An addition chain for n is an integer sequence <a0, a1,a2,...,am="">with the following four properties: a0 = 1 am = n 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.
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.
博客园logo 会员 众包 新闻 博问 闪存 赞助商 HarmonyOS Chat2DB 代码改变世界 搜索 注册 登录 风雨无阻 只有一条路不能选择——那就是放弃的路；只有一条路不能拒绝——那就是成长的路。 POJ 2248 Addition Chains Addition Chains Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 4480 Accepted: 2454 Special Judge Description An addition chain for n is an integer sequence <a0, a1,a2,...,am="">with the following four properties: a0 = 1 am = n 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 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. Sample Input 5 7 12 15 77 0
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
