       (lowerCAmelCase__))			:  List[Any]											= heapq.heappop(self.elements				)
          while x != item:
              temp.append((pro, x)				)
              ((lowerCAmelCase__)				,       (lowerCAmelCase__))			:  List[str]											= heapq.heappop(self.elements				)
          for prito, yyy in temp:
              heapq.heappush(self.elements  ,(prito, yyy)				)




  def 							UpperCAmelCase_     (   self				)   ->		List[Any]:
      return self.elements[0][1]






  def 							UpperCAmelCase_     (   self				)   ->		Optional[int]:
      ((lowerCAmelCase__)				,       (lowerCAmelCase__))			:  Any											= heapq.heappop(self.elements				)
      self.set.remove(__UpperCAmelCase				)
      return (priority, item)







def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    lowerCAmelCase__			:  Optional[Any]											= np.array(UpperCamelCase      )
    lowerCAmelCase__			:  List[str]											= np.array(UpperCamelCase      )
    return np.linalg.norm(a - b      )
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    return consistent_heuristic(UpperCamelCase							,   UpperCamelCase      ) // t
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    return abs(p[0] - goal[0]      ) + abs(p[1] - goal[1]      )
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    lowerCAmelCase__			:  Any											= g_function[start] + Wa * heuristics[i](UpperCamelCase							,   UpperCamelCase      )
    return ans
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    lowerCAmelCase__			:  Any											= np.chararray((n, n)      )
    for i in range(UpperCamelCase      ):
        for j in range(UpperCamelCase      ):
            lowerCAmelCase__			:  Dict											= """*"""

    for i in range(UpperCamelCase      ):
        for j in range(UpperCamelCase      ):
            if (j, (n - 1) - i) in blocks:
                lowerCAmelCase__			:  List[str]											= """#"""

    lowerCAmelCase__			:  int											= """-"""
    lowerCAmelCase__			:  Union[str, Any]											= back_pointer[goal]
    while x != start:
        ((lowerCAmelCase__)				,       (lowerCAmelCase__))			:  str											= x
        # print(x)
        lowerCAmelCase__			:  int											= """-"""
        lowerCAmelCase__			:  Optional[Any]											= back_pointer[x]
    lowerCAmelCase__			:  int											= """-"""

    for i in range(UpperCamelCase      ):
        for j in range(UpperCamelCase      ):
            if (i, j) == (0, n - 1):
                print(grid[i][j]							,   end=""" """      )
                print("""<-- End position"""							,   end=""" """      )
            else:
                print(grid[i][j]							,   end=""" """      )
        print()
    print("""^"""      )
    print("""Start position"""      )
    print()
    print("""# is an obstacle"""      )
    print("""- is the path taken by algorithm"""      )
    print("""PATH TAKEN BY THE ALGORITHM IS:-"""      )
    lowerCAmelCase__			:  str											= back_pointer[goal]
    while x != start:
        print(UpperCamelCase							,   end=""" """      )
        lowerCAmelCase__			:  Optional[Any]											= back_pointer[x]
    print(UpperCamelCase      )
    sys.exit()
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase      ):



    """simple docstring"""





    if p[0] < 0 or p[0] > n - 1:
        return False
    if p[1] < 0 or p[1] > n - 1:
        return False
    return True
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   ):



    """simple docstring"""





    for itera in range(UpperCamelCase      ):
        open_list[itera].remove_element(UpperCamelCase      )
    # print("s", s)
    # print("j", j)
    ((lowerCAmelCase__)				,       (lowerCAmelCase__))			:  str											= s
    lowerCAmelCase__			:  Any											= (x - 1, y)
    lowerCAmelCase__			:  Dict											= (x + 1, y)
    lowerCAmelCase__			:  Optional[int]											= (x, y + 1)
    lowerCAmelCase__			:  Union[str, Any]											= (x, y - 1)

