A. Energy necklace
https://www.luogu.org/problem/P1063
(This question and purple book the best chain matrix multiply like)
① Sample analysis:
4
2 3 5 10
We put it into four multiplication expression:
2*3 3*5 5*10 10*2
It requires 3 multiplications merger:
10 * 2 * 33 * 55 * 10 +60 energy
3 * 2 * 10 * 55 * 10 * 10 + 3 * Energy 5
10 * 2 * 3 * 5 * 10 + 10 * 5 * Energy 10
The total energy is 710
In fact, the expression also can write
2 * 3 * 5 * 10 * 2 * 3 * 5 * 10, then we have to do is to add parentheses (back to optimal chain matrix multiplication),
Every calculated values are added together,
2*10*3
+10*3*5
+10*5*10
We set f [i] [j] to take the maximum energy from i to j obtained
边界：f[ i ][ i ]=0，f[ i ][ i+2 ]=data[ i ]*data[ i+1]*data[ i+2 ];
f[ i ][ j ]=max(f[ i ][ k ]+f[ k ][ j ]+data[ i ]*data[ k ]*data[ j ]);
State transition:
for ( int L = . 3 ; L <= n-; L ++ )
for ( int I = . 1 , J = I + L; J <= n-* 2 ; I ++, J ++) // do the termination condition labeled i <= n , and so there will be some inter-cell does not sweep out
for ( int K = I + . 1 ; K <J; K ++ )
{
F [I] [J] = max ((F [I] [K] + F [K] [ J]) + D [I] * D [K] * D [J], F [I] [J]);
}
Finally, f [1] [1 + n] to f [n] [n + n] where to find out ans
(As for why is + n, the landlord think it is because you want to be n-1 times computation, if you have a better explanation, please leave a message
Is not that there is a problem, if the data is such that it
2
2 3
Do not worry: said Title: The first line is a positive integer N (4≤N≤100) N ( . 4 ≤ N ≤ . 1 0 0 ), indicates the number of beads on the necklace.
So you can do ac.
II. To be updated, the main floor to do other title