算法導論第15章習題15.1-4

定義全局變量k存儲子函數計算最大收益時的變量i

#include "stdafx.h"

#include <iostream>
using namespace std;
int k=0;
int Max(int a, int b)
{
return a>b ? a : b;
}
int MEMOIZED_CUT_ROD_AUX(int p[], int n, int r[],int &k)
{
static int q;

//int A[10];
if (r[n] >= 0)
{//保存已求過的值。
return r[n];
}
if (n == 0)
{
q = 0;
}
else
{
q = -0x7fffffff;
for (int i = 0; i<n; i++)
{
A[i] = MEMOIZED_CUT_ROD_AUX(p, n - i - 1, r,k);
// cout << A[i] << endl;
if (q < (p[i] + MEMOIZED_CUT_ROD_AUX(p, n - i - 1, r,k)))
{
q = p[i] + MEMOIZED_CUT_ROD_AUX(p, n - i - 1, r,k);

k = i;
}
}

}
r[n] = q; 

cout << q << endl;


return q;
}
int MEMOIZED_CUT_ROD(int p[], int n)
{//方法①自頂向下的動態規劃方案
int *r = new int[n];
for (int i = 0; i<n; i++)
{
r[i] = -0x7fffffff;
}
return MEMOIZED_CUT_ROD_AUX(p, n, r,k);
}
int BOTTOM_UP_CUT_ROD(int p[], int n)
{//方法②自底向下的動態規劃方案
int *r = new int[n];
r[0] = 0;
for (int j = 0; j<n; j++)
{
int q = -0x7fffffff;
//int q=p[j+1];
for (int i = 0; i <= j; i++)
{
q = Max(q, p[i] + r[j - i]);
}
r[j + 1] = q;
}
return r[n];
}


int _tmain(int argc, _TCHAR* argv[])
{
const int n = 10;
int p[10] = { 1, 5, 8, 9, 10, 17, 17, 20, 24, 30 };
cout << MEMOIZED_CUT_ROD(p, 9) << endl;
cout << BOTTOM_UP_CUT_ROD(p, 9) << endl;
cout << k << endl;


return 0;
}