53 lines
2.1 KiB
Markdown
53 lines
2.1 KiB
Markdown
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---
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title: Backtracking Algorithms
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localeTitle: 回溯算法
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---
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# 回溯算法
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回溯是一种通用算法，用于查找某些计算问题的所有（或某些）解决方案，特别是约束满足问题，逐步构建候选解决方案，并在确定候选不能时立即放弃每个部分候选_（“回溯”）_可能完成一个有效的解决方案。
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### 示例问题（骑士游览问题）
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_骑士被放置在空板的第一块上，按照国际象棋的规则移动，必须完全访问每个方块一次。_
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###路径跟随Knight覆盖所有细胞 以下是8 x 8单元的棋盘。单元格中的数字表示骑士的移动数量。 [](https://commons.wikimedia.org/wiki/File:Knights_tour_(Euler).png)
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### 骑士之旅的天真算法
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朴素算法是逐个生成所有游览并检查生成的游览是否满足约束。
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```
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while there are untried tours
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{
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generate the next tour
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if this tour covers all squares
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{
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print this path;
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}
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}
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```
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### 骑士巡回赛的回溯算法
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以下是奈特巡回赛问题的回溯算法。
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```
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If all squares are visited
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print the solution
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Else
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a) Add one of the next moves to solution vector and recursively
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check if this move leads to a solution. (A Knight can make maximum
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eight moves. We choose one of the 8 moves in this step).
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b) If the move chosen in the above step doesn't lead to a solution
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then remove this move from the solution vector and try other
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alternative moves.
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c) If none of the alternatives work then return false (Returning false
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will remove the previously added item in recursion and if false is
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returned by the initial call of recursion then "no solution exists" )
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```
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### 更多信息
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[维基百科](https://en.wikipedia.org/wiki/Backtracking)
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[极客4极客](http://www.geeksforgeeks.org/backtracking-set-1-the-knights-tour-problem/)
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[一个非常有趣的回溯介绍](https://www.hackerearth.com/practice/basic-programming/recursion/recursion-and-backtracking/tutorial/)
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