选非质数 笔试题

题目描述

给出一些不重复的数字，两人轮流选数字，规则要求后一次选的数字，和前一次选的数字不能互质。现在给出小A第一次选的数字X，问在游戏过程中，某个数字Y能否被选出？如果能，请输出两人至少需要选出几个数字？如果不能，请输出-1。

简单实现

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# ***************************************************************************
#
# Copyright (c) 2017 ByteDance.com, Inc. All Rights Reserved
#
# *************************************************************************/
#
# @file main.py
#
# @date   2018/6/4
#

import Queue

CURR_NUM = "curr_num"
STATUS = "status"
STEP = "step"


def gcd(b, a):
    '''
    辗转相除求最大公约数
    :param b:
    :param a:
    :return:
    '''
    b, a = a, b % a
    if a == 0:
        return b
    else:
        return gcd(b, a)


def select(status, x, y):
    '''
    从数组arr中，从x到y，按照游戏规则次数最小
    :param arr:
    :param x:
    :param y:
    :return:
    '''

    def new_status(curr, status, step):
        '''
        创建新状态
        :param curr:
        :param visited:
        :param step:
        :return:
        '''
        return {
            CURR_NUM: curr,
            STATUS: status,
            STEP: step,
        }

    # res
    res = -1
    finish_status = None

    queue = Queue.LifoQueue()
    # push
    curr_status = status
    curr_status[x] = 1
    queue.put(new_status(x, curr_status, 1))
    # bfs
    while (not queue.empty()):
        top = queue.get()
        curr_num = top[CURR_NUM]
        curr_step = top[STEP]
        curr_status = top[STATUS]
        if curr_num == y:
            if res == -1 or res > curr_step:
                res = curr_step
                finish_status = curr_status.copy()
            continue
        else:
            for k, v in curr_status.items():
                if v == 0 and gcd(k, curr_num) != 1:
                    # next_status
                    next_status = curr_status.copy()
                    next_status[k] = 1
                    # next_num
                    next_num = k
                    # next_step
                    next_step = curr_step + 1
                    queue.put(new_status(next_num, next_status, next_step))

    print finish_status, res
    return res


if __name__ == '__main__':
    '''
    main
    '''
    print select({3: 0, 5: 0, 15: 0}, 3, 5)
    print select({3: 0, 5: 0}, 3, 5)
    print select({3: 0, 15: 0, 2: 0, 4: 0, 12: 0, 20: 0}, 3, 20)