題干：

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 the 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 would take the cards in the opposite order, i.e. 50, then 20, then 1, the score would 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

6 10 1 50 50 20 5

Sample Output

3650

?

解題報告：

? ?dp[l][r]代表我要消掉 l~r 中間的所有數字。轉移顯然是枚舉最后一個操作需要刪掉的數字，然后轉移就行了。

AC代碼：

#include<cstdio> #include<iostream> #include<algorithm> #include<queue> #include<map> #include<vector> #include<set> #include<string> #include<cmath> #include<cstring> #define ll long long #define pb push_back #define pm make_pair using namespace std; const int MAX = 100 + 5; ll dp[MAX][MAX]; ll a[MAX]; int main() {int n;cin>>n;for(int i = 1; i<=n; i++) scanf("%lld",a+i);memset(dp,0x3f,sizeof dp);for(int i = 1; i<=n; i++) dp[i][i] = 0,dp[i][i+1] = 0;for(int len = 3; len<=n; len++) {for(int l = 1; l+len-1 <= n; l++) {int r = l + len - 1;if(len == 3) {dp[l][r] = a[l]*a[r]*a[l+1];continue;}for(int k = l+1; k<=r-1; k++) {dp[l][r] = min(dp[l][r] , dp[l][k] + dp[k][r] + a[l]*a[k]*a[r]);}}}cout <<dp[1][n];return 0 ; }

?

總結

以上是生活随笔為你收集整理的【POJ - 1651】Multiplication Puzzle（区间dp）的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。