【二叉查找树】02不同的二叉查找树个数II【Unique Binary Search Trees II】
提到二叉查找树,就得想到二叉查找树的递归定义,
左子树的节点值都小于根节点,右子树的节点值都大于根节点。
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给定一个n,问有多少个不同的二叉查找树,使得每个节点的值为 1...n?
例如,
给定n=3,你的程序应该返回所有的这5个不同的二叉排序树的个数。
1 3 3 2 1 \ / / / \ \ 3 2 1 1 3 2 / / \ \ 2 1 2 3
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Given n, generate all structurally unique BST's (binary search trees) that store values 1...n.
For example,
Given n = 3, your program should return all 5 unique BST's shown below.
1 3 3 2 1 \ / / / \ \ 3 2 1 1 3 2 / / \ \ 2 1 2 3
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test.cpp:
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#include <iostream>
#include <cstdio> #include <stack> #include <vector> #include "BinaryTree.h" using namespace std; /** * Definition for binary tree with next pointer. * struct TreeLinkNode { * int val; * TreeLinkNode *left, *right, *next; * TreeLinkNode(int x) : val(x), left(NULL), right(NULL), next(NULL) {} * }; */ vector<TreeNode *> generate(int start, int end) { vector<TreeNode *> subTree; if (start > end) { subTree.push_back(NULL); return subTree; } //对每个节点做root节点做遍历判断,当某个节点为root时候满足条件的二叉树可能有多个
for (int k = start; k <= end; ++k) { vector<TreeNode *> leftSubTree = generate(start, k - 1); vector<TreeNode *> rightSubTree = generate(k + 1, end); for (int i = 0; i < leftSubTree.size(); ++i) { for (int j = 0; j < rightSubTree.size(); ++j) { TreeNode *tmp = new TreeNode(k); tmp->left = leftSubTree[i]; tmp->right = rightSubTree[j]; subTree.push_back(tmp); } } } return subTree; } vector<TreeNode *> generateTrees(int n) { if (n == 0) { return generate(1, 0); } return generate(1, n); } vector<vector<int> > levelOrder(TreeNode *root) { vector<vector<int> > matrix; if(root == NULL) { return matrix; } vector<int> temp; temp.push_back(root->val); matrix.push_back(temp); vector<TreeNode *> path; path.push_back(root); int count = 1; while(!path.empty()) { TreeNode *tn = path.front(); if(tn->left) { path.push_back(tn->left); } if(tn->right) { path.push_back(tn->right); } path.erase(path.begin()); count--; if(count == 0) { vector<int> tmp; vector<TreeNode *>::iterator it = path.begin(); for(; it != path.end(); ++it) { tmp.push_back((*it)->val); } if(tmp.size() > 0) { matrix.push_back(tmp); } count = path.size(); } } return matrix; } int main() { vector<TreeNode *> vRoot; vector<vector<int> > ans; vRoot = generateTrees(3); for (int n = 0; n < vRoot.size(); ++n) { ans.clear(); ans = levelOrder(vRoot[n]); cout << "----------------------" << endl; for (int i = 0; i < ans.size(); ++i) { for (int j = 0; j < ans[i].size(); ++j) { cout << ans[i][j] << " "; } cout << endl; } } for (int i = 0; i < vRoot.size(); ++i) { DestroyTree(vRoot[i]); } return 0; } |
结果输出:
----------------------
1
2
3
----------------------
1
3
2
----------------------
2
1 3
----------------------
3
1
2
----------------------
3
2
1
BinaryTree.h:
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#ifndef _BINARY_TREE_H_
#define _BINARY_TREE_H_ struct TreeNode { int val; TreeNode *left; TreeNode *right; TreeNode(int x) : val(x), left(NULL), right(NULL) {} }; TreeNode *CreateBinaryTreeNode(int value); void ConnectTreeNodes(TreeNode *pParent, TreeNode *pLeft, TreeNode *pRight); void PrintTreeNode(TreeNode *pNode); void PrintTree(TreeNode *pRoot); void DestroyTree(TreeNode *pRoot); #endif /*_BINARY_TREE_H_*/ |
BinaryTree.cpp:
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#include <iostream>
#include <cstdio> #include "BinaryTree.h" using namespace std; /** * Definition for binary tree * struct TreeNode { * int val; * TreeNode *left; * TreeNode *right; * TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */ //创建结点 TreeNode *CreateBinaryTreeNode(int value) { TreeNode *pNode = new TreeNode(value); return pNode; } //连接结点 void ConnectTreeNodes(TreeNode *pParent, TreeNode *pLeft, TreeNode *pRight) { if(pParent != NULL) { pParent->left = pLeft; pParent->right = pRight; } } //打印节点内容以及左右子结点内容 void PrintTreeNode(TreeNode *pNode) { if(pNode != NULL) { printf("value of this node is: %d\n", pNode->val); if(pNode->left != NULL) printf("value of its left child is: %d.\n", pNode->left->val); else printf("left child is null.\n"); if(pNode->right != NULL) printf("value of its right child is: %d.\n", pNode->right->val); else printf("right child is null.\n"); } else { printf("this node is null.\n"); } printf("\n"); } //前序遍历递归方法打印结点内容 void PrintTree(TreeNode *pRoot) { PrintTreeNode(pRoot); if(pRoot != NULL) { if(pRoot->left != NULL) PrintTree(pRoot->left); if(pRoot->right != NULL) PrintTree(pRoot->right); } } void DestroyTree(TreeNode *pRoot) { if(pRoot != NULL) { TreeNode *pLeft = pRoot->left; TreeNode *pRight = pRoot->right; delete pRoot; pRoot = NULL; DestroyTree(pLeft); DestroyTree(pRight); } } |