The Balance

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 5706    Accepted Submission(s): 2311

Problem Description

Now you are asked to measure a dose of medicine with a balance and a number of weights. Certainly it is not always achievable. So you should find out the qualities which cannot be measured from the range [1,S]. S is the total quality of all the weights.

 

 

Input

The input consists of multiple test cases, and each case begins with a single positive integer N (1<=N<=100) on a line by itself indicating the number of weights you have. Followed by N integers Ai (1<=i<=N), indicating the quality of each weight where 1<=Ai<=100.

 

 

Output

For each input set, you should first print a line specifying the number of qualities which cannot be measured. Then print another line which consists all the irrealizable qualities if the number is not zero.

 

 

Sample Input

3

1 2 

4

3

9 2 1

 

 

Sample Output

0

2

4 5

 

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Mean: 

 给你N个砝码，每个砝码有自己的重量，现在要你计算从1~S中哪些重量是不能用这些砝码称出来的。(其中S为所有砝码的重量之和)。

analyse:

 就是一道母函数的运用题，要注意的是砝码可以摆放在两个托盘上，所以要注意的是两个托盘两边的差值也能称出来的情况，其他的和普通母函数差不多。

Time complexity：O(n^3)

 

Source code：

 

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