动态规划之最优二叉搜索树的结构 C++实现

原理

根据每个元素出现的频率，对应一个概率值，计算其整个二叉树的期望搜索代价，确定最优二叉树的结构。

源代码

#include <iostream>#include <utility>#include <vector>using namespace std;//Probability.vector<double> temp_dblP = { 0.0,0.15,0.10,0.05,0.10,0.20 }, temp_dblQ = { 0.05,0.10,0.05,0.05,0.05,0.10 };//Just Memoized of Optimal_BSTpair<vector<vector<double>>, vector<vector<int>>> Optimal_BST(const vector<double> &temp_dblP, const vector<double> &temp_dblQ, const size_t &temp_n) {    vector<vector<double>> temp_VecE, temp_VecW;    vector<vector<int>> temp_VecRoot;    temp_VecE.resize(temp_n + 2);    temp_VecW.resize(temp_n + 2);    temp_VecRoot.resize(temp_n + 1);    for(auto &i : temp_VecE) {        i.resize(temp_n + 1);    }    for(auto &i : temp_VecW) {        i.resize(temp_n + 1);    }    for(auto &i : temp_VecRoot) {        i.resize(temp_n + 1);    }    for(auto i = 1; i <= temp_n + 1; ++i) {        temp_VecE[i][i - 1] = temp_dblQ[i - 1];        temp_VecW[i][i - 1] = temp_dblQ[i - 1];    }    for(auto l = 1; l <= temp_n; ++l) {        for (auto i = 1; i <= temp_n - l + 1; ++i) {            auto j = i + l - 1;            temp_VecE[i][j] = DBL_MAX;            temp_VecW[i][j] = temp_VecW[i][j - 1] + temp_dblP[j] + temp_dblQ[j];            for (auto r = i; r <= j; ++r) {                auto temp_t = temp_VecE[i][r - 1] + temp_VecE[r + 1][j] + temp_VecW[i][j];                if(temp_t < temp_VecE[i][j]) {                    temp_VecE[i][j] = temp_t;                    temp_VecRoot[i][j] = r;                }            }        }    }    return make_pair(temp_VecE, temp_VecRoot);}void Print_BST(vector<vector<int>> const &temp_VecRoot, size_t const &temp_i, size_t const &temp_j, size_t const &temp_r) {    auto RootChild = 0;    if(temp_i < temp_dblP.size() && temp_j < temp_dblP.size()) {        RootChild = temp_VecRoot[temp_i][temp_j];    }    if (RootChild == temp_VecRoot[1][temp_dblP.size() - 1]) {        cout << "k" << RootChild << " is root" << endl;        Print_BST(temp_VecRoot, temp_i, RootChild - 1, RootChild);        Print_BST(temp_VecRoot, RootChild + 1, temp_j, RootChild);        return;    }    if (temp_j < temp_i - 1) { return; }    if(temp_j == temp_i - 1) {        if(temp_j < temp_r) {            cout << "d" << temp_j << " is " << "k" << temp_r << "'s left child" << endl;        }        else {            cout << "d" << temp_j << " is " << "k" << temp_r << "'s right child" << endl;        }        return;    }    if (RootChild < temp_r) {        cout << "k" << RootChild << " is " << "k" << temp_r << "'s left child" << endl;    }    else {        cout << "k" << RootChild << " is " << "k" << temp_r << "'s right child" << endl;    }    Print_BST(temp_VecRoot, temp_i, RootChild - 1, RootChild);    Print_BST(temp_VecRoot, RootChild + 1, temp_j, RootChild);}int main() {    auto temp_pair = Optimal_BST(temp_dblP, temp_dblQ, temp_dblP.size() - 1);    for(auto &i : temp_pair.first) {        for(auto &j : i) {            cout << j << " ";        }        cout << endl;    }    cout << endl;    for (auto &i : temp_pair.second) {        for (auto &j : i) {            cout << j << " ";        }        cout << endl;    }    cout << endl;    Print_BST(temp_pair.second, 1, temp_dblP.size() - 1, 0);    return 0;}