生成所有可能的搜索二叉树

product_all_tree(0, 5);

递归返回子树的指针集合。作为 左子树或右子树。

从而构建整颗树。

#include<iostream>
#include<vector>
using namespace std;
//double p[1000]{ 0,0.15,0.10,0.05,0.10,0.20 };
double p[1000]{ 1,2,3,4,5,6,7,8,9 };

#define N 5
class Tree
{
public:
	Tree*parent_;
	Tree*l_c_;
	Tree*r_c_;
	double data_;
	Tree(double a) {
		parent_ = nullptr;
		l_c_ = nullptr;
		r_c_ = nullptr;
		data_ = a;
	}
};
vector<Tree*> product_all_tree(int start,int end)//start end 起始下标，结束下标
{
	vector<Tree*> trees;
	if (start > end)
	{
		trees.push_back(nullptr);
		return trees;
	}
	if (start ==end)
	{
		trees.push_back(new Tree(p[start]));
		return trees;
	}
　　　　　　//以i作为分界点获取左右两部分的子树集合
	for (int i = start; i <= end; ++i)
	{
		auto lefts = product_all_tree(start,i-1);
		auto rights = product_all_tree(i+1, end);
		for(auto left: lefts)
			for (auto right : rights)
			{
				Tree* root = new Tree(p[i]);
				root->l_c_ = left;
				root->r_c_ = right;
				trees.push_back(root);
			}
	}
	return trees;
}
void PrintTree(Tree*T, int Layer=1)
{/*按竖向树状打印的二叉树*/
	int i;
	if (T == NULL)
		return;
	PrintTree(T->r_c_, Layer + 1);
	for (i = 0; i<Layer; i++)
		printf("  ");
	printf("%d
", static_cast<int>(T->data_)); //按逆中序输出结点，用层深决定结点的左右位置
	PrintTree(T->l_c_, Layer + 1);
}

int main()
{
	auto trees=product_all_tree(0, 5);//一共六个数
	for (auto tree : trees)
	{
		PrintTree(tree);
		cout << "-----------------"<< endl ;
	}
}

