2248：Addition Chains

Special Judge 特殊评判

题目描述

An addition chain for n is an integer sequence with the following four properties:

a0 = 1
am = n
a0 < a1 < a2 < ... < a_m-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.

输入解释

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.

输出解释

For each test case, print one line containing the required integer sequence. Separate 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.

输入样例

输出样例

1 2 4 5
1 2 4 6 7
1 2 4 8 12
1 2 4 5 10 15
1 2 4 8 9 17 34 68 77

该题目是Virtual Judge题目，来自北京大学POJ

题目来源 Ulm Local 1997

源链接： POJ-2248

最后修改于 2020-10-29T06:27:29+00:00 由爬虫自动更新

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时间上限	内存上限
1000	65536