C++编程完成动态规划法求解最优二叉搜索树，随机化查找数字及其查找成功概率，求出最优二叉搜索树。

以下是C++代码实现：

#include <iostream>
#include <vector>
#include <climits>
#include <ctime>
#include <cstdlib>

using namespace std;

double sum(vector<double> p, int i, int j) {
    double s = 0;
    for (int k = i; k <= j; k++) {
        s += p[k];
    }
    return s;
}

void optimal_bst(vector<double> p, int n) {
    vector<vector<double>> e(n + 1, vector<double>(n + 1, 0));
    vector<vector<double>> w(n + 1, vector<double>(n + 1, 0));
    vector<vector<int>> root(n + 1, vector<int>(n + 1, 0));
    for (int i = 1; i <= n; i++) {
        e[i][i - 1] = 0;
        w[i][i - 1] = 0;
    }
    for (int len = 1; len <= n; len++) {
        for (int i = 1; i <= n - len + 1; i++) {
            int j = i + len - 1;
            e[i][j] = INT_MAX;
            w[i][j] = w[i][j - 1] + p[j];
            for (int r = i; r <= j; r++) {
                double t = e[i][r - 1] + e[r + 1][j] + w[i][j];
                if (t < e[i][j]) {
                    e[i][j] = t;
                    root[i][j] = r;
                }
            }
        }
    }
    cout << "最小代价为：" << e[1][n] << endl;
    cout << "构造的最优二叉搜索树为：" << endl;
    cout << "根节点为" << root[1][n] << endl;
    vector<int> q;
    q.push_back(root[1][n]);
    vector<int> left(1, 1), right(1, n);
    while (!q.empty()) {
        int r = q.back();
        q.pop_back();
        int i = left.back();
        left.pop_back();
        int j = right.back();
        right.pop_back();
        if (r - 1 >= i && root[i][r - 1] != 0) {
            cout << "根节点为" << root[i][r - 1] << "的左子树为" << i << "到" << r - 1 << endl;
            left.push_back(i);
            right.push_back(r - 1);
            q.push_back(root[i][r - 1]);
        }
        if (r + 1 <= j && root[r + 1][j] != 0) {
            cout << "根节点为" << root[r + 1][j] << "的右子树为" << r + 1 << "到" << j << endl;
            left.push_back(r + 1);
            right.push_back(j);
            q.push_back(root[r + 1][j]);
        }
    }
}

int main() {
    srand(time(nullptr));
    vector<double> p{0, 0.15, 0.10, 0.05, 0.10, 0.20};
    optimal_bst(p, 5);
    cout << "随机化查找数字及其查找成功概率：" << endl;
    double s = sum(p, 1, 5);
    for (int i = 1; i <= 5; i++) {
        double r = (double) rand() / RAND_MAX;
        double sum = 0;
        for (int j = 1; j <= 5; j++) {
            sum += p[j];
            if (r < sum / s) {
                cout << "随机数为" << r << "，查找数字为" << j << "，查找成功概率为" << p[j] / s << endl;
                break;
            }
        }
    }
    return 0;
}

其中，`optimal_bst`函数实现动态规划求解最优二叉搜索树，`sum`函数用于计算概率之和，`main`函数中实现随机化查找数字及其查找成功概率。在本例中，我们以一组数据{0.15,0.10,0.05,0.10,0.20}为例进行了求解。