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N Puzzle with Depth First Search

I'm trying solve N Puzzle with Depth First Search using python 3.
With 3 x 3 puzzle it run good and fast but with 4 x 4 puzzle, it runs too slow and can't find solution with error: "MemoryError".
I also use "h(n) = depth + number of wrong tiles" to evaluate priority of each node.
I'm a newbie to python so hope you can help me with this
Here is my code:
import sys
import getopt
import random
import time
class State:
def __init__(self, parent, board, move, depth):
self.parent = parent
self.previousMove = move
self.board = board
self.map = ''.join(str(e) for e in board)
self.depth = depth
self.cost = self.calculateCost()
def calculateCost(self):
pos = 1
count = 0
for tile in self.board:
if tile == pos:
count += 1
pos += 1
return self.depth + 8 - count
class Puzzle:
def __init__(self, k, customBoard = None):
self.k = k
self.n = k*k - 1
self.sizeOfBoard = k*k
self.timeOfSolving = 0
self.timeOfGenerateSuccessors = 0
self.maxDeepSearch = 0
self.inititalState = State(None, self.createInitialBoard(customBoard), 'Start', 0)
self.goalBoard = self.createGoalBoard()
self.finalState = None
self.stateStorage = set() # Store states that have visited
self.path = [] # Store states that lead to goalstate
self.stack = []
def isSolvable(self, board):
# count invertion in puzzle's board
invCount = 0
for i in range(0, self.sizeOfBoard - 1):
if board[i] == 0:
continue
for j in range(i+1, self.sizeOfBoard):
if board[j] == 0:
continue
if board[i] > board[j]:
invCount += 1
# print(invCount)
if (invCount % 2 == 0):
return True
return False
def createInitialBoard(self, customBoard):
print("Creating initial state")
if customBoard is None:
board = []
lstAddSuccess = []
while 1:
board.clear()
lstAddSuccess.clear()
for count in range(0, self.k*self.k):
newTile = random.randint(0, self.n)
while newTile in lstAddSuccess:
newTile = random.randint(0, self.n)
lstAddSuccess += [newTile]
board += [newTile]
if self.isSolvable(board):
break
else:
board = [int(e) for e in customBoard]
if not self.isSolvable(board):
print("Cant find solution with this puzzle! Exiting...")
exit(-1)
return board
def createGoalBoard(self):
board = []
for count in range(1, self.n + 1):
board += [count]
board += [0]
return board
def printBoard(self, board):
for row in range(0, self.sizeOfBoard, self.k):
# for col in range(row, row + self.k):
print(board[row:row + self.k])
def generateSuccessors(self, currentState):
indexOfZero = currentState.board.index(0)
rowIndexOfZero = indexOfZero % self.k
colIndexOfZero = indexOfZero // self.k
lstSuccessors = []
# Slide to zero to up
if colIndexOfZero != 0:
newState = currentState.board.copy()
newState[indexOfZero] = newState[indexOfZero - self.k]
newState[indexOfZero - self.k] = 0
lstSuccessors.append(
State(currentState, newState, 'up', currentState.depth + 1))
# Slide zero to down
if colIndexOfZero != self.k - 1:
newState = currentState.board.copy()
newState[indexOfZero] = newState[indexOfZero + self.k]
newState[indexOfZero + self.k] = 0
lstSuccessors.append(
State(currentState, newState, 'down', currentState.depth + 1))
# slide zero to left
if rowIndexOfZero != 0:
newState = currentState.board.copy()
newState[indexOfZero] = newState[indexOfZero - 1]
newState[indexOfZero - 1] = 0
lstSuccessors.append(
State(currentState, newState, 'left', currentState.depth + 1))
# Slide zero to right
if rowIndexOfZero != self.k - 1:
newState = currentState.board.copy()
newState[indexOfZero] = newState[indexOfZero + 1]
newState[indexOfZero + 1] = 0
lstSuccessors.append(
State(currentState, newState, 'right', currentState.depth + 1))
lstSuccessorsCost = [ele.cost for ele in lstSuccessors]
lstSuccessorsInOrderOfCost = []
for i in range(0, len(lstSuccessorsCost)):
lstSuccessorsInOrderOfCost.append(lstSuccessors[lstSuccessorsCost.index(min(lstSuccessorsCost))])
lstSuccessorsCost[lstSuccessorsCost.index(min(lstSuccessorsCost))] = 100
return lstSuccessorsInOrderOfCost
def solvePuzzle(self, currentState):
self.stack.append(currentState)
self.stateStorage.add(currentState.map)
while len(self.stack) > 0:
currentState = self.stack.pop()
if currentState.board == self.goalBoard:
# find path
# self.printBoard(currentState.board)
self.finalState = currentState
print("Solving " + str(self.n) + " puzzle done!")
return
start_time_gen = time.time()
lstSuccessor = self.generateSuccessors(currentState)
end_time_gen = time.time()
timeOfGen = end_time_gen - start_time_gen
self.timeOfGenerateSuccessors += timeOfGen
for successor in lstSuccessor[::-1]:
if successor.map not in self.stateStorage:
self.stack.append(successor)
self.stateStorage.add(successor.map)
if successor.depth > self.maxDeepSearch:
self.maxDeepSearch += 1
print("Cant solve puzzle! Exiting...")
exit(-1)
def solve(self):
start_time = time.time()
self.solvePuzzle(self.inititalState)
end_time = time.time()
self.timeOfSolving = end_time - start_time
print("Running time: " + str(self.timeOfSolving))
print("Max Search Dept: " + str(self.maxDeepSearch))
print("Final State Dept: " + str(self.finalState.depth))
def printInitialBoard(self):
self.printBoard(self.inititalState.board)
def printPath(self):
if self.finalState is None:
print("No solution found!")
return
path = []
state = self.finalState
while (state is not None):
if state.previousMove is not None:
path.append(state.previousMove)
state = state.parent
print("path: "),
print(path[::-1])
def main(argv):
# if (len(argv) != 1 or int(argv[0]) not in range(1, 10000)):
# print("Input must be k of integer, which is k*k matrix of puzzle")
# exit()
# eight_puzzle = Puzzle(int(argv[0]))
k = int(input("Enter size of k * k puzzle, k = "))
while k not in range(2, 100):
print("k must be in range 2 - 100")
k = int(input("Enter size of k * k puzzle, k = "))
print("""
Choose:
1. Randome puzzle
2. Custome puzzle
""")
file = input()
if int(file) == 1:
puzzle = Puzzle(k)
elif int(file) == 2:
board = input("Enter puzzle: ")
puzzle = Puzzle(k ,list(board.split(" ")))
puzzle.printInitialBoard()
puzzle.solve()
puzzle.printPath()
if __name__ == "__main__":
main(sys.argv[1:])

