UVa 575 Skew Binary 歪斜二进制

最新推荐文章于 2018-04-08 23:28:02 发布

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#UVa #刘汝佳 #位运算

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本文介绍了一种特殊的二进制表示法——偏斜二进制，并提供了将偏斜二进制转换为十进制的算法实现。通过具体的示例和代码解释了偏斜二进制的特点及其转换过程。

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呵呵，这个翻译还是很直白的嘛，大家意会就好。

第一次看到这个高大上题目还是有点小害怕的，还好题没有做过深的文章。

只要按照规则转化成十进制就好了，而且题目本身也说了最大不超过一个int的范围（2^31-1 == 2147483647）。

直接位运算就好了。

Skew Binary

When a number is expressed in decimal, the k-th digit represents a multiple of 10^k. (Digits are numbered from right to left, where the least significant digit is number 0.) For example,

$\begin{displaymath}81307_{10} = 8 \times 10^4 + 1 \times 10^3 + 3 \times 10^2 + ......mes 10^1 +7 \times 10 0 = 80000 + 1000 + 300 + 0 + 7= 81307.\end{displaymath}$

When a number is expressed in binary, the k-th digit represents a multiple of 2^k. For example,

$\begin{displaymath}10011_2 = 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 +1 \times 2^0 = 16 + 0 + 0 + 2 + 1 = 19.\end{displaymath}$

In skew binary, the k-th digit represents a multiple of 2^k+1 - 1. The only possible digits are 0 and 1, except that the least-significant nonzero digit can be a 2. For example,

$\begin{displaymath}10120_{skew} = 1 \times (2^5 - 1) + 0 \times (2^4-1) + 1 \tim......2 \times (2^2-1) + 0 \times (2^1-1)= 31 + 0 + 7 + 6 + 0 = 44.\end{displaymath}$

The first 10 numbers in skew binary are 0, 1, 2, 10, 11, 12, 20, 100, 101, and 102. (Skew binary is useful in some applications because it is possible to add 1 with at most one carry. However, this has nothing to do with the current problem.)

10120
200000000000000000000000000000
10
1000000000000000000000000000000
11
100
11111000001110000101101102000
0

Sample Output

Miguel A. Revilla
1998-03-10

AC代码：

//#define LOCAL
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;

char SkBinary[35];

void Reverse(char s[], int l);

int main(void)
{
	#ifdef LOCAL
		freopen("575in.txt", "r", stdin);
	#endif

	while(gets(SkBinary) && SkBinary[0] != '0')
	{
		int l = strlen(SkBinary);
		Reverse(SkBinary, l);
		int i, n = 0;
		for(i = 0; i < l; ++i)
		{
			if(SkBinary[i] == '0')
				continue;
			if(SkBinary[i] == '1')
				n += (1 << (i + 1)) - 1;
			if(SkBinary[i] == '2')
				n += (1 << (i + 2)) - 2;
		}
		cout << n << endl;
	}
	return 0;
}
//用来反转数组
void Reverse(char s[], int l)
{
	int i;
	char t;
	for(i = 0; i < l / 2; ++i)
	{
		t = s[i];
		s[i] = s[l - i -1];
		s[l - i -1] = t;
	}
}