[Algo] backtracking 回溯法

回溯法 是暴力搜寻法中的一种
 Tree :
Start from the root, DFS , when the result is not optimized, we track back to the root node and redo.

For any centain solution : when we got a solution, we stop.
For all solution : when we finished  Traversal every child of the root.

WHEN :
the principle of Backtracking is trying! So it can be used for most complex and big problems.

HOW :

1.  define the space of solutions : give while a condition to stop
2. define the rule of trying: Tree
3. DFS the tree

Normal structure :
 Recursive :

   1: int a[n];

   2: try(int i)

   3: {

   4:     if(i>n)

   5:        输出结果;

   6:      else

   7:     {

   8:        for(j = 下界; j <= 上界; j=j+1)  // 枚举i所有可能的路径

   9:        {

  10:            if(fun(j))                 // 满足限界函数和约束条件

  11:              {

  12:                 a[i] = j;

  13:               ...                         // 其他操作

  14:                 try(i+1);

  15:               回溯前的清理工作（如a[i]置空值等）;

  16:               }

  17:          }

  18:      }

  19: } 

 Non- Recursive : 

   1: int a[n],i;

   2: 初始化数组a[];

   3: i = 1;

   4: while (i>0(有路可走)   and  (未达到目标))  // 还未回溯到头

   5: {

   6:     if(i > n)                                              // 搜索到叶结点

   7:     {   

   8:           搜索到一个解，输出；

   9:     }

  10:     else                                                   // 处理第i个元素

  11:     { 

  12:           a[i]第一个可能的值；

  13:           while(a[i]在不满足约束条件且在搜索空间内)          // until find a valid value for a 

  14:           {

  15:               a[i]下一个可能的值；

  16:           }

  17:           if(a[i]在搜索空间内)

  18:          {

  19:               标识占用的资源；

  20:               i = i+1;                              // 扩展下一个结点

  21:          }

  22:          else 

  23:         {

  24:               清理所占的状态空间；            // 回溯

  25:               i = i –1; 

  26:          }

  27: }

[http://www.cnblogs.com/steven_oyj/archive/2010/05/22/1741376.html] 

Ex : 8 queens : https://en.wikipedia.org/wiki/Eight_queens_puzzle


https://leetcode.com/problems/n-queens/