樹形選擇排序 (tree selection sort) 具體解釋 及 代碼(C++)

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

算法邏輯: 依據節點的大小, 建立樹, 輸出樹的根節點, 并把此重置為最大值, 再重構樹.

由于樹中保留了一些比較的邏輯, 所以降低了比較次數.

也稱錦標賽排序, 時間復雜度為O(nlogn), 由于每一個值(共n個)須要進行樹的深度(logn)次比較.

參考<數據結構>(嚴蔚敏版) 第278-279頁.

樹形選擇排序(tree selection sort)是堆排序的一個過渡, 并非核心算法.?

可是全然依照書上算法, 實現起來極其麻煩, 差點兒沒有不論什么人實現過.

須要記錄建樹的順序, 在重構時, 才干降低比較.

本著娛樂和分享的精神, 應人之邀, 簡單的實現了一下.

代碼:

/** 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;/*樹的結構*/ struct BinaryTreeNode{bool from; //推斷來源, 左true, 右falseint m_nValue;BinaryTreeNode* m_pLeft;BinaryTreeNode* m_pRight; };/*構建葉子節點*/ 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; }/*不足偶數時, 需補充節點*/ BinaryTreeNode* addMaxNode (BinaryTreeNode* list, int n) {/*最大節點*/BinaryTreeNode* maxNode = new BinaryTreeNode(); //最大節點, 用于填充maxNode->from = true;maxNode->m_nValue = INT_MAX;maxNode->m_pLeft = NULL;maxNode->m_pRight = NULL;/*復制數組*/BinaryTreeNode* childNodes = new BinaryTreeNode[n+1]; //添加一個節點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; }/*依據左右子樹大小, 創建樹*/ 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); } /*返回樹根, 又一次計算數*/ 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; } /*從上到下打印樹*/ 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; }

輸出:

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

總結

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