Poj1651multiplication puzzle (fetch number, interval DP)

Description

The multiplication puzzle is played with a row of cards, each containing a single positive integer. during the move player takes one card out of the row and scores the number of points equal to the product of the number on the card taken and the numbers on the cards on the left and on right of it. it is not allowed to take out the first and the last card in the row. after the final move, only two cards are left in the row.

The goal is to take cards in such order as to minimize the total number of scored points.

For example, if cards in the row contain numbers 10 1 50 20 5, player might take a card with 1, then 20 and 50, scoring
10*1*50 + 50*20*5 + 10*50*5 = 500 + 5000 + 2500 = 8000
If he wocould take the cards in the opposite order, I. e. 50, then 20, then 1, the score wocould be
1*50*20 + 1*20*5 + 10*1*5 = 1000 + 100 + 50 = 1150.

Input

The first line of the input contains the number of cards N (3 <= n <= 100). The second line contains N integers in the range from 1 to 100, separated by spaces.

Output

Output must contain a single integer-the minimal score.

Sample Input

 
610 1 50 50 20 5
 

Sample output

3650
 

 
Question: Take the number in a column. The value is to multiply the number between the left and the right. The two numbers cannot be taken from the left and the right. The total value and the minimum value are obtained based on the different number fetch methods.
 

 
# Include <stdio. h> int min (int A, int B) {return A> B? B: A;} int main () {int n, a [105], DP [105] [105]; while (scanf ("% d", & N)> 0) {for (INT I = 1; I <= N; I ++) {scanf ("% d", & A [I]); for (Int J = 1; j <= N; j ++) DP [I] [J] = 0;} For (INT r = 2; r <N; r ++) for (INT I = 1; I <= N-R; I ++) {Int J = I + R; DP [I] [J] = DP [I + 1] [J] + A [I] * A [I + 1] * A [J]; for (int K = I + 2; k <j; k ++) DP [I] [J] = min (DP [I] [J], DP [I] [k] + dp [k] [J] + A [I] * A [k] * A [J]);} printf ("% d \ n", DP [1] [N]);}


 

poj1651multiplication puzzle (number, interval DP)