一、V - The Fun Number System

V - The Fun Number System

POJ - 1023

In a k bit 2's complement number, where the bits are indexed from 0 to k-1, the weight of the most significant bit (i.e., in position k-1), is -2^(k-1), and the weight of a bit in any position i (0 ≤ i < k-1) is 2^i. For example, a 3 bit number 101 is -2^2 + 0 + 2^0 = -3. A negatively weighted bit is called a negabit (such as the most significant bit in a 2's complement number), and a positively weighted bit is called a posibit.
A Fun number system is a positional binary number system, where each bit can be either a negabit, or a posibit. For example consider a 3-bit fun number system Fun3, where bits in positions 0, and 2 are posibits, and the bit in position 1 is a negabit. (110)Fun3 is evaluated as 2^2-2^1 + 0 = 3. Now you are going to have fun with the Fun number systems! You are given the description of a k-bit Fun number system Funk, and an integer N (possibly negative. You should determine the k bits of a representation of N in Funk, or report that it is not possible to represent the given N in the given Funk. For example, a representation of -1 in the Fun3 number system (defined above), is 011 (evaluated as 0 - 2^1 + 2^0), and
representing 6 in Fun3 is impossible.

Input

The first line of the input file contains a single integer t (1 ≤ t ≤ 10), the number of test cases, followed by the input data for each test case. Each test case is given in three consecutive lines. In the first line there is a positive integer k (1 ≤ k ≤ 64). In the second line of a test data there is a string of length k, composed only of letters n, and p, describing the Fun number system for that test data, where each n (p) indicates that the bit in that position is a negabit (posibit).
The third line of each test data contains an integer N (-2^63 ≤ N < 2^63), the number to be represented in the Funk number
system by your program.

Output

For each test data, you should print one line containing either a k-bit string representing the given number N in the Funk number system, or the word Impossible, when it is impossible to represent the given number.

Sample Input

2
3
pnp
6
4
ppnn
10

Sample Output

Impossible
1110

题意： 给定一列二进制，这串二进制唯一不同的是能加能减 （n代表该位为负数，p代表正）接着给定一个N，问能否用这串二进制表示 。

 思路：从低位到高位进行判断

1.① n是偶数，最低位为0，此时该为为n或p是没有区别的，接着判断前一位，即n=n/2

  ②n是奇数，最后一位一定是1，因为只有2的0次方可产生奇数，其他都为偶数。最后一位若为p（正），则n=（n-1)/2；若为n（负）， 则n=（n+1)/2 。

2.重复步骤1 k次，即字符串判断结束

3.若n==0,则逆序输出即可；若n不为0，则无法表示。

#include <stdio.h>
#include <stdlib.h>

int main()
{
    int i,j,t,k,p[70];
    long long  n;
    char s[70];
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%s%I64d",&k,s,&n);
        j=0;
        for(i=k-1;i>=0;i--)
        {
            if(n%2!=0)
            {
                p[j]=1;
                if(s[i]=='p')n=(n-1)/2;
                else n=(n+1)/2;
            }
            else
            {
                p[j]=0;
                n/=2;
            }
            j++;
        }
        if(n)printf("Impossible\n");
        else
        {
            for(i=j-1;i>=0;i--) printf("%d",p[i]);
            printf("\n");
        }

    }

    return 0;
}