DP + state compression-codeforces 580D Kefa and dishes

Kefa and Dishes

problem ' s Link

 

Mean:

There are N-course dishes on the menu, which requires a little M-channel. The delicious value of each dish is AI.

There are k rules, each rule: after eating the first XI course after eating Yi can get more delicious value of VI.

Q: How many delicious values can I get?

(1≤m≤n≤18,0≤k≤n∗ (n−1))

Analyse:

Classic pressure DP.

Due to a maximum of 18 courses, a number of S (s<=2^18) can be used to uniquely identify a state.

For a state s, enumerate two positions I and j:i selected from the selected Dish, J is selected from the dish that has never been selected.

The next state SS is the maximum value of all states after eating I and then eating J.

Transfer process:ss=s| ( 1<<J)

State transition equation:dp[ss][j]=max (Dp[ss][j],dp[s][i]+sa[j]+ad[i][j])

The answer is the maximum value of all the selected quantities up to M.

Time complexity:o ((2^N) * ( n^2))

 

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DP + state compression-codeforces 580D Kefa and dishes