Backtracking Algorithm

本文介绍了回溯法这一递归算法的基本概念,通过示例详细解释了如何在面对多个选项时作出选择并达到目标状态的过程。从根节点开始,逐步深入探讨了如何在遇到不可行路径时返回上一级继续搜索。

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Backtracking is a form of recursion.

The usual scenario is that you are faced with a number of options, and you must choose one of these. After you make your choice you will get a new set of options; just what set of options you get depends on what choice you made. This procedure is repeated over and over until you reach a final state. If you made a good sequence of choices, your final state is agoal state; if you didn't, it isn't.

Conceptually, you start at the root of a tree; the tree probably has some good leaves and some bad leaves, though it may be that the leaves are all good or all bad. You want to get to a good leaf. At each node, beginning with the root, you choose one of its children to move to, and you keep this up until you get to a leaf.

Suppose you get to a bad leaf. You can backtrack to continue the search for a good leaf by revoking yourmost recent choice, and trying out the next option in that set of options. If you run out of options, revoke the choice that got you here, and try another choice at that node. If you end up at the root with no options left, there are no good leaves to be found.

This needs an example.

  1. Starting at Root, your options are A and B. You choose A.
  2. At A, your options are C and D. You choose C.
  3. C is bad. Go back to A.
  4. At A, you have already tried C, and it failed. Try D.
  5. D is bad. Go back to A.
  6. At A, you have no options left to try. Go back to Root.
  7. At Root, you have already tried A. Try B.
  8. At B, your options are E and F. Try E.
  9. E is good. Congratulations!

See more in Backtracking_wiki  and backtracking_case




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