UVA_437_The Tower of Babylon

#include<iostream>
#include<sstream>
#include<string>
#include<vector>
#include<list>
#include<set>
#include<map>
#include<stack>
#include<queue>
#include<algorithm>
#pragma warning(disable:4996)
#include<cstdio>
#include<cstdlib>
using std::cin;
using std::cout;
using std::endl;
using std::stringstream;
using std::string;
using std::vector;
using std::list;
using std::pair;
using std::set;
using std::multiset;
using std::map;
using std::multimap;
using std::stack;
using std::queue;
using std::priority_queue;
class Cube
{
public:
	int length, width, height;
	Cube()
	{
		length = width = height = 0;
	}
	Cube(const int &l,const int &w,const int &h)
	{
		length = l, width=w, height = h;
	}
	friend bool operator<(const Cube &c1,const Cube &c2)
	{
		if (c1.length != c2.length)
		{
			return c1.length>c2.length;
		}
		return c1.width > c2.width;
	}
};
int main()
{
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);  
	int n,count=0;
	while (cin >> n&&n)
	{
		vector<Cube>cube;
		for (int i = 0; i < n; i++)
		{
			vector<int>dimension(3);
			cin >> dimension[0] >> dimension[1] >> dimension[2];
			std::sort(dimension.begin(), dimension.end());
			do
			{
				cube.push_back({ dimension[0],dimension[1],dimension[2] });
			} while (std::next_permutation(dimension.begin(), dimension.end()));
		}
		vector<int>dp(cube.size());
		std::sort(cube.begin(), cube.end());
		dp[0] = cube[0].height;
		int height = dp[0];
		for (int i = 1; i < dp.size(); i++)
		{
			dp[i] = cube[i].height;
			height = std::max(height, cube[i].height);
			for (int j = i - 1; j >= 0; j--)
			{
				if (cube[i].length < cube[j].length&&cube[i].width < cube[j].width)
				{
					dp[i] = std::max(dp[i], dp[j] + cube[i].height);
				}
			}
			height = std::max(height, dp[i]);
		}
		cout << "Case "<<++count<<": maximum height = "<<height << endl;
	}
	return 0;
}