算法导论 ch15 动态规划 最优二叉查找树

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