UVA575 Skew Binary

思路：简单模拟题

#include <cstdio>
#include <cstring>
const int maxn = 33;

char num[maxn];

int main() {
int n;
while (gets(num) && num[0] != '0') {
int l = strlen(num);
int sum = 0;
for (int i = 0 ;i < l; i++)
sum += (num[i] - '0') * ((1 << (l - i)) - 1);
printf("%d\n", sum);
}
return 0;
}

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,

8130710 = 8 × 104 + 1 × 103 + 3 × 102 + 0 × 101 + 7 × 100 = 80000 + 1000 + 300 + 0 + 7 = 81307.

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

k

. For example,

100112 = 1 × 2

4 + 0 × 2

3 + 0 × 2

2 + 1 × 2

1 + 1 × 2

0 = 16 + 0 + 0 + 2 + 1 = 19.

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,

10120skew = 1×(25 −1)+ 0×(24 −1)+ 1×(23 −1)+ 2×(22 −1)+ 0×(21 −1) = 31+ 0+ 7+ 6+ 0 = 44.

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 2

31 − 1 =

2147483647.

Sample Input

10120

200000000000000000000000000000

10

1000000000000000000000000000000

11

100

11111000001110000101101102000

0

Sample Output

44

2147483646

3

2147483647

4

7

1041110737