寒假集训.Skew Binary

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本文介绍了一种特殊的数制——SkewBinary，并提供了一个C++程序实例来将SkewBinary数转换为十进制数。SkewBinary数制中，第k位的权值为2^(k+1)-1，且最低位可以为2。文章通过示例解释了SkewBinary数的特点，并给出了具体的转换算法。

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Skew Binary

Time Limit:3000MS Memory Limit:0KB 64bit IO Format:%lld & %llu

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Description

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

#include
     
      
#include
      
       
#include
       
        
using namespace std;
int main(){  
	long s,i,j,m,t;
    char a[2000];
    while(cin>>a){
	if(!(a[0]-48))break;
    i=0;
    s=0;
    j=strlen(a);
    for( ;j>=0;j--){
	  t=a[j]-48;            
      m=t*(pow(2,i)-1);        
      s+=m;
      i++;
    }
    cout<
        <