八皇后问题独立解Python代码

八皇后问题其实很有趣，借助这个问题可以很好检验对一门新的语言的理解程度。

使用生成器，在8皇后的时候，以下非独立解决代码的计算次数为46752次：

# !/usr/bin/python
# coding:utf-8
# __author__=watson


def conflict(state, nextx):
    nexty = len(state)
    for i in range(nexty):
        if abs(state[i]-nextx) in (0, nexty-i):
            return True
    return False


def queens(num=1, state=()):
    for pos in range(num):
        if not conflict(state, pos):
            if len(state) == num-1:
                yield (pos,)
            else:
                for result in queens(num, state + (pos,)):
                    yield (pos,) + result


if __name__ == "__main__":
    print list(queens(8))

使用记忆算法，在8皇后的时候，以下非独立解决代码的计算次数为15720次：

# !/usr/bin/python
# coding:utf-8
# __author__=watson

column = rup = lup = []

def conflict(line, col, num):
    if column[col] == 0 and rup[line+col] == 0 and lup[line-col+num] == 0:
        return False
    return True


def queens(num=1, line=1):
    for col in range(1, num + 1):
        if not conflict(line, col, num):
            if line == num:
                yield (col,)
            else:
                column[col] = rup[line+col] = lup[line-col+num] = 1
                for result in queens(num, line + 1):
                    yield (col,) + result
                column[col] = rup[line+col] = lup[line-col+num] = 0

if __name__ == "__main__":
    number = 8
    column = [0] * (number + 1)
    rup = [0] * (2*number + 1)
    lup = [0] * (2*number + 1)
    print list(queens(number))

 使用记忆算法，不使用生成器：

# !/usr/bin/python
# coding:utf-8
# __author__=watson

number = 0
result = [0]
column = [0]
rup = [0]
lup = [0]
no = 0


def backtrack(line):
    if line > number:
        show_result()
    else:
        for col in range(1, number+1):
            if column[col] == 0 and rup[line+col] == 0 and lup[line-col+number] == 0:
                result[line] = col
                column[col] = rup[line+col] = lup[line-col+number] = 1
                backtrack(line + 1)
                column[col] = rup[line+col] = lup[line-col+number] = 0


def show_result():
    global no
    no += 1
    print "result no %r:" % no
    for i in range(1, number + 1):
        for j in range(1, number + 1):
            if result[i] == j:
                print " Q ",
            else:
                print " . ",
        print "\n"

if __name__ == "__main__":
    number = 8
    result = [0] * (number + 1)
    column = [0] * (number + 1)
    rup = [0] * (2*number + 1)
    lup = [0] * (2*number + 1)
    # print column[number]
    backtrack(1)

上述算法都是递归算法，在皇后数多的都比较消耗内存。

独立解参考《八皇后问题独立解JAVA代码》：

http://kingxss.iteye.com/blog/2290026