2715: Addition Chains
Memory Limit：128 MB
Time Limit：1.000 S
Judge Style：Text Compare
Creator：
Submit：5
Solved：2
Description
An addition chain for n is an integer sequence with the following four properties:
You are given an integer n. Your job is to construct an addition chain for n with minimal length. If there is more than one such sequence, any one is acceptable.
For example, <1,2,3,5> and <1,2,4,5> are both valid solutions when you are asked for an addition chain for 5.
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a0 = 1
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am = n
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a0 < a1 < a2 < ... < am-1 < am
- For each k (1<=k<=m) there exist two (not necessarily different) integers i and j (0<=i, j<=k-1) with ak=ai+aj
You are given an integer n. Your job is to construct an addition chain for n with minimal length. If there is more than one such sequence, any one is acceptable.
For example, <1,2,3,5> and <1,2,4,5> are both valid solutions when you are asked for an addition chain for 5.
Input
The input will contain one or more test cases. Each test case consists of one line containing one integer n (1<=n<=100). Input is terminated by a value of zero (0) for n.
Output
For each test case, print one line containing one integer m, seperated by three blank, then print the required integer sequence, separating the numbers by one blank.
Hint: The problem is a little time-critical, so use proper break conditions where necessary to reduce the search space.
Hint: The problem is a little time-critical, so use proper break conditions where necessary to reduce the search space.
Sample Input Copy
5
7
12
15
77
0Sample Output Copy
4 1 2 4 5
5 1 2 4 6 7
5 1 2 4 8 12
6 1 2 4 5 10 15
9 1 2 4 8 9 17 34 68 77