Counting of shortest sequences of flips in pancake sorting

Now, finding the shortest sequence of flips in pancake sorting is alone NP-hard, yet I'd like to find each and all of them, and count them.
Meaning for each permutation I'd like to find all the sequences of prefix reversals that restores the identity but not longer than the shortest one.
Here's what I've got so far:
#!/bin/env python3
# coding: utf-8
from math import factorial
import itertools
from multiprocessing import cpu_count, Manager, Pool
import numpy
import scipy.sparse
def flip(x, value):
return tuple(value[:x][::-1] + value[x:])
def rank(perm):
n = len(perm)
fact = factorial(n)
r = 0
for i in range(n):
fact //= n - i
r += len([x for x in perm[i:] if x < perm[i]]) * fact
return r
def unrank(i, items):
its = items[:]
perm = []
n = len(items)
fact = factorial(n)
r = i % fact
while its:
fact //= n
c, r = divmod(r, fact)
perm.append(its.pop(c))
n -= 1
return tuple(perm)
def get_colex_row(r, n, _fact):
row = scipy.sparse.dok_matrix((
1, _fact[n - 1]), dtype=numpy.int8)
perm = unrank(r, [i for i in range(n)])
for i in range(n):
column = r - r % _fact[i] + rank(perm[:-i - 2:-1])
row[0, column] = i + 1
return row
def get_colex_matrix(n):
fact = [factorial(i) for i in range(1, n + 1)]
m = scipy.sparse.dok_matrix(
(fact[n - 1], fact[n - 1]), dtype=numpy.int8)
items = [_ for _ in range(1, n + 1)]
for r in range(fact[n - 1]):
row = get_colex_row(r, n, fact)
m[r] = row
return m
def get_distance(n, items):
nfact = factorial(n)
stack = {unrank(i, items) for i in range(nfact)}
m = get_colex_matrix(n)
distance = {unrank(nfact - 1, items)[::-1] : 0}
new_distance = {nfact - 1}
d = 0
while distance.keys() != stack:
new_new_distance = set()
d += 1
for visiting in new_distance:
for i in range(2, n + 1):
key_index = m[visiting].tolist().index(i)
key = unrank(key_index, items)[::-1]
if key not in distance:
distance[key] = d
new_new_distance.add(key_index)
new_distance = new_new_distance
return distance
def get_paths_serial(items):
n = len(items)
nfact = factorial(n)
stack = {unrank(i, items) for i in range(nfact)}
m = get_colex_matrix(n)
distance = {unrank(nfact - 1, items)[::-1]: {()}}
new_distance = {nfact - 1}
while distance.keys() != stack:
new_new_distance = set()
for visiting_index in new_distance:
for i in range(2, n + 1):
key_index = m[visiting_index].tolist().index(i)
key = unrank(key_index, items)[::-1]
visiting = unrank(visiting_index, items)[::-1]
paths = distance[visiting]
prev_sample = next(iter(paths))
if key not in distance:
distance[key] = {path + (i,) for path in paths}
new_new_distance.add(key_index)
else:
curr_sample = next(iter(distance[key]))
if len(prev_sample) + 1 < len(curr_sample):
print("Shouldn't happen!")
distance[key] = {path + (i,) for path in paths}
elif len(prev_sample) + 1 == len(curr_sample):
distance[key] |= {path + (i,) for path in paths}
else:
# not relevant
pass
new_distance = new_new_distance
return distance
def _worker(ns, index):
row = get_colex_row(index, ns.n, ns.fact).toarray().tolist()[0]
visiting = unrank(index, ns.items)[::-1]
paths = ns.distance[visiting]
prev_sample = next(iter(paths))
out = {}
my_new_distance = set()
for i in range(2, ns.n + 1):
