算法导论第15章 最优二叉树

#include <iostream>
#include <climits>
#include <cmath>
using namespace std;
#define EPSILON 0.0000000001
const int m = 7;
const int n = 6;

struct twoArray
{
float e[m]
;
float root

;
};
/**************************************************************/
/* w[i][j];对于一棵由ki,...kj的子树，定义的概率总和,辅助e[i][j]的计算
if j = i-1: w[i][j] = qi-1;
if j >= i; w[i][j] = w[i][j-1]+pj+qj;

e[i][j]:为搜索一棵包含关键字ki,....kj的最优二叉查找树的期望代价
最终计算e[1, n]
if j = i-1: e[i][j] = q[i-1];
if i <= j: e[i][j] = min{e[i][j-1]+e[r+1, j]+w[i][j]}; (i =< r <= j)

root[i][j];为kr的下标r, kr为选择的根  */
/**************************************************************/
twoArray *OptimalBST(float *p, float *q)
{
float w[m]
;
twoArray *ta = new twoArray;
//for (int i = 0; i < m; i++)
//{
//	for (int j = 0; j < n; j++)
//	{
//		w[i][j] = 0.0;
//		(ta->e)[i][j] = 0.0;
//	}
//}
for (int i = 1; i <= n; i++)    //if j = i-1: e[i][j] = q[i-1];
{
(ta->e)[i][i-1] = q[i-1];
w[i][i-1] = q[i-1];
}
for (int len = 1; len < n; len++)
for (int i = 1; i < n-len+1; i++)
{
int j = i+len-1;
(ta->e)[i][j] = _I32_MAX;
w[i][j] = w[i][j-1]+p[j]+q[j];
//if i <= j: e[i][j] = min{e[i][j-1]+e[r+1, j]+w[i][j]}; (i =< r <= j)
for (int r = i; r <= j; r++)
{
int t = (ta->e)[i][r-1]+(ta->e)[r+1][j]+w[i][j];
if (((ta->e)[i][j] - t) > EPSILON)
{
(ta->e)[i][j] = t;
(ta->root)[i][j] = r;
}
}
}
return ta;
}

int main()
{
float p[] = {0.0, 0.15, 0.10, 0.05, 0.10, 0.20};
float q[] = {0.05, 0.10, 0.05, 0.05, 0.05, 0.10};

twoArray *ta = OptimalBST(p, q);

system("pause");
return 0;
}