动态规划之最优二叉搜索树的结构 C++实现

动态规划之最优二叉搜索树的结构 C++实现

原理

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_BST
pair<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;
}