codeforces 580D. Kefa and Dishes

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

When Kefa came to the restaurant and sat at a table, the waiter immediately brought him the menu. There were n dishes. Kefa knows that
he needs exactly m dishes. But at that, he doesn't want to order the same dish twice to taste as many dishes as possible.

Kefa knows that the i-th dish gives him ai units
of satisfaction. But some dishes do not go well together and some dishes go very well together. Kefa set to himself k rules of eating
food of the following type — if he eats dish x exactly before dish y (there
should be no other dishes between x and y),
then his satisfaction level raises by c.

Of course, our parrot wants to get some maximal possible satisfaction from going to the restaurant. Help him in this hard task!

Input

The first line of the input contains three space-separated numbers, n, m and k (1 ≤ m ≤ n ≤ 18, 0 ≤ k ≤ n * (n - 1))
— the number of dishes on the menu, the number of portions Kefa needs to eat to get full and the number of eating rules.

The second line contains n space-separated numbers ai,
(0 ≤ ai ≤ 109)
— the satisfaction he gets from the i-th dish.

Next k lines contain the rules. The i-th
rule is described by the three numbers xi, yi and ci (1 ≤ xi, yi ≤ n, 0 ≤ ci ≤ 109).
That means that if you eat dish xi right
before dish yi,
then the Kefa's satisfaction increases by ci.
It is guaranteed that there are no such pairs of indexesi and j (1 ≤ i < j ≤ k),
that xi = xj and yi = yj.

Output

In the single line of the output print the maximum satisfaction that Kefa can get from going to the restaurant.

Sample test(s)

input

2 2 1
1 1
2 1 1

output

3

input

4 3 2
1 2 3 4
2 1 5
3 4 2

output

12

Note

In the first sample it is best to first eat the second dish, then the first one. Then we get one unit of satisfaction for each dish and plus one more for the rule.

In the second test the fitting sequences of choice are 4 2 1 or 2 1 4. In both cases we get satisfaction 7 for dishes and also, if we fulfill rule 1, we get an additional satisfaction 5.

这题可以用状压dp做，用dp[state][j]表示取了state里的1的这些菜，最后取的菜是j最多能得到的价值。状态转移方程是dp[state1][j]=max(dp[state1][j],dp[state][i]+a[i][j]+value[j] );

#include<iostream>
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<string>
#include<algorithm>
using namespace std;
typedef __int64 ll;
#define inf 99999999
#define pi acos(-1.0)
ll dp[280000][20],value[20];
ll a[20][20];

int panduan(int state,int m)
{
    int tot=0;
    while(state){
        if(state&1)tot++;
        state>>=1;
    }
    if(tot==m)return 1;
    return 0;
}
int main()
{
    int i,j,c,d,k,n,m,state,state1;
    ll e;
    while(scanf("%d%d%d",&n,&m,&k)!=EOF)
    {
        memset(dp,0,sizeof(dp));
        memset(a,0,sizeof(a));
        for(i=1;i<=n;i++){
            scanf("%I64d",&value[i]);
        }
        for(i=1;i<=k;i++){
            scanf("%d%d%I64d",&c,&d,&e);
            a[c][d]=e;
        }
        ll maxnum=0;
        if(m==1){
            for(i=1;i<=n;i++){
                maxnum=max(maxnum,value[i]);
            }
            printf("%I64d\n",maxnum);
            continue;
        }

        for(state=1;state<=(1<<n)-1;state++){
            for(i=1;i<=n;i++){
                if(state&(1<<(i-1))){
                    if(state==(1<<(i-1) )){
                        dp[state][i]=value[i];
                    }
                    for(j=1;j<=n;j++){
                        if( (state&(1<<(j-1) ) )==0){
                            state1=( state|(1<<(j-1)) );
                            dp[state1][j]=max(dp[state1][j],dp[state][i]+a[i][j]+value[j] );
                        }
                    }

                }
            }
        }

        maxnum=0;
        for(state=1;state<=(1<<n)-1;state++){
            if(panduan(state,m)){
                for(i=1;i<=n;i++){
                    maxnum=max(maxnum,dp[state][i]);
                }
            }
        }
        printf("%I64d\n",maxnum);
    }
    return 0;
}