projecteuler---->problem=36----Double-base palindromes

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于 2014-08-25 09:21:20 发布

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本文介绍了一个寻找特定回文数的方法，这些回文数不仅在十进制中是对称的，在二进制中同样也是对称的。通过一个Python程序实现，筛选出小于一百万的所有符合条件的整数，并计算它们的总和。

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Problem 36

The decimal number, 585 = 1001001001₂ (binary), is palindromic in both bases.

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

(Please note that the palindromic number, in either base, may not include leading zeros.)

def isCycle(n):
    if n%10 == 0:
        return False
    tempN = n
    num=list()
    while n > 0:
        num.insert(0,n%2)
        n /= 2
    for i in range(0,int(len(num)/2)):
        if num[i] != num[len(num)-i-1] :
            return False

    value = list()
    while tempN > 0:
        value.insert(0, tempN%10)
        tempN /= 10
    for i in range(0, int(len(value)/2)):
        if value[i] != value[len(value)-1-i]:
            return False
    return True

def main():
    resu = 0
    for i in range(1,1000000):
        if isCycle(i):
            resu += i
    print resu
if __name__ == "__main__":
    main()

class String
    def isCycle?
        self == self.reverse
    end
end

puts (1..1000000).select{|i| i.to_s.isCycle? && i.to_s(2).isCycle? }.reduce(:+)