key_index = row.index(i)
key = unrank(key_index, ns.items)[::-1]
if key not in ns.distance:
out[key] = {path + (i,) for path in paths}
my_new_distance.add(key_index)
else:
curr_sample = next(iter(ns.distance[key]))
if len(prev_sample) + 1 < len(curr_sample):
print("Shouldn't happen!")
out[key] = {path + (i,) for path in paths}
elif len(prev_sample) + 1 == len(curr_sample):
out[key].update(path + (i,) for path in paths)
return my_new_distance, out
def get_paths_parallel(items):
n = len(items)
fact = [factorial(i) for i in range(1, n + 1)]
distance = {unrank(fact[n - 1] - 1, items)[::-1]: {()}}
stack = {unrank(i, items) for i in range(fact[n - 1])}
already_visited = set()
visiting = {fact[n - 1] - 1}
mgr = Manager()
namespace = mgr.Namespace()
namespace.fact = fact
namespace.distance = distance
namespace.items = items
namespace.n = n
with Pool(2 * cpu_count()) as pool:
while distance.keys() != stack:
result = pool.starmap(_worker, ((namespace, job)
for job in visiting))
visiting = set()
for next_to_visit, visited in result:
visiting |= next_to_visit
for k, v in visited.items():
if k in distance:
distance[k] |= v
else:
distance[k] = v
visiting -= already_visited
already_visited |= visiting
namespace.distance = distance
return distance
def colex(value, other):
for i in range(len(value) - 1, 0, -1):
if value[i] == other[i]:
continue
return value[i] > other[i]
return False
def ordered_by(order_cmp):
'Convert a cmp= function into a key= function'
if order_cmp is None:
return None
class K(object):
def __init__(self, obj):
self.value = obj
def __gt__(self, other):
if len(self.value) != len(other.value):
assert "Not the same length"
return order_cmp(self.value, other.value)
return K
def get_ordered(n, order):
return sorted(itertools.permutations(range(1, n + 1)),
key=ordered_by(order))
def get_matrix(n, order=None):
stack = get_ordered(n, order)
m = numpy.zeros((len(stack), len(stack)), numpy.int8)
for i,s in enumerate(stack):
for x in range(1, n + 1):
m[i, stack.index(flip(x, s))] = x
return m
I'm not sure what I'm doing wrong, but get_paths_parallel runs slower than get_paths_serial, please help!
I really should (and probably will soon) document my code better.
So for the time being, I'll say a few additional words:
It uses co-lexicographic ordering to rank the permutations and to find the indices in the adjacency matrix. Where I store the length of the flip that transforms the permutations, e.g. A(i,j) = k if performing a k length prefix reversal on the permutation with rank i results the ranked j permutation. In order to save on memory instead of storing the whole matrix I generate the rows on demand and limit the access by excluding already visited ones also I'm using scipy.sparse.dok_matrix for the same reason.
Other than these it's simply floods the graph till all permutations are reached.
There are some functions that doesn't use all or any of the consideration above like get_matrix, but presented only to validate that others, like get_colex_matrix are working as intended.
I'm creating the key function in a little bit convoluted manner, but that's just because I've tried other sorting before I've settled on co-lex.

