zoj1232Adventure of Super Mario（图上dp）

题目连接:

啊哈哈，点我点我

思路：

这个题目是一个图上dp问题，先floyd预处理出图上所有点的最短路，但是在floyd的时候，把能够用神器的地方预处理出来，也就是转折点地方不能为城堡。。预处理完毕后，就是一个dp问题了。。。dp[][],两维分别表示到达的地点和使用神器的次数。。这样这个问题就得到了解决。。

题目：

Adventure of Super Mario

There are A Villages and B Castles in the world. Villages are numbered 1..A, and Castles are numbered A+1..A+B. Mario lives in Village 1, and the castle he starts from is numbered A+B. Also, there are two-way roads connecting them. Two places are connected
by at most one road and a place never has a road connecting to itself. Mario has already measured the length of every road, but they don‘t want to walk all the time, since he walks one unit time for one unit distance(how slow!).

Luckily, in the Castle where he saved the princess, Mario found a magic boot. If he wears it, he can super-run from one place to another IN NO TIME. (Don‘t worry about the princess, Mario
has found a way to take her with him when super-running, but he wouldn‘t tell you :-P)

Since there are traps in the Castles, Mario NEVER super-runs through a Castle. He always stops when there is a castle on the way. Also, he starts/stops super-runnings ONLY at Villages
or Castles.

Unfortunately, the magic boot is too old, so he cannot use it to cover more than L kilometers at a time, and he cannot use more than K times in total. When he comes back home, he can
have it repaired and make it usable again.

Input

The first line in the input contains a single integer T, indicating the number of test cases. (1<=T<=20) Each test case begins with five integers A, B, M, L and K -- the number of Villages,
the number of Castles(1<=A,B<=50), the number of roads, the maximal distance that can be covered at a time(1<=L<=500), and the number of times the boot can be used. (0<=K<=10) The next M lines each contains three integers Xi, Yi, Li. That means there is a
road connecting place Xi and Yi. The distance is Li, so the walk time is also Li. (1<=Li<=100)

Output

For each test case in the input print a line containing a single integer indicating the minimal time needed to go home with the beautiful princess. It‘s guaranteed that Super Mario can
always go home.

Sample Input

1

4 2 6 9 1

4 6 1

5 6 10

4 5 5

3 5 4

2 3 4

1 2 3

Sample Output

9

代码：

#include<cstdio>
#include<cstring>
#include<cstdio>
#include<iostream>
#include<algorithm>
#define INF 0x3f3f3f3f
using namespace std;

const int maxn=100+10;
int gra[maxn][maxn],dp[maxn][10+10];
bool is_true[maxn][maxn];
int A,B,M,L,K;
int t,u,v,w;

void floyd()
{
    for(int k=1;k<=A+B;k++)
        for(int i=1;i<=A+B;i++)
            for(int j=1;j<=A+B;j++)
        {
            if(gra[i][j]>gra[i][k]+gra[k][j])
                gra[i][j]=gra[i][k]+gra[k][j];
            if(k<=A&&gra[i][j]<=L)
                is_true[i][j]=is_true[j][i]=true;
        }
}

void read_Graph()
{
    memset(is_true,false,sizeof(is_true));
    scanf("%d%d%d%d%d",&A,&B,&M,&L,&K);
    for(int i=1;i<=A+B;i++)
        for(int j=1;j<=A+B;j++)
    {
        if(i==j)  gra[i][j]=0;
        else gra[i][j]=INF;
    }
    for(int i=1;i<=M;i++)
    {
        scanf("%d%d%d",&u,&v,&w);
        gra[u][v]=gra[v][u]=w;
        if(w<=L) is_true[u][v]=is_true[v][u]=true;
    }
}

void solve()
{
   memset(dp,0x3f,sizeof(dp));
   for(int i=1;i<=A+B;i++)
      dp[i][0]=gra[1][i];
   for(int k=0;k<=K;k++)
      dp[1][k]=0;
   for(int i=1;i<=A+B;i++)
       for(int k=1;k<=K;k++)
          for(int j=1;j<i;j++)
     {
       if(is_true[j][i])
            dp[i][k]=min(dp[i][k],dp[j][k-1]);
        dp[i][k]=min(dp[i][k],dp[j][k]+gra[j][i]);
     }
    printf("%d\n",dp[A+B][K]);
}

int main()
{
    scanf("%d",&t);
    while(t--)
    {
        read_Graph();
        floyd();
        solve();
    }
    return 0;
}

zoj1232Adventure of Super Mario（图上dp）