　　结果：二叉树的输出有点丑 横向的，主要关注点，这是个搜索二叉树，

• 当前根节点的值大于左子树节点的值
• 当前根节点的值小于右子树节点的值
• 左右子树同样是二叉搜索树

            6
          5
        4
      3
    2
  1
--------------------------
          6
            5
        4
      3
    2
  1
--------------------------
          6
        5
          4
      3
    2
  1
--------------------------
        6
            5
          4
      3
    2
  1
--------------------------
        6
          5
            4
      3
    2
  1
--------------------------
          6
        5
      4
        3
    2
  1
--------------------------
        6
          5
      4
        3
    2
  1
--------------------------
        6
      5
          4
        3
    2
  1
--------------------------
        6
      5
        4
          3
    2
  1
--------------------------
      6
            5
          4
        3
    2
  1
--------------------------
      6
          5
            4
        3
    2
  1
--------------------------
      6
          5
        4
          3
    2
  1
--------------------------
      6
        5
            4
          3
    2
  1
--------------------------
      6
        5
          4
            3
    2
  1
--------------------------
          6
        5
      4
    3
      2
  1
--------------------------
        6
          5
      4
    3
      2
  1
--------------------------
        6
      5
        4
    3
      2
  1
--------------------------
      6
          5
        4
    3
      2
  1
--------------------------
      6
        5
          4
    3
      2
  1
--------------------------
        6
      5
    4
        3
      2
  1
--------------------------
      6
        5
    4
        3
      2
  1
--------------------------
        6
      5
    4
      3
        2
  1
--------------------------
      6
        5
    4
      3
        2
  1
--------------------------
      6
    5
          4
        3
      2
  1
--------------------------
      6
    5
        4
          3
      2
  1
--------------------------
      6
    5
        4
      3
        2
  1
--------------------------
      6
    5
      4
          3
        2
  1
--------------------------
      6
    5
      4
        3
          2
  1
--------------------------
    6
            5
          4
        3
      2
  1
--------------------------
    6
          5
            4
        3
      2
  1
--------------------------
    6
          5
        4
          3
      2
  1
--------------------------
    6
        5
            4
          3
      2
  1
--------------------------
    6
        5
          4
            3
      2
  1
--------------------------
    6
          5
        4
      3
        2
  1
--------------------------
    6
        5
          4
      3
        2
  1
--------------------------
    6
        5
      4
          3
        2
  1
--------------------------
    6
        5
      4
        3
          2
  1
--------------------------
    6
      5
            4
          3
        2
  1
--------------------------
    6
      5
          4
            3
        2
  1
--------------------------
    6
      5
          4
        3
          2
  1
--------------------------
    6
      5
        4
            3
          2
  1
--------------------------
    6
      5
        4
          3
            2
  1
--------------------------
          6
        5
      4
    3
  2
    1
--------------------------
        6
          5
      4
    3
  2
    1
--------------------------
        6
      5
        4
    3
  2
    1
--------------------------
      6
          5
        4
    3
  2
    1
--------------------------
      6
        5
          4
    3
  2
    1
--------------------------
        6
      5
    4
      3
  2
    1
--------------------------
      6
        5
    4
      3
  2
    1
--------------------------
      6
    5
        4
      3
  2
    1
--------------------------
      6
    5
      4
        3
  2
    1
--------------------------
    6
          5
        4
      3
  2
    1
--------------------------
    6
        5
          4
      3
  2
    1
--------------------------
    6
        5
      4
        3
  2
    1
--------------------------
    6
      5
          4
        3
  2
    1
--------------------------
    6
      5
        4
          3
  2
    1
--------------------------
        6
      5
    4
  3
      2
    1
--------------------------
      6
        5
    4
  3
      2
    1
--------------------------
      6
    5
      4
  3
      2
    1
--------------------------
    6
        5
      4
  3
      2
    1
--------------------------
    6
      5
        4
  3
      2
    1
--------------------------
        6
      5
    4
  3
    2
      1
--------------------------
      6
        5
    4
  3
    2
      1
--------------------------
      6
    5
      4
  3
    2
      1
--------------------------
    6
        5
      4
  3
    2
      1
--------------------------
    6
      5
        4
  3
    2
      1
--------------------------
      6
    5
  4
        3
      2
    1
--------------------------
    6
      5
  4
        3
      2
    1
--------------------------
      6
    5
  4
      3
        2
    1
--------------------------
    6
      5
  4
      3
        2
    1
--------------------------
      6
    5
  4
      3
    2
      1
--------------------------
    6
      5
  4
      3
    2
      1
--------------------------
      6
    5
  4
    3
        2
      1
--------------------------
    6
      5
  4
    3
        2
      1
--------------------------
      6
    5
  4
    3
      2
        1
--------------------------
    6
      5
  4
    3
      2
        1
--------------------------
    6
  5
          4
        3
      2
    1
--------------------------
    6
  5
        4
          3
      2
    1
--------------------------
    6
  5
        4
      3
        2
    1
--------------------------
    6
  5
      4
          3
        2
    1
--------------------------
    6
  5
      4
        3
          2
    1
--------------------------
    6
  5
        4
      3
    2
      1
--------------------------
    6
  5
      4
        3
    2
      1
--------------------------
    6
  5
      4
    3
        2
      1
--------------------------
    6
  5
      4
    3
      2
        1
--------------------------
    6
  5
    4
          3
        2
      1
--------------------------
    6
  5
    4
        3
          2
      1
--------------------------
    6
  5
    4
        3
      2
        1
--------------------------
    6
  5
    4
      3
          2
        1
--------------------------
    6
  5
    4
      3
        2
          1
--------------------------
  6
            5
          4
        3
      2
    1
--------------------------
  6
          5
            4
        3
      2
    1
--------------------------
  6
          5
        4
          3
      2
    1
--------------------------
  6
        5
            4
          3
      2
    1
--------------------------
  6
        5
          4
            3
      2
    1
--------------------------
  6
          5
        4
      3
        2
    1
--------------------------
  6
        5
          4
      3
        2
    1
--------------------------
  6
        5
      4
          3
        2
    1
--------------------------
  6
        5
      4
        3
          2
    1
--------------------------
  6
      5
            4
          3
        2
    1
--------------------------
  6
      5
          4
            3
        2
    1
--------------------------
  6
      5
          4
        3
          2
    1
--------------------------
  6
      5
        4
            3
          2
    1
--------------------------
  6
      5
        4
          3
            2
    1
--------------------------
  6
          5
        4
      3
    2
      1
--------------------------
  6
        5
          4
      3
    2
      1
--------------------------
  6
        5
      4
        3
    2
      1
--------------------------
  6
      5
          4
        3
    2
      1
--------------------------
  6
      5
        4
          3
    2
      1
--------------------------
  6
        5
      4
    3
        2
      1
--------------------------
  6
      5
        4
    3
        2
      1
--------------------------
  6
        5
      4
    3
      2
        1
--------------------------
  6
      5
        4
    3
      2
        1
--------------------------
  6
      5
    4
          3
        2
      1
--------------------------
  6
      5
    4
        3
          2
      1
--------------------------
  6
      5
    4
        3
      2
        1
--------------------------
  6
      5
    4
      3
          2
        1
--------------------------
  6
      5
    4
      3
        2
          1
--------------------------
  6
    5
            4
          3
        2
      1
--------------------------
  6
    5
          4
            3
        2
      1
--------------------------
  6
    5
          4
        3
          2
      1
--------------------------
  6
    5
        4
            3
          2
      1
--------------------------
  6
    5
        4
          3
            2
      1
--------------------------
  6
    5
          4
        3
      2
        1
--------------------------
  6
    5
        4
          3
      2
        1
--------------------------
  6
    5
        4
      3
          2
        1
--------------------------
  6
    5
        4
      3
        2
          1
--------------------------
  6
    5
      4
            3
          2
        1
--------------------------
  6
    5
      4
          3
            2
        1
--------------------------
  6
    5
      4
          3
        2
          1
--------------------------
  6
    5
      4
        3
            2
          1
--------------------------
  6
    5
      4
        3
          2
            1
--------------------------
请按任意键继续. . .

　　

cout << "--------------------------" << endl ;