Using multiprocessing.Manager to share data between processes makes them slow down.
Solution is to copy the needed data into each process's memory space (passing them as argument) or to use global variables for them.
Also using scipy.sparse.dok_matrix is overkill, dict would do.
I'll grab the literature I've found on the subject and link it hare later.

knapsack branch and bound wrong result

I have converted the code given at this link into a python version. The code is supposed to calculate the correct value of maximum value to be filled in knapsack of weight W. I have attached the code below:
#http://www.geeksforgeeks.org/branch-and-bound-set-2-implementation-of-01-knapsack/
from queue import Queue
class Node:
def __init__(self):
self.level = None
self.profit = None
self.bound = None
self.weight = None
def __str__(self):
return "Level: %s Profit: %s Bound: %s Weight: %s" % (self.level, self.profit, self.bound, self.weight)
def bound(node, n, W, items):
if(node.weight >= W):
return 0
profit_bound = int(node.profit)
j = node.level + 1
totweight = int(node.weight)
while ((j < n) and (totweight + items[j].weight) <= W):
totweight += items[j].weight
profit_bound += items[j].value
j += 1
if(j < n):
profit_bound += (W - totweight) * items[j].value / float(items[j].weight)
return profit_bound
Q = Queue()
def KnapSackBranchNBound(weight, items, total_items):
items = sorted(items, key=lambda x: x.value/float(x.weight), reverse=True)
u = Node()
v = Node()
u.level = -1
u.profit = 0
u.weight = 0
Q.put(u)
maxProfit = 0;
while not Q.empty():
u = Q.get()
if u.level == -1:
v.level = 0
if u.level == total_items - 1:
continue
v.level = u.level + 1
v.weight = u.weight + items[v.level].weight
v.profit = u.profit + items[v.level].value
if (v.weight <= weight and v.profit > maxProfit):
maxProfit = v.profit;
v.bound = bound(v, total_items, weight, items)
if (v.bound > maxProfit):
Q.put(v)
v.weight = u.weight
v.profit = u.profit
v.bound = bound(v, total_items, weight, items)
if (v.bound > maxProfit):
# print items[v.level]
Q.put(v)
return maxProfit
if __name__ == "__main__":
from collections import namedtuple
Item = namedtuple("Item", ['index', 'value', 'weight'])
input_data = open("test.data").read()
lines = input_data.split('\n')
firstLine = lines[0].split()
item_count = int(firstLine[0])
capacity = int(firstLine[1])
print "running from main"
items = []
for i in range(1, item_count+1):
line = lines[i]
parts = line.split()
items.append(Item(i-1, int(parts[0]), float(parts[1])))
kbb = KnapSackBranchNBound(capacity, items, item_count)
print kbb
The program is supposed to calculate value of 235 for following items inside file test.data:
5 10
40 2
50 3.14
100 1.98
95 5
30 3
The first line shows number of items and knapsack weight. Lines below first line shows the value and weight of those items. Items are made using a namedtuple and sorted according to value/weight. For this problem I am getting 135 instead of 235. What am I doing wrong here?
EDIT:
I have solved the problem of finding correct items based on branch and bound. If needed, one can check it here