    for neighbours in [left, right, up, down]:
        if neighbours not in blocks:
            if valid(UpperCamelCase      ) and neighbours not in visited:
                # print("neighbour", neighbours)
                visited.add(UpperCamelCase      )
                lowerCAmelCase__			:  List[Any]											= -1
                lowerCAmelCase__			:  Any											= float("""inf"""      )

            if valid(UpperCamelCase      ) and g_function[neighbours] > g_function[s] + 1:
                lowerCAmelCase__			:  Tuple											= g_function[s] + 1
                lowerCAmelCase__			:  int											= s
                if neighbours not in close_list_anchor:
                    open_list[0].put(UpperCamelCase							,   key(UpperCamelCase							,   0							,   UpperCamelCase							,   UpperCamelCase      )      )
                    if neighbours not in close_list_inad:
                        for var in range(1							,   UpperCamelCase      ):
                            if key(UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      ) <= Wa * key(
                                UpperCamelCase							,   0							,   UpperCamelCase							,   UpperCamelCase      ):
                                open_list[j].put(
                                    UpperCamelCase							,   key(UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      )      )
def        _SCREAMING_SNAKE_CASE  (	):



    """simple docstring"""





    lowerCAmelCase__			:  int											= []
    for x in range(1							,   5      ):
        for y in range(1							,   6      ):
            some_list.append((x, y)      )

    for x in range(15							,   20      ):
        some_list.append((x, 17)      )

    for x in range(10							,   19      ):
        for y in range(1							,   15      ):
            some_list.append((x, y)      )

    # L block
    for x in range(1							,   4      ):
        for y in range(12							,   19      ):
            some_list.append((x, y)      )
    for x in range(3							,   13      ):
        for y in range(16							,   19      ):
            some_list.append((x, y)      )
    return some_list


_lowerCAmelCase										=     {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

_lowerCAmelCase										=     [
    (0, 1),
    (1, 1),
    (2, 1),
    (3, 1),
    (4, 1),
    (5, 1),
    (6, 1),
    (7, 1),
    (8, 1),
    (9, 1),
    (10, 1),
    (11, 1),
    (12, 1),
    (13, 1),
    (14, 1),
    (15, 1),
    (16, 1),
    (17, 1),
    (18, 1),
    (19, 1),
]
_lowerCAmelCase										=     make_common_ground()


_lowerCAmelCase										=     blocks_blk
# hyper parameters
_lowerCAmelCase										=     1
_lowerCAmelCase										=     1
_lowerCAmelCase										=     20
_lowerCAmelCase										=     3  # one consistent and two other inconsistent

# start and end destination
_lowerCAmelCase										=     (0, 0)
_lowerCAmelCase										=     (n - 1, n - 1)

_lowerCAmelCase										=     1
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    lowerCAmelCase__			:  Union[str, Any]											= {start: 0, goal: float("""inf"""      )}
    lowerCAmelCase__			:  str											= {start: -1, goal: -1}
    lowerCAmelCase__			:  Optional[Any]											= []
    lowerCAmelCase__			:  str											= set()

    for i in range(UpperCamelCase      ):
        open_list.append(PriorityQueue()      )
        open_list[i].put(UpperCamelCase							,   key(UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      )      )

