UVA437 - The Tower of Babylon

有向无环图最长路径算法

每个立方体都可以分别以三个边为高，这样一个立方体确定高后，就有三个状态，存储在cube中。

在用Graph邻接数组存储每个状态之间的关系，这样就形成了有向无环图。在用dp[i] = max(dp[i], solve(j) + cube[i].h)(i -> j),求出每个d[i],取最大值输出.

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <map>
#include <vector>
using namespace std;

struct Cube{
Cube(){}
Cube(int a, int b, int c)
{
x = a;
y = b;
h = c;
}
int x, y;
int h;
}cube[100];
int Graph[100][100];
int dp[100], n;
bool judge(Cube &a, Cube &b)
{
if(a.x < a.y)
swap(a.x, a.y);
if(b.x < b.y)
swap(b.x, b.y);
if(a.x > b.x && a.y > b.y)
return true;
return false;
}
int solve(int m)
{
if(dp[m])return dp[m];
dp[m] = cube[m].h;
for(int i = 1; i <= 3 * n; i++)
{
if(Graph[m][i])
dp[m] = max(dp[m], solve(i) + cube[m].h);
}
return dp[m];
}
int main()
{
//  freopen("in.txt", "r", stdin);
int cas =0;
while(cin >> n && n)
{
memset(Graph, 0, sizeof(Graph));
memset(dp, 0, sizeof(dp));
for(int i = 1; i <= n; i++)
{
int x, y, z;
cin >> x >> y >> z;
cube[3*i] = Cube(x, y, z);
cube[3*i-1] = Cube(x, z, y);
cube[3*i-2] = Cube(y, z, x);
}
for(int i = 1; i <= 3 * n; i++)
for(int j = i+1; j <= 3 * n; j++)
{
if(judge(cube[i], cube[j]))
Graph[i][j] = 1;
else if(judge(cube[j], cube[i]))
Graph[j][i] = 1;
}
int maxs = 0;
for(int i = 1; i <= 3 * n; i++)
{
dp[i] = solve(i);
maxs = max(maxs, dp[i]);
}

printf("Case %d: maximum height = %d\n", ++cas, maxs);
}

return 0;
}