算法导论 ch15 动态规划最优二叉查找树-优快云博客

本文介绍了一种用于计算最优二叉搜索树的算法，并通过示例展示了算法的具体实现过程。该算法使用动态规划方法来确定使搜索期望代价最小化的二叉搜索树结构。

1. source code

#include <iostream> using namespace std; void optimalBST(double *p, double *q, int n) { const int COL = n + 2; double *e = new double[(n + 2) * COL]; double *w = new double[(n + 2) * COL]; int *root = new int[(n + 2) * COL]; for (int i = 1; i <= n + 1; i++) { e[i * COL + (i - 1)] = q[i - 1]; w[i * COL + (i - 1)] = q[i - 1]; } for (int l = 1; l <= n; l++) { for (int i = 1; i <= n - l + 1; i++) { int j = i + l - 1; e[i * COL + j] = numeric_limits<int>::max(); w[i * COL + j] = w[i * COL + j - 1] + p[j]+ q[j]; for (int r = i ; r <= j; r++) { double t = e[i * COL + r - 1] + e[(r + 1) * COL + j]+ w[i * COL + j]; if (t < e[i * COL + j]) { e[i * COL + j] = t; root[i * COL + j] = r; } } } } cout << "matrix e :"<< endl; for (int i = 1; i < COL; i++) { for (int j = 0; j <= n; j++) { cout << e[i * COL + j]<< " "; } cout << endl; } cout << "matrix w :"<< endl; for (int i = 1; i < COL; i++) { for (int j = 0; j <= n; j++) { cout << w[i * COL + j]<< " "; } cout << endl; } cout << "matrix root :"<< endl; for (int i = 1; i < COL - 1; i++) { for (int j = 1; j < COL - 1; j++) { cout << root[i * COL + j]<< " "; } cout << endl; } } int main() { double p[] = { 0, 0.15, 0.1, 0.05, 0.1, 0.2 }; double q[] = { 0.05, 0.1, 0.05, 0.05, 0.05, 0.1 }; int n = sizeof(p)/sizeof(double); optimalBST(p, q, n - 1); }

2. test result

matrix e : 0.05 0.45 0.9 1.25 1.75 2.75 0 0.1 0.4 0.7 1.2 2 0 0 0.05 0.25 0.6 1.3 0 0 0 0.05 0.3 0.9 0 0 0 0 0.05 0.5 0 0 0 0 0 0.1 matrix w : 0.05 0.3 0.45 0.55 0.7 1 0 0.1 0.25 0.35 0.5 0.8 0 0 0.05 0.15 0.3 0.6 0 0 0 0.05 0.2 0.5 0 0 0 0 0.05 0.35 0 0 0 0 0 0.1 matrix root : 1 1 2 2 4 0 2 2 2 4 0 0 3 4 5 0 0 0 4 5 0 0 0 0 5