树形选择排序 (tree selection sort) 具体解释 及 代码(C++)

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

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

由于树中保留了一些比較的逻辑, 所以降低了比較次数.

也称锦标赛排序, 时间复杂度为O(nlogn), 由于每一个值(共n个)须要进行树的深度(logn)次比較.

參考<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, 并非核心算法.

可是全然依照书上算法, 实现起来极其麻烦, 差点儿没有不论什么人实现过.

须要记录建树的顺序, 在重构时, 才干降低比較.

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; //推断来源, 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]; //添加一个节点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;
}/*依据左右子树大小, 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, 又一次计算数*/ 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