The problem is that you're inserting multiple references to the same Node() object into your queue. The fix is to initialize two new v objects in each iteration of the while-loop as follows:
while not Q.empty():
u = Q.get()
v = Node() # Added line
if u.level == -1:
v.level = 0
if u.level == total_items - 1:
continue
v.level = u.level + 1
v.weight = u.weight + items[v.level].weight
v.profit = u.profit + items[v.level].value
if (v.weight <= weight and v.profit > maxProfit):
maxProfit = v.profit;
v.bound = bound(v, total_items, weight, items)
if (v.bound > maxProfit):
Q.put(v)
v = Node() # Added line
v.level = u.level + 1 # Added line
v.weight = u.weight
v.profit = u.profit
v.bound = bound(v, total_items, weight, items)
if (v.bound > maxProfit):
# print(items[v.level])
Q.put(v)
Without these reinitializations, you're modifying the v object that you already inserted into the queue.
This is different from C++ where the Node objects are values that are implicitly copied into the queue to avoid aliasing problems such as these.

Python: Recursion problems

I am trying to make a sudoku solver that solves boards very quickly. At the moment my solver works on easy boards but never terminates on harder boards. I believe it has something to do with my recursion because easy boards do not require recursion and hard boards do. Any help is appreciated.
import sys
def rowno(i):
return i // 9
def colno(i):
return i % 9
def boxno(i):
return (i // 9 // 3 )*3 + (i // 3) % 3
def isNeighbor(i, j):
if rowno(i) == rowno(j) or colno(i) == colno(j) or boxno(i) == boxno(j):
return True
else:
return False
def getFileName():
if sys.platform == "win32":
filename = input("Filename? ")
else:
filename = sys.argv[-1]
return filename
solutionlist = []
class Board(object):
def __init__(self, puzzle):
self.puzzle = puzzle
self.board = [Cell(int(value), idx) for idx, value in enumerate(puzzle)]
self.change = False
def printAll(self):
print [cell.candidates for cell in self.board]
#return str(" ")
def update(self):
self.change = False
l = [cell for cell in self.board if len(cell.candidates) == 1]
for i in l:
for j in xrange(81):
if isNeighbor(i.dex, j) and i.dex != j:
old = self.board[j].candidates
self.board[j].delCandidate(i.value)
if len(old) != len(self.board[j].candidates):
self.change = True
def toString(self):
str1 = ''.join(str(e.value) for e in self.board)
return str1
def solved(self):
for cell in self.board:
if len(cell.candidates) != 1:
return False
return True
def solve(self):
self.change = True
while self.change == True:
self.update()
if self.solved():
solutionlist.append(self.board)
return
l = [cell for cell in self.board if len(cell.candidates) > 1]
for i in l:
for j in i.candidates:
newBoard = Board(self.toString())
curLen = 12
curCell = -1
for u in l:
if len(u.candidates)<curLen:
curLen=len(u.candidates)
curCell = u.dex
for c in newBoard.board[curCell].candidates:
newBoard.board[curCell].candidates = [int(c)]
newBoard.board[curCell].value = int(c)
newBoard.solve()
return
def __repr__(self):
l = [cell.value for cell in self.board]
return str(l)
class Cell(object):
def __init__(self, value, dex):
self.value = value
self.dex = dex
if value == 0:
self.candidates = [1,2,3,4,5,6,7,8,9]
else:
self.candidates = [int(value)]
def __str__(self):
return str(self.value)
def delCandidate(self, value):
# deletes value from candidate list
#return self.candidate.remove(value);
self.candidates = [x for x in self.candidates if x != value]
if len(self.candidates) == 1:
self.value = self.candidates[0]
easy = "700583006006001405052006083300200958500078060648010300060802500003150072215600030"
twosol = "000805200800000401705040009000100702040000000006430000030900000010006080000000000"
hard = "040090008000000070060000120030020000005839060080600700050170600000043000003000200"
#easy solution: 794583216836721495152496783371264958529378164648915327967832541483159672215647839
b = Board(hard)
print b
b.solve()
print "end of the line"
for i in solutionlist:
print [cell.value for cell in i]
print "\n"

