给定成功检索概率和失败检索概率，用c++实现最优二叉搜索树先根序列打印

以下是用C++实现最优二叉搜索树打印先根序列的代码：

#include <iostream>
#include <vector>
#include <limits>
using namespace std;

void printOptimalBST(vector<vector<int>>& root, int i, int j, int parent) {
    if (i > j) {
        return;
    }
    int rootIdx = root[i][j];
    if (parent == 0) {
        cout << "k" << rootIdx << " is the root" << endl;
    } else {
        cout << "k" << rootIdx << " is the left child of " << "k" << parent << endl;
    }
    printOptimalBST(root, i, rootIdx - 1, rootIdx);
    printOptimalBST(root, rootIdx + 1, j, rootIdx);
}

void optimalBST(double p[], double q[], int n) {
    double e[n + 1][n + 1], w[n + 1][n + 1];
    vector<vector<int>> root(n + 1, vector<int>(n + 1, 0));
    for (int i = 1; i <= n + 1; i++) {
        e[i - 1][i - 1] = q[i - 1];
        w[i - 1][i - 1] = q[i - 1];
    }
    for (int len = 1; len <= n; len++) {
        for (int i = 0; i <= n - len; i++) {
            int j = i + len;
            e[i][j] = numeric_limits<double>::max();
            w[i][j] = w[i][j - 1] + p[j] + q[j];
            for (int k = i; k < j; k++) {
                double temp = e[i][k] + e[k + 1][j] + w[i][j];
                if (temp < e[i][j]) {
                    e[i][j] = temp;
                    root[i][j] = k;
                }
            }
        }
    }
    cout << "The optimal BST is: " << endl;
    printOptimalBST(root, 0, n - 1, 0);
}

int main() {
    double p[] = {0.15, 0.10, 0.05, 0.10, 0.20};
    double q[] = {0.05, 0.10, 0.05, 0.05, 0.05, 0.10};
    int n = sizeof(p) / sizeof(p[0]);
    optimalBST(p, q, n - 1);
    return 0;
}

其中，`optimalBST`函数实现了最优二叉搜索树的构建，`printOptimalBST`函数实现了先根序列的打印。在`main`函数中，我们给出了一个例子，其中$p$数组为成功检索概率，$q$数组为失败检索概率。