数据结构 - 树形选择排序 (tree selection sort) 详解 及 代码(C++)

树形选择排序 (tree selection sort) 详解 及 代码(C++)

本文地址: http://blog.csdn.net/caroline_wendy

算法逻辑: 根据节点的大小, 建立树, 输出树的根节点, 并把此重置为最大值, 再重构树.

因为树中保留了一些比较的逻辑, 所以减少了比较次数.

也称锦标赛排序, 时间复杂度为O(nlogn), 因为每个值(共n个)需要进行树的深度(logn)次比较.

参考<数据结构>(严蔚敏版) 第278-279页.

树形选择排序(tree selection sort)是堆排序的一个过渡, 并不是核心算法. 

但是完全按照书上算法, 实现起来极其麻烦, 几乎没有任何人实现过.

需要记录建树的顺序, 在重构时, 才能减少比较.

本着娱乐和分享的精神, 应人之邀, 简单的实现了一下.

代码:

/* * TreeSelectionSort.cpp * *  Created on: 2014.6.11 *      Author: Spike *//*eclipse cdt,  gcc 4.8.1*/#include <iostream>#include <vector>#include <stack>#include <queue>#include <utility>#include <climits>using namespace std;/*树的结构*/struct BinaryTreeNode{bool from; //判断来源, 左true, 右falseint m_nValue;BinaryTreeNode* m_pLeft;BinaryTreeNode* m_pRight;};/*构建叶子节点*/BinaryTreeNode* buildList (const std::vector<int>& L){BinaryTreeNode* btnList = new BinaryTreeNode[L.size()];for (std::size_t i=0; i<L.size(); ++i){btnList[i].from = true;btnList[i].m_nValue = L[i];btnList[i].m_pLeft = NULL;btnList[i].m_pRight = NULL;}return btnList;}/*不足偶数时, 需补充节点*/BinaryTreeNode* addMaxNode (BinaryTreeNode* list, int n){/*最大节点*/BinaryTreeNode* maxNode = new BinaryTreeNode(); //最大节点, 用于填充maxNode->from = true;maxNode->m_nValue = INT_MAX;maxNode->m_pLeft = NULL;maxNode->m_pRight = NULL;/*复制数组*/BinaryTreeNode* childNodes = new BinaryTreeNode[n+1]; //增加一个节点for (int i=0; i<n; ++i) {childNodes[i].from = list[i].from;childNodes[i].m_nValue = list[i].m_nValue;childNodes[i].m_pLeft = list[i].m_pLeft;childNodes[i].m_pRight = list[i].m_pRight;}childNodes[n] = *maxNode;delete[] list;list = NULL;return childNodes;}/*根据左右子树大小, 创建树*/BinaryTreeNode* buildTree (BinaryTreeNode* childNodes, int n){if (n == 1) {return childNodes;}if (n%2 == 1) {childNodes = addMaxNode(childNodes, n);}int num = n/2 + n%2;BinaryTreeNode* btnList = new BinaryTreeNode[num];for (int i=0; i<num; ++i) {btnList[i].m_pLeft = &childNodes[2*i];btnList[i].m_pRight = &childNodes[2*i+1];bool less = btnList[i].m_pLeft->m_nValue <= btnList[i].m_pRight->m_nValue;btnList[i].from = less;btnList[i].m_nValue = less ?btnList[i].m_pLeft->m_nValue : btnList[i].m_pRight->m_nValue;}buildTree(btnList, num);}/*返回树根, 重新计算数*/int rebuildTree (BinaryTreeNode* tree){int result = tree[0].m_nValue;std::stack<BinaryTreeNode*> nodes;BinaryTreeNode* node = &tree[0];nodes.push(node);while (node->m_pLeft != NULL) {node = node->from ? node->m_pLeft : node->m_pRight;nodes.push(node);}node->m_nValue = INT_MAX;nodes.pop();while (!nodes.empty()){node = nodes.top();nodes.pop();bool less = node->m_pLeft->m_nValue <= node->m_pRight->m_nValue;node->from = less;node->m_nValue = less ?node->m_pLeft->m_nValue : node->m_pRight->m_nValue;}return result;}/*从上到下打印树*/void printTree (BinaryTreeNode* tree) {BinaryTreeNode* node = &tree[0];std::queue<BinaryTreeNode*> temp1;std::queue<BinaryTreeNode*> temp2;temp1.push(node);while (!temp1.empty()){node = temp1.front();if (node->m_pLeft != NULL && node->m_pRight != NULL) {temp2.push(node->m_pLeft);temp2.push(node->m_pRight);}temp1.pop();if (node->m_nValue == INT_MAX) {std::cout << "MAX"  << " ";} else {std::cout << node->m_nValue  << " ";}if (temp1.empty()){std::cout << std::endl;temp1 = temp2;std::queue<BinaryTreeNode*> empty;std::swap(temp2, empty);}}}int main (){std::vector<int> L = {49, 38, 65, 97, 76, 13, 27, 49};BinaryTreeNode* tree = buildTree(buildList(L), L.size());std::cout << "Begin : " << std::endl;printTree(tree); std::cout << std::endl;std::vector<int> result;for (std::size_t i=0; i<L.size(); ++i){int value = rebuildTree (tree);std::cout << "Round[" << i+1 << "] : " << std::endl;printTree(tree); std::cout << std::endl;result.push_back(value);}std::cout << "result : ";for (std::size_t i=0; i<L.size(); ++i) {std::cout << result[i] << " ";}std::cout << std::endl;return 0;}

输出:

Begin : 13 38 13 38 65 13 27 49 38 65 97 76 13 27 49 Round[1] : 27 38 27 38 65 76 27 49 38 65 97 76 MAX 27 49 Round[2] : 38 38 49 38 65 76 49 49 38 65 97 76 MAX MAX 49 Round[3] : 49 49 49 49 65 76 49 49 MAX 65 97 76 MAX MAX 49 Round[4] : 49 65 49 MAX 65 76 49 MAX MAX 65 97 76 MAX MAX 49 Round[5] : 65 65 76 MAX 65 76 MAX MAX MAX 65 97 76 MAX MAX MAX Round[6] : 76 97 76 MAX 97 76 MAX MAX MAX MAX 97 76 MAX MAX MAX Round[7] : 97 97 MAX MAX 97 MAX MAX MAX MAX MAX 97 MAX MAX MAX MAX Round[8] : MAX MAX MAX MAX MAX MAX MAX MAX MAX MAX MAX MAX MAX MAX MAX result : 13 27 38 49 49 65 76 97