钢条切割

#include <iostream>
#include <vector>
#include <algorithm>
#include <iterator>
using namespace std;

int cutRod(int *p, int n)
{
	if (n == 0)
		return 0;
	int q = -1;
	for(int i = 1; i <= n; i++)
		q = max(q, p[i]+cutRod(p, n-i));   
	return q;
}

//自顶向下辅助函数 
int memoizedCutRodAux(int *p, int n, int *r)
{
	if (r[n] >= 0)
		return r[n];
	int q = -1;
	if (n == 0)
		q = 0;
	else
	{
		for (int i = 1; i <= n; i++)
			q = max(q, p[i]+memoizedCutRodAux(p, n-i, r));
	}
	r[n] = q;
	return q;
}

//带备忘录的自顶向下，用r[i]记录已经求出的最优解，避免重复调用 
int memoizedCutRod(int *p, int n)
{
	int r[11] = {};
	for (int i = 0; i <= n; i++)
		r[i] = -1;
	int q = memoizedCutRodAux(p, n, r);
	return q;    
}

//自底向下 
int bottomUpCutRod(int *p, int n)
{
	int r[11] = {0};
	int q; 
	for (int j = 1; j <= n; j++)
	{
		q = -1;
		for (int i = 1; i <= j; i++)
			q = max(q, p[i]+r[j-i]);
		r[j] = q;
	}
	return r[n];           
}

//下面使用的是vector...都生疏了...T_T
//r[]: 记录最优解
//s[]：记录最优解的第一段的钢条的切割长度
pair<vector<int>, vector<int> > 
extendedBottomUpCutRod(vector<int> p, int n)
{
	vector<int> r, s(p.size());
	int q = -1;

	r.push_back(0);
	for (int j = 1; j <= n; j++)
	{
		q = -1;
		int i;
		for (i = 1; i <= j; i++)
		{
             if (q < p[i] + r[j-i])
			 {
				 q = p[i] + r[j-i];
				 s[j] = i;
			 }
		}
		r.push_back(q);
	}
	return make_pair(r, s);
}

void printCutRodSolution(vector<int> p, int n)
{
	pair<vector<int>, vector<int> > vvp =
		extendedBottomUpCutRod(p, n);

	cout << vvp.first.at(n) << endl;
	vector<int> s = vvp.second;
	while (n > 0)
	{
		cout << s[n] << endl;
		n -= s[n];
	}
}

int main()
{
	//使price[0]为0，在程序里不使用， 
	//只是为了使截断的左右两端与数组下标保持一致，方便代码  
	int price[] = {0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 30};
	int n;
	cout << "请输入n (ctrl+z结束):";
	while (cin >> n)
	{
		cout << "n=" << n << endl;
		cout << "普通递归法：\n" << cutRod(price, n) << endl;
		cout << "带备忘录的自顶向下法：\n" << memoizedCutRod(price, n) << endl; 
		cout << "自底向下法：\n" << bottomUpCutRod(price, n) << endl;
		vector<int> p(price, price+sizeof(price)/sizeof(price[0]));
		cout << "扩展的自底向下法：" << endl;
		printCutRodSolution(p, n);
		cout << endl << "请输入n (ctrl+z结束): ";
	}

	system("pause");
	return 0;
}