[POJ3191] The Moronic Cowmpouter

# 题目

题目描述

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.

输入输出格式

输入格式:

A single integer to be converted to base -2

输出格式:

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.

输入输出样例

输入样例1:

输出样例1:

提示

Hint
Explanation of the sample:
Reading from right-to-left:
1*1 + 1*-2 + 1*4 + 0*-8 +1*16 + 1*-32 = -13

题目大意

输入一个十进制\(N(−2,000,000,000≤N≤2,000,000,000)\),输出它的\(−2\)进制数

题解

平常我们很少会涉及到负进制,按照提示所给内容,我们应该很快能想到第一种做法,
第一种想法,我们去枚举每一个负二进制数,对于每一个负二进制数,我们将它转换成十进制数,看看是不是一样。
代码如下:

然而上面的做法会T,那么我们能不能直接从十进制算到负二进制呢?
这个需要好好观察一下提示,
我们发现如果要确定当前位是0还是1,只要对下一个为1时取余就知道了,如果余数为0,那么当前这个数自然是后面位的倍数了,取0,否则就取1.

然后减去当前还剩的数,继续往后走。

最后减到0就可以了。

代码

另外,这里还有一道题和这个几乎一样
UVA11121 Base -2

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