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UVa 575 Skew Binary 歪斜二进制

2024-07-10 08:27:18   222人阅读

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 10k. (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 2k. 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 2k+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.)

 

Input 

The input file contains one or more lines, each of which contains an integer n. If n = 0 it signals the end of the input, and otherwise n is a nonnegative integer in skew binary.

 

Output 

For each number, output the decimal equivalent. The decimal value of n will be at most 231 - 1 = 2147483647.

 

Sample Input 

1012020000000000000000000000000000010100000000000000000000000000000011100111110000011100001011011020000

 

Sample Output 

44214748364632147483647471041110737

 

 

Miguel A. Revilla 
1998-03-10

AC代码：

 1 //#define LOCAL 2 #include <iostream> 3 #include <cstdio> 4 #include <cstring> 5 using namespace std; 6  7 char SkBinary[35]; 8  9 void Reverse(char s[], int l);10 11 int main(void)12 {13     #ifdef LOCAL14         freopen("575in.txt", "r", stdin);15     #endif16 17     while(gets(SkBinary) && SkBinary[0] != ‘0‘)18     {19         int l = strlen(SkBinary);20         Reverse(SkBinary, l);21         int i, n = 0;22         for(i = 0; i < l; ++i)23         {24             if(SkBinary[i] == ‘0‘)25                 continue;26             if(SkBinary[i] == ‘1‘)27                 n += (1 << (i + 1)) - 1;28             if(SkBinary[i] == ‘2‘)29                 n += (1 << (i + 2)) - 2;30         }31         cout << n << endl;32     }33     return 0;34 }35 //用来反转数组36 void Reverse(char s[], int l)37 {38     int i;39     char t;40     for(i = 0; i < l / 2; ++i)41     {42         t = s[i];43         s[i] = s[l - i -1];44         s[l - i -1] = t;45     }46 }
代码君

 


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