http://poj.org/problem?id=3191
The Moronic Cowmpouter
Time Limit:1000MS |
|
Memory Limit:65536K |
Description
Inexperienced in the digital arts, the cows tried to build a calculating engine (yes, it's a cowmpouter) using binary numbers (base 2) but instead built one based on base negative 2! They were quite pleased since numbers expressed in base −2 do not have a sign bit.
You know number bases have place values that start at 1 (base to the 0 power) and proceed right-to-left to base^1, base^2, and so on. In base −2, the place values are 1, −2, 4, −8, 16, −32, ... (reading from right to left). Thus, counting from 1 goes like this: 1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, and so on.
Eerily, negative numbers are also represented with 1's and 0's but no sign. Consider counting from −1 downward: 11, 10, 1101, 1100, 1111, and so on.
Please help the cows convert ordinary decimal integers (range -2,000,000,000..2,000,000,000) to their counterpart representation in base −2.
Input
Line 1: A single integer to be converted to base −2
Output
Line 1: A single integer with no leading zeroes that is the input integer converted to base −2. The value 0 is expressed as 0, with exactly one 0.
Sample Input
-13
Sample Output
110111
Hint
Explanation of the sample:
Reading from right-to-left:
1*1 + 1*-2 + 1*4 + 0*-8 +1*16 + 1*-32 = -13
此题的解法基于以下几点:
(1) 如果一个数是奇数,那么它的二进制形式的最后一位肯定是1,我们可以去掉此 1,就是(x-1)/-2,进入(2)
(2) 如果一个数的最后一位为 0 ,我们可以把这个数右移(可以类比以 2 为基的二进制数的操作)一位,然后它的
二进制的倒数第二个数就成了最后一个,就是 x=x/-2,然后进入(1)迭代,直到变为 0
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