    lowerCAmelCase__			:  list[int]											= []
    lowerCAmelCase__			:  list[int]											= []
    while open_list[0].minkey() < float("""inf"""      ):
        for i in range(1							,   UpperCamelCase      ):
            # print(open_list[0].minkey(), open_list[i].minkey())
            if open_list[i].minkey() <= Wa * open_list[0].minkey():
                global t
                t += 1
                if g_function[goal] <= open_list[i].minkey():
                    if g_function[goal] < float("""inf"""      ):
                        do_something(UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      )
                else:
                    lowerCAmelCase__				,       lowerCAmelCase__			:  List[Any]											= open_list[i].top_show()
                    visited.add(UpperCamelCase      )
                    expand_state(
                        UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   )
                    close_list_inad.append(UpperCamelCase      )
            else:
                if g_function[goal] <= open_list[0].minkey():
                    if g_function[goal] < float("""inf"""      ):
                        do_something(UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      )
                else:
                    lowerCAmelCase__			:  str											= open_list[0].top_show()
                    visited.add(UpperCamelCase      )
                    expand_state(
                        UpperCamelCase							,   0							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   )
                    close_list_anchor.append(UpperCamelCase      )
    print("""No path found to goal"""      )
    print()
    for i in range(n - 1							,   -1							,   -1      ):
        for j in range(UpperCamelCase      ):
            if (j, i) in blocks:
                print("""#"""							,   end=""" """      )
            elif (j, i) in back_pointer:
                if (j, i) == (n - 1, n - 1):
                    print("""*"""							,   end=""" """      )
                else:
                    print("""-"""							,   end=""" """      )
            else:
                print("""*"""							,   end=""" """      )
            if (j, i) == (n - 1, n - 1):
                print("""<-- End position"""							,   end=""" """      )
        print()
    print("""^"""      )
    print("""Start position"""      )
    print()
    print("""# is an obstacle"""      )
    print("""- is the path taken by algorithm"""      )


if __name__ == "__main__":
 multi_a_star(start, goal, n_heuristic)







'''simple docstring'''





from __future__ import annotations

# This is the precision for this function which can be altered.
# It is recommended for users to keep this number greater than or equal to 10.
_lowerCAmelCase										=     10
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    for i in range(UpperCamelCase							,   UpperCamelCase      ):
        if array[i] == target:
            return i
    return -1
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    lowerCAmelCase__			:  Optional[Any]											= 0
    lowerCAmelCase__			:  Optional[int]											= len(UpperCamelCase      )
    while left <= right:
        if right - left < precision:
            return lin_search(UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      )

        lowerCAmelCase__			:  Tuple											= (left + right) // 3 + 1
        lowerCAmelCase__			:  List[str]											= 2 * (left + right) // 3 + 1

        if array[one_third] == target:
            return one_third
        elif array[two_third] == target:
            return two_third

        elif target < array[one_third]:
            lowerCAmelCase__			:  int											= one_third - 1
        elif array[two_third] < target:
            lowerCAmelCase__			:  Union[str, Any]											= two_third + 1

        else:
            lowerCAmelCase__			:  List[Any]											= one_third + 1
            lowerCAmelCase__			:  List[str]											= two_third - 1
    else:
        return -1
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      ):



    """simple docstring"""





    if left < right:
        if right - left < precision:
            return lin_search(UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      )
        lowerCAmelCase__			:  Dict											= (left + right) // 3 + 1
        lowerCAmelCase__			:  Tuple											= 2 * (left + right) // 3 + 1

        if array[one_third] == target:
            return one_third
        elif array[two_third] == target:
            return two_third

        elif target < array[one_third]:
            return rec_ternary_search(UpperCamelCase							,   one_third - 1							,   UpperCamelCase							,   UpperCamelCase      )
        elif array[two_third] < target:
            return rec_ternary_search(two_third + 1							,   UpperCamelCase							,   UpperCamelCase							,   UpperCamelCase      )
        else:
            return rec_ternary_search(one_third + 1							,   two_third - 1							,   UpperCamelCase							,   UpperCamelCase      )
    else:
        return -1


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 _lowerCAmelCase										=     input('''Enter numbers separated by comma:\n''').strip()
 _lowerCAmelCase										=     [int(item.strip()) for item in user_input.split(''',''')]
 assert collection == sorted(collection), F"List must be ordered.\n{collection}."
 _lowerCAmelCase										=     int(input('''Enter the number to be found in the list:\n''').strip())
 _lowerCAmelCase										=     ite_ternary_search(collection, target)
 _lowerCAmelCase										=     rec_ternary_search(0, len(collection) - 1, collection, target)
 if resulta != -1:
  print(F"""Iterative search: {target} found at positions: {resulta}""")
  print(F"""Recursive search: {target} found at positions: {resulta}""")
 else:
  print('''Not found''')


