Tuesday, March 29, 2016

Algorithm Problem Solving Approaches


http://www.jiuzhang.com/qa/623/
能不能系统讲讲什么时候用BFS和DFS

我就稍微说几句,BFS 和 DFS 都是搜索算法,我就比较一下他们的优缺点。
1.BFS是用来搜索最短径路的解是比较合适的,比如求最少步数的解,最少交换次数的解,因为BFS搜索过程中遇到的解一定是离根最近的,所以遇到一个解,一定就是最优解,此时搜索算法可以终止。这个时候不适宜使用DFS,因为DFS搜索到的解不一定是离根最近的,只有全局搜索完毕,才能从所有解中找出离根的最近的解。(当然这个DFS的不足,可以使用迭代加深搜索ID-DFS去弥补)

2.空间优劣上,DFS是有优势的,DFS不需要保存搜索过程中的状态,而BFS在搜索过程中需要保存搜索过的状态,而且一般情况需要一个队列来记录。

3.DFS适合搜索全部的解,因为要搜索全部的解,那么BFS搜索过程中,遇到离根最近的解,并没有什么用,也必须遍历完整棵搜索树,DFS搜索也会搜索全部,但是相比DFS不用记录过多信息,所以搜素全部解的问题,DFS显然更加合适。

上面提到的迭代加深搜索(ID-dfs)我觉得充分吸收了BFS和DFS各自的长处
基本原则:能用BFS的时候就用BFS,不能用的时候再用DFS。

https://segmentfault.com/a/1190000006059081
波利亚用三本书:《How To Solve It》、《数学的发现》、《数学与猜想》)来试图阐明人类解决问题的一般性的思维方法,总结起来主要有以下几种:
  • 时刻不忘未知量。即时刻别忘记你到底想要求什么,问题是什么。(动态规划中问题状态的设定)
  • 试错。对题目这里捅捅那里捣捣,用上所有的已知量,或使用所有你想到的操作手法,尝试着看看能不能得到有用的结论,能不能离答案近一步(回溯算法中走不通就回退)。
  • 求解一个类似的题目。类似的题目也许有类似的结构,类似的性质,类似的解方案。通过考察或回忆一个类似的题目是如何解决的,也许就能够借用一些重要的点子(比较 Ugly Number 的三个题目:263. Ugly Number, 264. Ugly Number II, 313. Super Ugly Number)。
  • 用特例启发思考。通过考虑一个合适的特例,可以方便我们快速寻找出一般问题的解。
  • 反过来推导。对于许多题目而言,其要求的结论本身就隐藏了推论,不管这个推论是充分的还是必要的,都很可能对解题有帮助。
刷 LeetCode 的最大好处就是可以锻炼解决问题的思维能力,相信我,如何去思考本身也是一个需要不断学习和练习的技能。


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