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