poj 1023 --The Fun Number System(分析题)

The Fun Number SystemTime Limit: 1000MS Memory Limit: 10000K
Total Submissions: 6988 Accepted: 2176


Description
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

 

 

 

大意 ：给你一个串的串长P，再给你一个串s（只包含p和n），再给你一个目标数字 n

 

 求通过串s变换后能达到数字n的一个二进制串

 

其中s中为p的位置表示该位权值为2^ i,n表示该位权值为-2^ i

 

做法 举例2：从低位向高位看，将目标数字转化为二进制,逐位取一个符合的值

 

ppnn

1010 

 

如果该位为 0,则n或p起的作用是一样的，该位的总权值为 0，s[p]取0

如果该位为 1 ,则当p作用时 ，不会对这个结果有任何影响，因为p的作用与正常二进制的作用是一样的，s[p]取1

如果该位为 1 ,则当n作用时，本来是应该这个位+1的，变成-1，显然丢失了2，所以要加上2，

又因为该位为1，所以+1后右移一位和+2后右移一位的效果是一样的。

 

如果算完整个串，则此时n应该为0。

如果还不理解自己读下代码 

 

#include <STDIO.H>int main(){ __int64 n; int t,p; char s[70]; scanf("%d",&t); while(t--) { scanf("%d%s%I64d",&p,s,&n); while(p--) { if(n&1) {  if(s[p]=='n')  n++; //or n+=2  s[p]='1'; } elses[p]='0'; n>>=1; } if(n) printf("Impossible\n"); else printf("%s\n",s); }}