【迭代加深搜索】Addition Chains

念JL___初蝶

于 2018-04-08 14:05:32 发布

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分类专栏： openjudge题库刷题日志

本文链接：https://blog.youkuaiyun.com/qq_37862149/article/details/79851124

该博客介绍了一个利用迭代加深搜索（IDDFS）来构造整数n的最小长度加法链的问题。加法链需满足特定条件，包括起始值为1，最终值为n，序列递增，且每个元素可以通过序列中前两个元素相加得到。博客提供了输入输出示例，并讨论了解题思路，指出当需要寻找长度最短的加法链时，可以采用IDDFS策略。给出了具体的AC代码作为解决方案。

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【迭代加深搜索】Addition Chains

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 neccessarily 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 file will contain one or more test cases. Each test case consists of one line containing one
integer n (1 ≤ n ≤ 10000). Input is terminated by a value of zero (0) for n.