One major issue is the line for i in l: in the solve method. Since you're recursing, you only need to fill in one cell - the recursion will take care of the rest. So instead of for i in l:, just recurse on the one cell that is the best candidate (curCell):
l = [cell for cell in self.board if len(cell.candidates) > 1]
if len(l) > 0:
newBoard = Board(self.toString())
curLen = 12
curCell = -1
for u in l:
if len(u.candidates)<curLen:
curLen=len(u.candidates)
curCell = u.dex
for c in newBoard.board[curCell].candidates:
newBoard.board[curCell].candidates = [int(c)]
newBoard.board[curCell].value = int(c)
newBoard.solve()

Python minimax for tictactoe

After completely failing the minimax implementation for tic tac toe, I fail to see what's wrong. Right now, my AI just goes around in a circle...
import collections
class InvalidLocationError(Exception): pass
import copy
class Board(object):
def __init__(self, board=None):
if board is None:
self.clear()
else:
self._board = board[:]
def place(self, i, row, column):
if not ((0 <= row <= 2) and (0 <= column <= 2)):
raise InvalidLocationError("Invalid Location.")
if self._board[row][column]:
raise InvalidLocationError("There's already a piece there")
self._board[row][column] = i
return self.checkVictory()
def check(self, row, column):
return self._board[row][column]
def checkVictory(self, board=None):
if board is None:
board = self._board
draw = True
for i in xrange(3):
r = self.rowcount(i)
c = self.colcount(i)
if i < 3:
d = self.diagcount(i)
else:
d = {0: 0, 1: 0, 2: 0}
for j in xrange(1, 3):
if d[j] == 3 or r[j] == 3 or c[j] == 3:
return j
if r[0] > 0 or c[0] > 0:
draw = False
if draw:
return -1
return 0
def rowcount(self, row):
return collections.Counter(self._board[row])
def colcount(self, col):
return collections.Counter([self._board[i][col] for i in xrange(3)])
def diagcount(self, left=True):
if left:
a = [self._board[0][0], self._board[1][1], self._board[2][2]]
else:
a = [self._board[0][2], self._board[1][1], self._board[2][0]]
return collections.Counter(a)
def clear(self):
self._board = ([0, 0, 0], [0, 0, 0], [0, 0, 0])
def __str__(self):
return "\n".join(map(lambda x: " ".join(map(lambda y : str(y), x)), self._board))
#staticmethod
def flipPiece(p):
return int(not (p - 1)) + 1
class AI(object):
class Node(object):
def __init__(self, board, nextMove):
self.board = board
self.nextMove = nextMove
self.paths = []
self.score = None
template = self.board._board[:]
for r, row in enumerate(template):
for c, val in enumerate(row):
if val == 0:
template[r][c] = nextMove
self.paths.append(copy.deepcopy(template))
template[r][c] = 0
def __init__(self, mypiece, depth=8):
self.mypiece = mypiece
self.enemypiece = Board.flipPiece(mypiece)
self.depth = depth
def decide(self, board):
startNode = self.Node(board, self.mypiece)
best = self.minimax(startNode, self.depth)
for node in startNode.paths:
if node.value == best:
break
found = False
for row in xrange(3):
for col in xrange(3):
if board.check(row, col) != node.board.check(row, col):
found = True
break
if found:
break
print row, col
return row, col
def minimax(self, node, depth):
victory = node.board.checkVictory()
if victory:
if victory == self.mypiece:
h = 1
elif victory == -1:
h = 0
else:
h = -1
node.value = h
return h
if depth <= 0:
# h = self.heuristic(node.board, node.nextMove) # This is to the heuristic, which uses nextMove to evalate.
node.value = 0
return 0
h = -1
flip = Board.flipPiece(node.nextMove)
for i, board in enumerate(node.paths):
node.paths[i] = self.Node(Board(board), flip) # This is to the Node, which takes the nextMove of itself (which translates to the next next move from the current node)
score = self.minimax(node.paths[i], depth-1)
h = max(h, score) if node.nextMove == self.mypiece else min(h, score)
node.value = h
return h
Why is this happening?